Brifi¢ Hatt See inr afiamtty Font Se ALSEE camaro ane a3 : als arn AC take ape a fae aalidangner tut eiMlaapei th oA AED CUS AHP SHO OO DADE IOARHA GS HINGIS sf asisaragasssss SORKIN! So at | L i ead a ee Woods Hole Oceanograpnic Institution ARCHIVE COLLECTION OCEANOGRAPHIC INSTITUTION 7 42ar 1963 Onder Nb. 17030 LABORATORY BOOK COLLECTION Referees ey ieee WOWLW ANN ‘ 4a an : ’ ye Se a wi 4 Prey a Oe wa, o Fim WOODS BULE OCEANOGRAPHIC |. STITUTION LABORATCRY BOOK COLLECTION PURCHASE ORDER NO. 170 30 MAR ¢ 4963 Reference Room Cydeasojoyd AAGN ‘SD TRO) ‘S187 BAL oSouRdt LP ul ‘Bas LAveY B SuTddiys a9aqje ‘Sulsit 1afoajsop AABN *S ‘O VW—HOMIASTLNOWS WIND WAVES AT SEA BREAKERS AND SURF By Henry B. BiceLtow, Museum of Comparative Zoology, Cambridge, Massachusetts and W. T. Epmonpson, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts H. O. PUB. NO. 602 ISSUED UNDER THE AUTHORITY OF THE SECRETARY OF THE NAVY, WASHINGTON : 1947 REPRINTED 1953 a EEE ET I LETT ID For sale by the Hydrographic Office, Washington 25,D.C. ----------..- Price $2.80 : a re eS > oe ) CONTENTS PGR ON OL Dis a a Eee me ye re ee eee JEP IB TACT. a. ie aot erecta en ei ie eh Be ye aS Si ee Se ee ae CHAPTER 1. THE PHysicaL NATURE OF WIND WAVES___--_------_-- inesGrowth and Decay of Waves=-=-=2--- 2. _- 72 " eC eye ee ee @he Depth of Wave Action_-_-_------- Se ee Ae eee Hurricane or “‘Tidal’”’ Waves___-_- test ne eae oe SINS yas eta he Be tas, 8 GuaPpern 2) LHe DIMENSIONS OF WAVES_2---------2-2-222- 22-25. | ee teeneSTOW AVES! ace nee ee ee oe Se ee ee ihevAwerage leights of Waves. .9- 222-225 225222-.22 522 0325 28 ihe Maximum Heights of Storm Waves-_----.-----.---._.=.-._=..- Single High Waves and Groups of High Waves________-______--__-- ihe Lengths of Waves_-..-_<------- S25 Be BNA oe A kh tintin ea SEER rCCIMIEHS OF WW AVGS= 9 Hare eae So Dew ee ek Se eae sire velocities and: Periods of "Waves_..-..---=222 222.22 = ese sce The Directions in Which Wind Waves Advance._____________-_____-_- CHAPTER 3. THE Contours OF WAVES; THE EFFECTS OF CURRENTS AND OF SHOAL WATER; THE MEASUREMENT OF WAVES-_~_-_________-_- The Profiles and Surface Contours of Waves___._._..____-_-_-_---_-- The Effects of Currents on the Dimensions of Waves_-______________- Alterations in the Dimensions of Waves Over a Shoaling Bottom___ ___ The Sizes of Waves That Are Developed in Shallow Water___________- MichuidaronMvienslring WAVES..+.-2- 2. .2.22.s22l2--62n-een Ltn CHAPRUREA SHAS HAND SWELLS: 22-20-88 ee el J eee ee MNtersationvolmseaselntomwells: 2.02 So" 2 ee a ee shes DirectionsiOiowellses = 0. eo eee es ae UE Se ee iircehersistence OMmowellseee = — et Ly Nah ee eee HorecnsunesSearanGrowelleee 9 == 2). a en SE te ee eee CHAPTER 5. THE FREQUENCY OF HIGH AND Low SEAS AND SWELLS IN DIK RENT eRe GTONS 22s tle = tn te eee te ee a ee ee INOnineAtIAntIC! =") esse). 8. Se MA) gat. SN Rt a eee yen AS SUM Cr een serena eres wth we Pee ee fe) 88. Eee ee SOMUN PAC CS eee wae hs Te BS ee ee ee NorthpindiantOceante sas. onan ens ee ae” ae eee SNOT TE Os alr: ce Te IE GU ED ee ee ee eae ee ee VN TURTE EY cp La ce A gd ec SouthmnciansOceania— = o- 455 Se ae oe ek ey Se CHAPTER 6. BREAKERS AND SURF; THEIR IMPORTANCE AND ORIGIN__- ithesimportanceof ‘Surf... ..2.20- 2.2. a eho OL Mee aioe MieRe ARES OU OUTTe = | see ee 2 ee ety oe ELE ok Alterations in Length and in Velocity Over a Shoaling Bottom_______ Alterations in Height Over a Shoaling Bottom__._________________- INICELAvIONSeIN StCeDIeESS seer nee ee ote Me eo ee Alterations in the Orbital Velneities of the Water Particless=s-= === 102 106 109 109 IV CONTENTS CHAPTER 6. BREAKERS AND SurF—Continued Page ithe: Characteristics of Breakers. 22225. s--5=-c-s-2eoee eee eee 110 Waves OF Dbranslstionlss).=s2242252<5c.4 52. eee oe ae 115 CHAPTER 7, THE CHARACTER OF SuRF UNDER DiIrrERENT ConpiTions.._ 119 The HeightoliSurl = 4.2. . see ee eee aa. eee 119 Depth of Water in which Surf Develops_—--..2-...-.-=.-=_-sc ssa 126 Phe stage of the: Lidevas It Affects the Surfa_--225-2-- == 2 22 eee 132 Distance of the First Line of Breakers out from the Shore; Effects of Bars: Number of LinesiofBreakers.-- 25) ---- =) -_ 2-252. 133 Factors that Hinder the Development of Surf or that Tend to Interrupt Te op ar An ee Se EE aS, = in ol ee ee oh a 145 Ihedves. ‘Shoals: ‘and Islands-.2. 22200 = ee 145 Pi GalNCuErenuS <=, 2 = 28 ye ee a ee ek ke ge 145 Rip Currents: 2. 122s dt oe eo ae oe eee ee eee ee 146 Miaiksnddlee. 2 —. 8 Se ee ee as De oe 147 Miarsh) Grasses and Ses weeds22_5. 2. 32222 oe eee ee eee 147 C0 7h CR eee epee em oe as nf ERR pe INE IE 149 The Persistence of Surf and Its Relationship to the Wind_____________ 150 CHAPTER 8. Di1RECTION AND HEIGHT OF BREAKERS IN RELATION TO THE SHAPERION THE COAST... = 5-625 2 aoe oe 155 Ahe iReirachion Ob WAVES. 6 2 ee 155 The Iboss of Wave Height by Refraction... 22. - 2 ee ee 157 Surk drone toe Sbures of Maven. 8... ee 159 Surf around (Headlands... -...- 2 esce eee eee 163 Surarouna (slands 2-5.) 4) = 8 ee ee 168 Submarine Troughs and Ridges as Affecting Surf___-__-------------- 175 Horecasting. Breakers/and Suri... =. ... _-- 2-4 -<- oc 176 Selected sINCLGLGl CGS (5 sees oe ee ee Se es ee ee eee 1: 177 TABLES TABLE 1. Mass transport in waves of different dimensions_______________-__-_ 2. Relative diameters of orbital motion with inereasing depth____-___-__ 3. Maximum heights of waves with winds of different strengths__—______ 4. Heights of waves with winds of different strengths and durations_____ 5. Heights of waves with winds of different strengths blowing over dif- feTrenigetehes sas! = sa sies Pete Sos Fe se ee an nee eS 6. Minimum, maximum, and average wave heights for the Trade Wind TBS oS eos ohh ps = pt a ee ger 5 eo a ee Set 7. Fetches and durations required to produce waves 75 percent of maxi- munmvheight, with different winds: 2... 222222 2k eee ee 8. Frequency of waves of different heights in different regions__________ 9. Frequency of waves of different heights at South Beach, Martha’s Whim yay tole — Ss eos Ree So i eee en Oo ee ne = OE ee ee 10. Average lengths of waves according to the strength of the wind___-__~_ 26. 27. 28. 29. 30. . Lengths of storm waves observed in different oceans_______________~ . Average steepness of waves for winds of different strengths and ND NREY UE OF OTS) Soe ene an, ae er yt en = Ee . Maximum, minimum, and mean steepness of waves of different heights_ . Correlation between age and steepness of growing waves___________. . Theoretical wave periods and velocities in relation to the strength and TTL O NOleEb hes (eae mre Se ie ee ee . Theoretical velocities and lengths for waves of different periods______ . Lengths and periods of waves computed from observed periods and lencths in different parts Of theloceans.---~- =. .=2 222222 22 222. . Ratios between the dimensions of waves in still water aad in currents_ . Distribution of low, medium, and high seas in different latitudinal belts of the North Atlantic in August._.._..._._.___- 2 : . Frequencies of high swells on the American and European sides A the North Atlantic in January and Fehruary______________- _- " . Frequencies of low and high seas and swells on the loneceae ad African sides of the South Atlantie in July and August_____-__ __ . Frequencies of low and high seas and swells on the American and African sides of the South Atlantic in January and February —-_-—_-__ . Frequency of no swell in the Japan and South China seas in summer DOAOLNNMBOU HON CS et oa eres ee ee . Frequencies of high seas and swells off the west coast of South America_ . Frequencies of low and high seas and swells in the Arabian Sea and Bay of Bengallim winter’and stmmer .--.--..---222 222... ___-=2 Frequencies of low and high seas and swells along the Equatorial Belt and Southeast Trades Belt of the South Indian Ocean in winter EU TN CLU-S {KUEN Ties ep ge es Se I Pe ok Pressures of breakers on the west coast of Scotland_________________ Pressures of waves at St. Augustine, Florida and Duluth Canal, Lake STEROLS © pee ls a a oe, Decrease in wave lengths and velocities over a shoaling bottom____-__ Frequencies of waves of different periods at South Beach, Martha's NTO ES EEF C0 TR Page 6 10 17 18 18 18 20 21 22 27 28 A) 30 31 32 35 36 53 73 80 82 82 90 91 95 98 101 101 104 106 VI TABLES TABLE Page 31. Alterations in wave height over a shoaling bottom_____--_______---_-_ 108 32. Breaker heights, and depths at which breaking occurs for waves of different diImenslons s5.26 325 sas eo ee ee ee 121 33. Ratio of breaker height to offshore height for waves of different degrees of steepness= 2 = Pe eee ee 121 34. Frequencies of breakers higher than 5 and 10 feet along the east coast ohthesUnited(States®=— "22.2 2 ee ee 151 35. Angles of breakers with the beach for waves of different degrees of steepness approaching at different angles____________---_-_-------- 157 36. Alteration of the angle between wave crest and shore line in shoaling WaAtGREe eee et eee ee ee) ee 157 37. Decrease in wave height due to refraction over a shoaling bottom __-- 159 ILLUSTRATIONS Figures in Text FIGURE Page aa Navay, destroyer im a heavy Sea_. ==. 2 =~ 58s Frontispiece ie Viovements of beach grass ina low swelli_--..._._........-..22.-=- 3 2. Orbital movements of water particles in wind waves_______________- 4 3. Movements of water particles in shallow water___________________-_ 4 4. Ripple marks at the hottom of the Gulf of Maine tS A. eS 2 5. Graph showing the theoretical relationship between wave i sats velocities, and periods in deep water... .-—._=-.-.--.... =.=... =. 36 6. Isobarie distribution over the North Atlantie______- Z 2a 39 7. Diagram showing the relative directions of the advance oe waves and Gtawimasipy whichsthey are penerateds= 225 = 8-2 = 2 ee 40 8. Directions of winds and waves in a tropical hurricane___-_-__ __. ___ - 40 9. Profile of a wave of trochoid form___ _____ pee 43 10. Profile of a trochoid wave showing angle of a hart at stee eet part of CS NN IS dy as Ae a 8 a a ae oe es ae 44 11. Theoretical profile of steepest possible wave_____________----__---- 44 12. Profiles of waves of different degrees of steepness___________-__-_-_-_- 45 13. Smaller waves running on top of an older swell____-_-___-_-__-__-____-_- 47 14. Moderately heavy sea in the North Atlantie _- Th Pt Oe 48 15. Surface configuration of the front of a wave about 19 feet high ee 49 16. Surface configuration of the back of a wave 27 feet high. ____ __ See 50 iWaseeaks developed by interference. —..=-.--=.=..---~--..2-..-=!..+- 52 18. A moderately high and breaking sea___-___.-_____-_--__----- Ce 64 19. Back of the crest of a high and breaking storm wave____ ___ ___- 65 20. Diagram to show changes in directions from which swells come with the advance of a storm center... . --.-.-.-....- El 68 21. Graph showing the theoretical alteration of waves fae aneing over a SUMAN ga OOLOMs aaa Ae ee 103 22. A breaker of the plunging type, showing stages of dev dane ee 11] 25. Oblique view of a breaker of the plunging type__--_-.----_-------- 112 24. Aerial photograph of breakers of the plunging type_----_------------ 113 Zoe oreakersior spilling, ang plunging: bypes.—-— 2) =-2- =) 225-22 114 26. A breaker intermediate between plunging and spilling types_______-_- 116 27. A wave of translation preceding a breaker up a gently sloping beach__ 117 28. Heavy surf beating against the boulevard at Winthrop, Mass ______- i) 29. Surf almost wholly enveloping Minot’s Light, Massachusetts ——-___~ 120 30. Breakers caused by swells which are hardly visible offshore________-_- 125 31. Pattern produced by breakers from different directions _~___-_______ 128 32. Waves breaking farther out at the mouth of a tidal inlet than along the HEIMHDORINCHDCACHE ==. eee a ee ee ae oe ee ge Raye P43) 33. Breaker developing against the base of Minot’s bient Massachusetts __ 133 34. Wave breaking close to the tide line on a steeply sloping beach. _—___ 134 SO OUrinextendine o.O00Mect out from shores. _-) 2-2) 22) ) 8 ee 136 36. Surf developing over bars, with and without surf on the beach__. _~ - 137 37. Surf with two chief lines of breakers off the Hawaiian Islands_____ _- 138 38. Moderately heavy breakers on two bars and on the beach behind CHET EM Eee ee ee eee ee ae eee ete sss 139 VIII ILLUSTRATIONS FIGURE 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. Five or six lines of breakers with breaking waves farther offshore_____ Low breakers over neighboring shoals, and same locality at low tide__ Heavy breakers off Adak, Aleutians. 222252. ssc02-csasseete see Aerial photerraph of arip current: o.- 22sec ee oe ee ee Smoouh seal an ice field. 2. oe. eee oe eee Breaker developing against an offshore wind______________________- Refraction of waves around headland and islet into a bay__________-_ Diagram illustrating the refraction of waves along a straight shore Chart of St. Mary Bay Nova:Scotiat £ so ees 2 a Se eee Surf around a low-lying projection of the Hawaiian coast__________- Surf dashing against headland at the entrance to Havana Harbor ____ Diagram illustrating the refraction of waves around an abrupt corner OL UNE CORS Us ok ene ee eae cp eee eyS een ee eee Sel ae ee Sketeh map of Datuth: Harbor: >.< 2. re oe oe ae eee Diagram illustrating the refraction of waves around a circular island__ Chart of No Man's Wand; Massachusetts. “_-----_._---—_-- Chart of St. Pierre Island, off the south coast of Newfoundland____-- Chart of NukuoroPAtoll; Caroline Groups22_-----_-_ ee Chart of Ario-Atoll, Marshall"Group. 2° - 92.02 1 2 eee PLATE LEGENDS Plates follow Chapter 5 Plate I.—Distribution of high seas in the North Atlantic in August and in the South Atlantic in July and August. Plate II.—Distribution of low seas in the North Atlantic in August and in the South Atlantic in July and August. Plate III.—Distribution of high swells in the North Atlantic in August and in the South Atlantic in July and August. Plate 1V.—Distribution of low swells in the North Atlantic in August and in the South Atlantic in July and August. Plate V.—Distribution of high seas in the North and South Atlantic in January and February. Plate VI.—Distribution of low seas in the North and South Atlantic in January and February. Plate VII.—Distribution of high swells in the North and South Atlantic in Jan- uary and February. Plate VIII.—Distribution of low swells in the North and South Atlantic in Jan- uary and February. Plate IX.—Distribution of high seas in the North Pacific in August and in the South Pacific in July and August. Plate X.—Distribution of low seas in the North Pacific in August and in the South Pacific in July and August. Plate XI.—Distribution of high swells in the North Pacific in August and in the South Pacific in July and August. Plate XII.—Distribution of low swells in the North Pacific in August and in the South Pacific in July and August. Plate XIII.—Distribution of high seas in the North Pacific in February and in the South Pacific in January and February. Plate XIV.—Distribution of low seas in the North Pacific in February and in the South Pacific in January and February. Plate XV.—Distribution of high swells in the North Pacific in February and in the South Pacific in January and February. Plate XVI.—Distribution of low swells in the North Pacific in February and in the South Pacific in January and February. Plate XVII.—Distribution of high seas in the Indian Ocean in July and August. Plate XVIII.—Distribution of low seas in the Indian Ocean in July and August. Plate XIX.—Distribution of high swells in the Indian Ocean in July and August. Plate XX.—Distribution of low swells in the Indian Ocean in July and August. Plate XXI.—Distribution of high seas in the Indian Ocean in January and February. Plate XXII.—Distribution of low seas in the Indian Ocean in January and February. Plate XXIII.—Distribution of high swells in the Indian Ocean in January and February. Plate XXIV.—Distribution of low swells in the Indian Ocean in January and February. Ix FOREWORD The prolific use of amphibious craft and other small vessels during World War II required that a detailed knowledge of wave conditions throughout the world be available to the Armed Services of the United States. To meet this requirement, the Hydrographic Office, under the direction of Rear Adm. G. S. Bryan, USN, (Ret.) and in con- junction with several scientific and governmental institutions, pre- pared a number of publications that dealt with the occurrence of ocean waves from both the climatic and the synoptic aspects. Treatment of the climatic aspect involved the preparation of a series of Sea and Swell Atlases (H. O. Misc. No. 10,712 series) for the major oceans, the first atlas being published by the Hydrographic Office in 1943. Treatment of the synoptic aspect hinged on the development of a technique for quantitatively forecasting sea, swell, and surf condi- tions. This program was initiated by Dr. H. U. Sverdrup and Dr. W. H. Munk of the Scripps Institution of Oceanography under a con- tract with the Directorate of Weather, Army Air Forces, in 1942. Tn 1943, the work was transferred to the Navy Department and con- tinued under contracts with the Bureau of Ships and with the Hydro- graphic Office. By late 1943, the Hydrographic Office issued the first forecasting manual, Wind Waves and Swell; Principles in Fore- casting (H. O. Misc. No. 11,275). Following expansion of the work which included establishing related contracts with other institutions, a sister volume, Breakers and Surf; Principles in Forecasting (H. O. Pub. No. 234) was issued in 1944. Since the end of hostilities, the Hydrographic Office has been able to publish Wind, Sea and Swell; Theory of Relations for Forecasting (H. O. Pub. No. 601). Wind Waves at Sea, Breakers and Surf, the first popular book on the subject in more than a decade, develops further the Hydrographic Office series of publications dealing with sea, swell, and surf condi- tions. It is particularly fitting that the senior author should be Dr. Bigelow, who, as chairman of a special committee appointed by the National Academy of Science, was instrumental in suggesting that the United States Navy review how it might best assist in the acquisition of basic knowledge about the oceans. Asa result of this committee’s work, the Secretary of the Navy appointed the Schofield Board; and it is the work of this board during the year 1928 that provides the basis for the program in oceanography now being carried out by the x FOREWORD XI Navy. Dr. Edmondson, the junior author, participated in wave investigations carried out at the American Museum of Natural History in New York City and at the Woods Hole Oceanographic Institution between the years 1942-45, This book not only incorporates much of the published findings of recent date but also includes part of the unpublished work carried out under various wartime Navy contracts with the Woods Hole Oceano- graphic Institution, the Scripps Institution of Oceanography, and the Department of Mechanical Engineering of the University of Cali- fornia at Berkeley. as well as studies conducted by the Beach Erosion Board of the Army Engineers. Wind Waves at Sea, Breakers and Surf is a detailed and non- technical discussion of the subject based on the researches of eminent scientists and on the observations of thousands of seafaring men throughout the past century. The mariner will find in this volume much of value that will assist him in the safe and economical operation of vessels on the high seas, in restricted waters, and in the surf zone. R. O. Gover, Rear Admiral, U. S. Navy, Hydrographer. PREFACE Anything that disturbs the equilibrium of the water will start a system of undulations; that is, it will produce waves. This will hap- pen, for example, if one drops a stone in the water. A ship as she steams along starts a system of waves; and so does a submarine earth- quake, a volcanic eruption, or a rapid change in the barometric pres- sure of the atmosphere. The gravitational forces that cause the tides also produce waves. Other events that do this, commonly falling under the eyes of seafarers, are a porpoise leaping and dropping back again, or the tail of a flying fish cutting a pattern on the surface in calm weather. But the most familiar cause of waves that furrow the sea is the wind; and_it is of these wind waves that this book treats. Waves force themselves on the attention of everyone who follows the sea. No seafarer can ignore them, whether fisherman, merchant sailor, yachtsman, or member of the naval establishment; nor can the seaside dweller ignore the breakers as they thunder on the beach. It is no wonder, then, that the waves of the sea have attracted attention since time immemorial, or that more or less extended accounts of waves are to be found in many of the texts that have appeared in recent years on seamanship, on oceanography, on meteorology, on shore line proc- esses, on the construction of breakwaters, and on the protection of beaches from erosion. Waves also have been the subject of many theoretical studies. Yet, no simple, comprehensive account of wind waves from the standpoint of the man at sea has yet appeared in the English language. And it is in the hope of filling this gap that the following description is offered. Most of the information here presented has been drawn from pub- lished sources. We also owe a debt of gratitude to many persons for assistance, especially to Dr. H. U. Sverdrup for his kindness in re- viewing some of the theoretical discussions and to Capt. Fenner A. Chase, Jr., AUS, of the Hydrographic Office, Navy Department, who has aided in the editing of the manuscript. We wish it expressly un- derstood that we have made no contributions to the theory of waves. But we would not have dared to undertake the task, if we had not ob- served the behavior of waves at sea, from large craft and from small, in various parts of the world, under various conditions of wind and weather; or if we had not had many an opportunity to watch the de- velopment of breakers—and to cope with the smaller sizes—off beaches of various shapes, off rocky coastlines, and over submerged ledges. xII Chapter 1 THE PHYSICAL NATURE OF WIND WAVES It is difficult to frame a definition, in everyday terms, that will cover all the types of phenomena that are commonly named “waves.” As applied to the surface of the sea, however, they may be defined as suc- cessive ridges with intervening troughs or valleys which, in the case of wind waves, advance in undulatory motion. Our knowledge of the processes by which the waves of the sea are generated and subsequently developed is still far from complete, in spite of all the attention that has been devoted to the subject. There are two reasons for this. In the first place, it is extremely difficult to take accurate measurements of waves or to analyze their complex contours at any given moment from a ship at sea, or even from the shore. In the second place, the theories that aim to harmonize such observations as have been made with infor- mation of other sorts are still in a fluid state, largely because it has been necessary to assume in most theoretical discussions that waves are produced under ideal conditions such as never exist in the open sea. (For recent summaries of wave theory, as applied to wind waves at sea, we refer the reader to the following publications: Kriimmel, 1911; Gaillard, 1904; Thorade, 1931; O’Brien and others, 1942; and Sver- drup, Johnson, and Fleming, 1942.) And difficulties of this same sort also complicate the results of laboratory experiments on waves. Con- sequently, it is not astonishing that various discrepancies still exist between the characteristics of wave action as deduced by theory and as observed at sea or from the beach. Nevertheless, theory checked against empirical observations has advanced to a point where it is our most reliable guide to the dimensions of the waves that are to be ex- pected under a given set of circumstances. After all, water is very nearly a perfect fluid, and conditions in the open ocean, therefore, do at least approximate the ideal state assumed in classical hydro- dynamics; then too, the underlying principles are known for the par- ticular departures from this ideal state that most commonly occur at sea, as for example when waves run from deep water into shoal. Wind waves present themselves to the onlooker as a series of irregu- lar crests separated by intervening troughs which advance across the surface of the sea one after another in unending succession from hori- zon to horizon. Depending on the state of the wind locally or on the distribution of wind systems elsewhere, they may range in size from 1 2 PHYSICAL NATURE OF WIND WAVES the tiniest ripples that stir the surface here and there, when a breeze first springs up, to the fiercest of storm seas; or in a flat calm, the glassy surface may heave itself upward at intervals in the long, smooth ridges of a swell that comes from afar. Owing to the extreme mobility of water, to the fact that truly wind- less areas seldom reach far, and to the rapidity with which even a light breeze sets up a series of undulations, it is rare indeed that waves of some sort are not running out at sea anywhere, though they may be so low as to escape notice. And it is unusual to encounter a truly plane sea surface of more than a few hundred yards in extent or for more than a brief period of time, even in coastal waters. The natural impression of anyone viewing waves for the first time— or even after viewing them for years, unless he has paid attention— might well be that the mass of water composing each successive crest was moving bodily ahead across the surface of the sea. But it does not require much study to convince the observer that such is not the case. If he watches the movements of any floating object, such as a piece of wood or a seine cork, when waves are running, he will see that his marker does not drift along continuously as it would if the water in which it floats were constantly advancing, but that it moves ahead only a short distance as it is lifted by each crest, to recede again as it de- scends into each successive trough at so nearly the same velocity at which it had advanced that it returns almost to its original position (but see below, p. 6, for further discussion of this last point). On the other hand, no argument is needed to convince one that the wave forms do progress, even if the water particles composing them do not do so to any appreciable extent. In short, two distinct types of motion are combined in the advance of a wave. The one, mirrored by the movements of the floating cork, is the oscillatory motion of the water particles of which the waves are composed; the other is the undulatory advance of the wave form. Waves in their advance indeed recall, though they do not truly par- allel, the “waves” that one can see running across a field of grain or tall grass on a windy day, when the tips of the grasses are carried ahead with each gust of wind but then return to their original posi- tions, just as any bit of flotsam nearly does on the surface of the sea. And it is fortunate that this is the case, as has often been pointed out; so rapidly do waves often run that, if the enormous masses of water of which storm waves are composed advanced bodily across the sea, the ocean would not be navigable. A convincing demonstration of the forward and backward move- ments of the water particles, with the passage of a wave, can often be obtained if one looks down upon a field of submerged beach grass in an estuarine situation at high tide when the sea surface is unrippled and GROWTH AND DECAY 3 small swells are running. The grasses sway forward as the top of each crest passes over them, then sway backward under the following trough, to rise again under the next crest (fig. 1). If one watches a floating marker in moderately deep water, and if conditions are favorable for estimating how much it rises and falls, and how far it advances and recedes with the passage of each wave, the observer will also see that the length of each of its horizontal jour- neys is about as great as the vertical distance between the point to which it is raised by the crest and that to which it falls in the trough; this is, of course, equally true of the water particles in which the FiguRE 1.—The movements of beach grass, over which a low swell is running. (From observations at Cohasset, Massachusetts.) object is floating, since it is these water particles that carry it to and fro, and up and down. The motions, however, of our marker and of the water particles are not simply upward-forward with the passage of the wave crests, and downward-backward with the passage of the troughs, but form a curved path, corresponding to the convex contours of the wave crests, and the concave contours of the wave troughs. Further, it has long been established, both theoretically and by experiments (usually car- ried out by watching or by photographing the tracks of small particles suspended in the water), that the particles actually move along cir- cular orbits, in a vertical plane parallel to the direction in which the wave forms are advancing (fig. 2); when the water is so shoal that the proximity of the bottom interferes with the development of the wave, however, the orbits are rendered more or less elliptical (fig. 3). It should be emphasized, too, that all the water particles along any given perpendicular are moving in the same direction at any 226794 O - 53 - 2 4 PHYSICAL NATURE OF WIND WAVES given instant, throughout the whole of the depth zone that is affected by the wave. Thus, at the instant of passage of the top of the crest, all the water particles that lie below it are moving horizontally for- ward. During the passage of the back of the crest, all of the water particles below it are moving first obliquely forward and downward, next perpendicularly downward, then obliquely downward and back- — E << Z = - Fe Sse Gees Z csi anes ee ek Figure 2.—Directions of orbital movement of water particles in different parts of wind waves that are advancing in the direction of the long arrow. (Adapted from Berget.) Ficure 3.—Photograph showing movements of water particles in a wave in water so shallow that their orbits are elliptical. The exposure was for half a wave period. (After Alborn.) ward. At the instant of passage of the bottom of the trough, all of the water particles below it are moving horizontally backward. During the passage of the front of the next crest, all the water particles below it are moving first obliquely upward-backward, next vertically upward, then obliquely upward-forward, to move horizontally for- GROWTH AND DECAY 9) ward again at the instant of passage of the top of the next crest. (See fig. 2.) It is obvious that if any given water particle is close to the surface of the water the vertical distance between the points that it occupies in its orbit when it is at the top of a wave crest and when it is at the bottom of the succeeding trough is equal to the vertical distance be- tween the crest and the trough. In other words, the diameter of its orbit is equal to the height of the wave from crest to trough and is entirely independent of the length of the wave from crest to crest, or of the speed of its advance. It is further clear that the velocity with which each water particle circles its orbit is governed (a) by the distance the water particle must cover during each circuit and (0) by the length of time during which each circuit is completed. The length of the circuit of a water particle at the surface is, of course, equal to the circumference of the orbit, or (the diameter of the latter being equal to the height of the wave) about 3.14 times as long as the vertical height of the wave, crest above trough, at the time. The time occupied by it in each circuit is equal to the time interval that intervenes between the passage of every two successive crests past any given point, for each water particle is at the top of its orbit when each successive crest passes by. This time interval, in turn, depends on the velocity at which the wave forms are advancing, and on the distance from one crest to the next, 1.e., on the so-called “period” of the wave, as explained on page 31. Since there can be no one fixed relationship between the heights of waves and their periods, there is no one fixed relationship between the velocities at which the wave forms advance and the velocities at which the water particles circle their orbits. But the orbits traced by the individual water particles are invariably much shorter than are the distances from crest to crest, because wind waves at sea are always many times longer than they are high. Hence (since the period is the same for the wave as it is for the water particles of which it is composed), the velocities of the water particles around these orbits are always much lower than the velocity at which the wave form is advancing. In the case of a wave, for example, 200 feet long from crest to crest and 10 feet high from crest to trough, each water particle at the surface would trace an orbit of 10 x 3.14 feet, or about 31 feet, i.e., a little more than one-seventh as long as the wave, so that the velocity at which it circled its orbit would be a little more than one- seventh as great as that at which the wave form was advancing. And the longer a wave is, relative to its height, the greater will be the differ- ence between the velocity at which it is advancing and the velocities at which its water particles are circling their orbits. If, for example, the 10-foot wave just discussed were 400 feet long instead of 200 feet, 6 PHYSICAL NATURE OF WIND WAVES its velocity would be about 27 knots (p. 35), but the velocities of its water particles would be only about 2 knots. And in the case of long, low swells, the orbital velocities may be as little as 1/100 to 1/200 as great as the velocity of the wave. Consequently, the effects of the alternating following and opposing motions due to the orbital veloc- ities of water particles that a ship encounters are so small as to be negligible; then too, it is only for a very brief instant when the water particles are at the top of each of their orbits (at the crest of the wave), or at the bottom (in the trough of the wave), that their movement is purely horizontal. We should also note, in passing, that the passage of a wave also involves some actual progress of the water particles in the same di- rection, as has long been appreciated. In the case of small and not very steep waves, this “heave of the sea,” as it is sometimes called, is so small that it is not of practical importance in navigation, though it may be for drifting objects; it is somewhat larger for very large waves, especially if these are very steep. (See table 1.) TaBLE 1.—Velocity, in knots, of mass transport at the surface for waves of various heights, periods, and lengths ; / HY? ; ; {Derived from the basic formula u -( 7 )e where w’ is the velocity of mass transport, H the height of the wave, L its length, and Cits velocity] Height (feet) Period (seconds) ana — 4 6 8 10 12 20 30 Pe RS ee en aes 82 0.3 0.7 1.3 1:9 |... eee eee ee re eee 184 ei 54 .4 6 0.8 2:0 (a (ie A a Se ee ee 328 04 . 08 -15 ay. 4 .9 2.0 Qe eee ee oe ee can eee 512 | <.04 . 04 . 08 1 2 -5 1.0 Val ceo Ses Fae see eee neo ae 738 | <.04| <.04 05 07 1 ae .6 1) Se ee eee 1,003 | <.04) <.04| <.04 04 07 Ad, 4 This mass transport, caused by the orbital motions of the water particles with the passage of waves, has no direct connection with the drifts, or currents, that are set in motion by the frictional drag of the wind across the water, though it often is in the same general direction. THE GROWTH AND DECAY OF WAVES Whoever watches a passing “cat’s paw” of wind as it ruffles the glassy surface on a calm day sees the first stage in the process of wave forma- tion by the wind. But while it is obvious enough why the wind blow- ing across the surface of the sea should start a mass movement of water in the same general direction, i. e., should set up a wind current it is not so apparent why the wind should first transform the previ- ously level surface of the sea into a series of minute undulations and then build up these tiny crests and troughs to the very considerable GROWTH AND DECAY 7 heights to which waves actually rise. The explanation most com- monly offered in the older writings is that the gustiness of the wind, pressing upon the surface more strongly in some places and less strongly in others, is responsible by producing depressions and eleva- tions. which then run ahead as waves. And it is certain that this does happen when strong gusts of wind strike the water here and there with what might be termed a plunging motion. This we ob- served when looking out across a flooded meadow, during a recent gale when each of the more violent gusts instantaneously produced a well-marked depression a few inches deep and several yards across, preceded by an equally well-marked elevation several inches high and advancing at a velocity much greater than that of the smaller wavelets. It is equally certain, however, that this is not the usual process by which the ripples, that are set up when the surface of the sea is first ruffled, grow into waves, for while gusts of wind are apt to extend over areas at least some yards in extent (as any one can see who watches a field of grain waving under the wind) and are often to be measured in acres or even larger units, the first tiny ripples are only a few centi- meters long and few millimeters high. The wave pattern is thus far too small to fit the pattern of gustiness. Further, these tiny ripples are at first astonishingly regular in ares of long radius; that is to say, they are also much too regular to fit the wind pattern. In fact, no fully satisfactory explanation, how the wind does produce waves from ripples, has yet been offered. There is, moreover, a clean-cut difference in physical nature between the one and the other. The smallest ripples are what is known as “capillary” in nature, i. e., they are due to the surface tension of water, not to the force of gravity. They arise instantaneously when a breeze springs up, to die down when the breeze dies; and they advance the more rapidly the smaller they are, whereas the larger gravitational waves advance the more rapidly the longer they are and may continue to run long after the originating force has ceased to act upon them. Capillary or “ripple” waves become transformed, somehow, into ordinary gravitational waves when they reach a length of about 0.68 inches from crest to crest, and are moving at a velocity of about 0.76 feet per second. It has been variously reported that it requires a wind of about one half nautical mile per hour to about 2 nautical miles per hour to generate ripples. A stronger wind alters ripples into gravi- tational waves. Once the alteration has taken place, the waves continue to receive energy from the wind and, hence, to increase in size by the direct push of the wind against the upwind slopes of their crests and by its frictional pull upon the water. The first of these processes acts only as long as the wind is blowing at a velocity greater than that of the waves, And its efficiency in building up the latter depends 8 PHYSICAL NATURE OF WIND WAVES not only on how great the difference in velocity is between the two, but also on the shapes of the waves, for the more nearly streamlined these are, relative to the wind, the less hold does the latter have on them. The wind, however, exerts its friction, not only on the upwind side of the waves, but also on their troughs. But its effect is different on different parts of a wave, for while it tends to speed up the water particles at the crest, because these are also moving in the same direc- tion as the wind, it tends to slow down those in the trough, since these are moving against the wind. And we should point out that if a strong wind be blowing, the effects of its drag on the wave will be the same, even if the wave form be advancing faster than the wind, because the velocity of the latter always is much greater than the orbital velocities of the water particles of which the wave is composed. The wind also exerts a suction on the leeward slopes of the crests, if the waves are traveling more slowly than the wind, much as it does on the leeward side of a sail. And, while the combination of these actions requires complex computation for its exact evaluation, the net result is that waves continue to gain both in height and in length until they reach the maximum heights to which a wind of given strength can lift them (see p. 20); or if they have already reached that limiting height, they still continue to gain in length. Meantime, newer and smaller waves are constantly being formed on the older and longer ones, into which they then become incorporated, and so on throughout the period during which the waves are gaining energy from the wind. Thus each of the higher crests to be seen at any given moment is really a combination of an indeterminate number of smaller waves of successive generations. Every seaman knows that after a blow passes, the storm waves that accompany it die down before long, and that a counterwind knocks the sea down very soon indeed. At first sight, this might seem to contradict the rule stated above, that waves of oscillation continue to run, once they are set in motion by the wind. But there is no real contradiction, for it is only when the wave is not opposed by any counterforce that it conserves its energy and hence its form. And it is obvious that a wave is opposed, not only by the interference of any cross sea that is set in motion when the wind changes, but still more strongly by the counterthrust and counter drag of a wind that springs up against the run of the waves. A strong wind from a new direction may, in fact, flatten the waves with spectacular abruptness. Many times we have seen a tumultuous sea killed in this way within a few hours, as has everyone who has traversed the more stormy parts of the ocean; nor is there anything astonishing in this. The positive difference in velocity, for example, between a counter- wind of 20 miles per hour and the rate of advance of a wave no more DEPTH OF WAVE ACTION 9 than 100 feet long (1. e., of one advancing at a rate of about 13 knots) would be 33 miles per hour, and anyone knows that even a 10-mile wind is a very decided obstacle to his own advance, if he is walking against it. And even if the wind dies down entirely, still the waves are opposed by the resistance of the air that they must displace in their advance. The rate at which a counterwind will actually flatten the waves down in any given case, and the rate at which the resistance of the air will do the same to the waves running in a calm, depends largely on the shapes of the waves, by which we mean how nearly streamlined they may be, for it is obvious that the counterpush of a headwind will act much more effectively in this respect on a steep wave and on one of irregular contour than on one that is long, low, and more evenly rounded. And the greater the energy of the wave, the longer will the latter survive. The general rule is that storm seas are reduced much more rapidly in height by head winds or by air resistance than old, low swells are. The latter may even survive a series of head winds, if these are gentle, though a stiff head breeze may kill a swell in short order. THE DEPTH OF WAVE ACTION If an observer crumples a ball of paper or white cloth, wets it, and then drops it overside from a ship lying at anchor when waves of moderate size are running past her, or from a pier under similar circumstances, and if he watches as this marker slowly sinks, he will see that it continues to circle in the vertical plane as just described, with the passage over it of successive crests and troughs, for as long as it remains visible. He may be able to watch it make several such circuits, for it may remain in sight for as long as a minute, if the water is clear. (This demonstration of the orbital motion of the water particles in wind waves, first suggested by Hagen, is cited from Kriim- mel, 1911, vol. 2, p. 2.) This simple experiment is a visual demonstration of the fact, well- established both by experiment and by theory, that the orbits along which the water particles move continue circular down to the greatest depths to which wave action is perceptible, provided only that the water be deeper than this, as is the case over the open ocean generally. If, however, the water is so shoal that wave action extends right down to the bottom, as may be the case near land, the orbits followed by the water particles become elliptical, until the particles next to the bottom simply surge to and fro without any vertical component of motion at all. It has long been known that the diameters of the orbits (and, con- sequently, wave action) diminishes from the surface downward, although the period occupied by each water particle in circling its 10 PHYSICAL NATURE OF WIND WAVES orbit remains the same. Theoretically (and this is supported by laboratory observations) this decrease in the size of the orbits is in geometric progression as the depth increases in arithmetic proportion, the diameters of the orbits decreasing by approximately one-half, with each additional increase in depth equal to one-ninth of the length of the wave (table 2). TABLE 2.—Diameters of orbital motion, relative to the diameter at the surface, with increasing depth {According to the equation Ha= Tige**4, where F/g is the diameter of the orbit, H¢ the height of the wave, d the mean depth of the particle, Z the wave length, e a constant equal to 2.72, and a the constant 3.14. (From Johnson)] Propor- Propor- Depth below mean sea level in fractions | tionate || Depth below mean sea level in fractions | tienate of wave length diameter of wave length iameter of orbit of orbit Ee oe ee a eee 1 ee See ee ee aee ee Vo WG ee ee re ee Oe Se Ee Dal SQn288 oo Saou sana enone Soe ee Vis ge eee ee a eee VAN Ou ho can asa ee ne 428 ee oe ee De ee Pee eee 7 | Nia, er a gs 1656 5 ee ee ee ener Wel) 96--2---sch-- 3525 Ssco seo aoe eae Vo12 The orbits calculated by this ratio, for a wave 16 feet high and 360 feet long, for example, which would be 16 feet in diameter at the surface, would be 8 feet in diameter at a depth of 40 feet, 2 feet at a depth of 120 feet, and only 0.059 foot in diameter at 320 feet, and soon. Even fora wave 40 feet high, the orbits circled by each particle would be less than an inch in diameter at a depth of 360 feet. And the velocities with which the water particles circle their orbits decrease in a corresponding ratio as the depth increases, because the period occupied by them in so doing is dependent solely on the time required for the passage of two successive crests past a given point and so continues the same no matter what the depth. For example, the orbital velocity of the particles in a wave 10 feet high and 360 feet long from crest to crest, which would be about 3.9 feet per second at the surface, would be about 0.8 foot per second at a depth of 90 feet, 0.17 foot per second at 180 feet, and 0.04 foot per second at 270 feet. The effects of choppy seas 6 to 8 feet high, such as are common when the wind is rising, would not be great enough to be of any practical importance deeper than 40 to 50 feet, or those of waves 100 to 200 feet long deeper than say 50 to 100 feet, while wave action is wholly negli- gible, even from the theoretical standpoint, at depths greater than the length of the waves in question. The most interesting illustra- tion, from the navigational standpoint, of the decrease in wave action as the depth increases is afforded by the operation of submarines, for these seldom roll or pitch appreciably when submerged deeper than 90 feet. It is for this reason that it is easy to take pendulum measure- DEPTH OF WAVE ACTION 11 ments of the force of gravity from a submerged submarine—some- thing that can rarely be done from a surfaced vessel because of its uneasy motions. We might note in passing that deep-sea divers have reported being tossed to and fro when working as deep as 100 feet. The question of the depth to which wave action may extend is also a matter of interest to the student of submarine geology, because move- ments of the water, so small that they would be of no concern to the seaman, may still be great enough to shift sand, mud, or even small stones about from place to place over the bottom. It is known by ex- perimental measurements that a velocity of 0.3 foot per second is strong enough to move grains of sand or gravel as large as 0.1 inch in diam- eter, and it is at this velocity that the water particles would, theoreti- cally, be moving to and fro’at a depth of 92 feet, in a wave that was 10 feet high at the surface and 200 feet long. In the case of swells no higher but longer, say one 500 feet long, such as are often encountered at sea, the orbital velocities and, consequently, their abrasive power would be as great as this down to a depth of at least 192 feet; the in- fluence would be noticeable to an even greater depth with still longer waves. And the observations that have been made on the depth at which sand and even stones may actually be shifted about on the bot- tom are in line with the foregoing. Thus, swells have been said to wash stones as heavy as one pound into lobster pots off the mouth of the English Channel in depths as great as 180 feet; rocks weighing several hundred pounds have been reported as moved by wave action in depths of 90 to 120 feet off the western coast of Ireland; and coarse sand is sometimes brought up from 150 feet by storm waves, to be dashed against Bishop Rock Lighthouse, England, to quote a few in- cidents only. It has even been stated repeatedly—though not on very strong evidence—that wave action may affect the distribution of sub- marine sediments to a depth as deep as six hundred feet along the slopes that front the continents. But it is generally held that this is about the extreme depth to which wave action affects the water, in any part of the sea or at any time. (For further discussion of this sub- ject, with additional examples and references, we refer the reader to Johnson, 1919, p. 76.) We ought perhaps to caution the reader, in this connection, that the presence of ripple marks on the bottom, such as have been regarded sometimes as evidence of wave action in deep water, may equally be the result of currents flowing over the sea floor. For example, sub- marine photographs have proven the presence of ripple marks at a depth of 498 feet in the Gulf of Maine, although the waves that had been running for some days previous had been far too small to have disturbed the sand at so great a depth (fig. 4). 12 PHYSICAL NATURE OF WIND WAVES HURRICANE OR “TIDAL” WAVES One other type of wind wave remains to be considered, namely, the very high and long waves—distinct from swell—that sometimes pre- cede or accompany a tropical hurricane; these have done enormous damage along the coast, at great cost in human life in different parts of the world on many occasions. The most characteristic feature of waves of this sort (often erro- neously called “tidal waves”) is that they inundate low coastal areas ae Ser Figure 4.—Submarine photograph showing ripple marks at the bottom of the Gulf of Maine at a depth of 498 feet. (Photograph, courtesy of Dr. Maurice Ewing, Woods Hole Oceanographic Institution. ) that are not normally subject to overflow by the tides, sometimes to a vertical height of as much as 40 feet, so suddenly and so overwhelm- ingly at times that there is no escape. It has, in fact, been estimated that such waves (they may come in trains of 2 or 3 or more) have been responsible for more than three-fourths of all the loss of life that has been caused by tropical hurricanes in one part of the world or another. The wave that overwhelmed the city of Galveston, Tex., on Septem- ber 8, 1900, at a cost of nearly 6,000 lives and of tens of millions HURRICANE OR “TIDAL” WAVES 13 of dollars worth of damage to property, was of this sort. Again, in November 1932, such a wave cost the lives of about 2,500 persons out of a total population of about 4,000 in Santa Cruz del Sur, Cuba; on September 2 and 3, 1935, a hurricane wave rising 30 feet above ordinary sea level overwhelmed the Florida Keys at a cost of 409 lives; while on September 21, 1938, a hurricane raised the water to such a height along the southern coast of New England that some 600 lives were lost. But these tolls are insignificant compared to 20,000 people wiped out at Coringa on the Bay of Bengal in December 1789; or 50,000 lives lost and 100,000 cattle drowned at the mouth of the Hoogly River in 1864; or—greatest catastrophe of the sort on record—20,000 boats destroyed, of one kind or another, and about 300,000 people drowned on the shores of the Bay of Bengal by hurricane waves on October 7, 1737. (For a further account of hurricane waves, see Tannehill, 1938, pp. 30-43.) It is certain that waves of this class are not ordinary waves of oscillation. Probably, they more nearly resemble what are known as “waves of translation” (p. 115), for the inundation is caused by a tide-like movement of a vast mass of water up a shelving shore. And this explanation is supported by the fact that similar inundations— though on a much smaller scale—sometimes take place in shallow sounds, when the water that has been “banked up” as it were by a gale on the one shore, is driven suddenly against the opposite shore by a shift in the direction of the wind. Events of this sort are well known, for example, in Pamlico Sound, North Carolina, when a southerly gale or hurricane shifts suddenly to the northwest. Many of the fish houses standing on piles in the shallow waters of the eastern side of the sound, and also more permanent dwelling houses on the beach, were washed down or damaged in this way by the August hurricane of 1917. a 7 > es _— 2. o aa iit So . ) Soe \ | : el Palle : oe es eo ww ns * <4 Chapter 2 THE DIMENSIONS OF WAVES The dimensions of waves, by which their shapes and sizes are usu- ally defined, are: a. Height, 1. e., the elevation of each crest above the succeeding trough, expressed here in feet. 6. Length, from one crest to the next, also expressed here in feet. e. Velocity at which the wave form advances across the sea, ex- pressed here in knots. d. Period, i. e., the length of time required for the passage of two succeeding crests passing a stationary point, stated here in seconds. Many measurements, more or less reliable, of the dimensions of waves have been made at sea in various parts of the world and under various conditions. Among them we might mention, especially, the series made by Lt. A. Paris on French naval vessels in the Atlantic Trade Wind Belt and the southern West Wind Belt of the Indian Ocean, in the East China Seas, and in the western Pacific; by R. Aber- crombie in the West Wind Belt of the South Pacific; by the officers of the German research ship Gazelle in the North Atlantic, South At- lantic, and Indian Ocean; by G. Schott, during a voyage on a sailing ship in the North Atlantic, South Atlantic, and Indian Ocean in 1891- 92; those by Lt. O. Gassenmayr of the Austro-Hungarian Navy on the Donau in the Atlantic in 1895; those by V. Cornish in the North Atlantic; especially the very large series of measurements by Ameri- can officers that were taken during the years 1883-87 and assembled by Capt. D. D. Gaillard of the United States Army; and the dimen- sions derived by A. Schumacher, from stereophotogrammetric pictures taken of waves during the J/eteor Expedition to the South Atlantic, as well as from the liner Deutschland in the North Atlantic. The dimen- sions of waves have also been the subject of many theoretical discussions. THE HEIGHTS OF WAVES The question, how high are the waves at sea, is one to which very various answers have been given, partly because it is difficult to measure wave heights exactly on shipboard, partly also because three rather distinct problems are involved: the relationship between wave heights and the character of the wind; the heights of the common run of waves at different times and places; and the heights of the largest waves that accompany severe and prolonged gales. 15 16 WAVE DIMENSIONS The last of these three problems has received the most attention, no doubt because exceptional and spectacular phenomena are naturally the most impressive, especially if they involve imminent danger to human life and property, as really large storm waves do. But the heights of the common run of waves is of equal or greater importance from the practical standpoint, because the seaman has to do with these every day that he is at sea, but may never, in a lifetime, encounter waves of the great heights that are sometimes reliably reported, even if his voyages regularly cross and recross the stormier parts of the ocean in stormy seasons. The relationship that the heights of waves bear to the wind is also of concern, not only from the theoretical stand- point, but very directly from the practical, as indicating the general dimensions of the waves that are to be expected in different parts of the ocean and at different seasons, according to the prevailing condi- tions of the weather. And discussion of this phase of the problem is the logical introduction to any account of the heights of the waves that ships do actually meet. The heights of waves are determined by the strength of the wind, combined with the length of time during which a wind of any given force may have been acting on them. It is a matter of common knowledge that high winds do not generate high waves instantaneously, but require a considerable period to do so. Since the waves are con- stantly advancing, meanwhile, the time during which the wind may have been acting upon them is proportional to the distance that they have run, or to the “fetch” as this is termed. And it is for this reason that the sea is always smooth under the windward shore, no matter how strong the wind nor how long it may have been blowing, with the waves increasing in height out from the land. In other words, large waves can develop only in comparatively broad bodies of water. The rate at which waves gain in height, under winds of different strengths, has been much discussed and the values given in table 3 are taken from one of the most authoritative attempts that has been made to discover empirically the maximum heights of the waves that winds of different strengths ordinarily produce (given sufficient time and fetch). The growth of waves in relation to the wind has also been subjected to theoretical analyses. These yield the most trustworthy information now available as to the rates at which waves grow in height under winds of different strengths, for the fact that waves are constantly ad- vancing has so far prevented any one from bringing the growth of a wave under close observation. The theoretical relationship between height of wave, strength of wind, and duration and fetch of the latter is summarized in tables 4 and 5. HEIGHT 17 TABLE 3.—Probable maximum heights of waves with winds of different strengths, combined from various observations at sea [Adapted from Kriimmel]] Wind Wave height Nautical Meters per second miles per Meters Feet hour Soe eel eh ob pte ee ee eee ee 2 eee 8 0.8 2.6 Far 2 eee Se eee oe eo oo eae 12 1.4 4.6 Wee eee cece wet eed ee es a ee ee, eee eee 16 2.4 7.9 le eee cena oe ee ee ee eee ee 19 3.5 115 Ee, er ose oe seek oe cane oe seek el ok ene 27 6.0 19.7 Wo... pe. +23) SEE ee ee ree 31 7.5 24.6 Dj = SS a ee ee Vth ey a aS) 28 eee o 3 35 9.1 29.9 Bees one 2 eee Se ee. ee 39 10.9 36.0 Ween cone ceed bene ee 43 12.0 39.4 The theoretical relationship between heights of waves and strengths of winds agrees fairly closely with the relationship between wave heights and winds of different velocities, up to 40 miles per hour, that have actually been observed. (See table 3.) But we may point out that the statement, sometimes made, that the heights of storm waves, in feet, average 0.6 to 0.8 of the velocity of the wind, in nautical miles per hour, is not borne out by either tabulation. And the heights of waves, as observed, differ considerably from the theoretical values for stronger winds. Thus the theoretical height of waves for a 56-mile wind is 63 feet, whereas it has been the repeated experience of observers at sea that the upper limit for the average run of waves that accompany winds of 50 to 60 miles per hour, such as are not infrequently en- countered during severe gales, is not more than about 40 feet at most. And waves higher than this are unusual, no matter how high the wind, unless indeed two large waves chance to unite (p. 25). This discrepancy results in part from the fact that the theoretical values, given in tables 4 and 5, are for the highest waves, and these have seldom been actually measured. But the chief reason why waves are seldom as high as should theoretically be possible during severe gales is that winds stronger than 40 to 50 miles per hour seldom blow in a uniform direction far enough for them to produce waves more than 30 to 40 feet high or so. Thus the effective fetch (p. 19) for winter gales in the North Atlantic is not often more than 500 to 600 miles, or enough for the waves produced by a 40-mile gale to rise to only about 32 feet, or three-fourths of the height possible with a wind of that strength over an unlimited fetch. And a fetch of even 800 miles, such as develops occasionally in the North Atlantic with a pro- longed gale, is no more than is needed for a 50-mile wind to produce 50-foot waves. But the effective fetch is longer still in Atlantic gales on rare occasions, as it more often is in the North Pacific, and the 18 WAVE DIMENSIONS general run of the waves may be expected to rise then to the maximum heights possible for 40- to 55-mile winds, 1. e., to 55 feet or even higher. It is because the winds in the tropical hurricanes of the Atlantic and in the typhoons of the Indian and western Pacific Oceans do not blow far in any one direction that these—the most violent storms of all—do not produce the highest waves. A case in point is the much longer fetch of the westerly storm, in high latitudes of the Atlantic, illus- trated in figure 6, as contrasted with the wind of the tropical cyclone that was centered north of Puerto Rico and of Hispaniola on the same day. And while the Trades do blow along fetches long enough to allow their waves to develop fully, they are not strong enough to generate very high waves. (See table 6.) TABLE 4.— The heights of waves, in feet, theoretically produced by winds of various strengths blowing for different lengths of time ! Duration in hours Wind velocity, nautical miles per hour = |— ea Fike 10 | 15 20 30 40 | 50 | | | eS ee Sn eee ee ae eee Paes 2.0 | 2.0 2.0 | 2.0 | 2.0 2.0 2.0 eee een eee he ee eT 3.5 4.0 4.5 5.0 5.0 5.0 5.0 7. | PE SENS SER Ne Se es ee ee ae el ee 5.0 | 7.0 8.0 8.0 8.5 9.0 9.0 5g ES aie al a ES RE OE So eae ee Ne 9.0 | 13.5 15.5 | 17.0 18.0 18.5 19. 0 ae En ac, Se Se Ee ee Ig a 13. 5 21.0} 25.0 27.5 31.0 32.0 33. 0 TL eae a ee een eae ns FER URES Se 18. 0 29.0 | 36.0 40.0 46.0) 48.0 50. 0 Oe ee Se eh ee ee Ge a ee 23.0 37.0 46.0 53.0 61.0 | 66.0 70. 0 | TaBLE 5.—The heights of waves, in feet, theoretically produced by winds of various strengths blowing over different fetches } Fetch in nautical miles Wind velocity, nautical miles per hour ] 10 | 50 | 100 300 500 1,000 ice Se ost 2 eee eee 1 ee See ee eee Eee 1X5 | 2.0 | 2.0 2.0 2.0 2.0 Lee me eee ey RU Ah A ee eee 3.0 | 4.0 | 4.5 | 5.0 5.0 5.5 Li ay Sy ly PS Sa A ee an te Sa ee eR De 4.0 | 6.5 8.0 9.0 9.0 9.5 See nee ee ee ene oe eee See ie 6.0 | 12.5 15.0 | 18.0 19. 0 19.5 Be eee a eae ee eke eee Te Ue Peres CU ePIC PRL 30. 0 32.0 35. 0 Ce 8 Se eS 9.0] 22.0} 30.0 43.0 47.0 | 52.0 1 | 1 Based on H. O. Pub. No. 604. TaBLE 6.—Minimum, maximum, and average heights in feet of waves for the Trade Wind Belts {After Kriimmel, based on measurements by Paris] Area Minimum | Maximum] Average AtInHtiC nTade Wing belt..." 2. 95 Vel. os ee ee ee 0 20 6 Pncianeerade Wild Bele.) 52 25ie i) as yn. 65 yl eee 3 16 9 Western Pacific, including the Trade Wind Belt____________________ 0 25 10 HEIGHT 19 Another reason why the waves that accompany strong gales usually are not as high as theory demands is that the increase in the height of a wave is not likely to be continuous throughout the period of its development, as it is represented in tables 4 and 5. This is partly because the wind is gusty and does not blow steadily at maximum strength. But it is also due to the fact that the tops of the crests of waves that are being acted upon by strong winds frequently break, Whereupon they lose more or less in height. They then gradually build up once more (as anyone favorably situated can easily see), to break again, and so on. Or they may break continuously along the tops of their crests for considerable periods, which hinders their gain- ing in height as rapidly as they would otherwise do under a wind of a given strength. This process is discussed more fully on page 31, in connection with the steepness of waves. A fourth phenomenon directly tending to reduce the heights of the waves in stormy weather, and one with which seamen are familiar, is that the waves often are not at their highest when the wind is blow- ing the most fiercely, but after it has begun to die down, probably because the most violent gusts carry the tops of the crests off bodily, thus reducing the heights of the waves for the time being. The relationship between storm waves and the winds that they ac- company is complicated further by the fact that the stronger gales of stormy latitudes “commonly come in groups, one succeeding another after a short interval of time. Thus there may be a stormy month during which one cyclonic storm quickly succeeds another, all pursuing the same general track across the ocean. Between times the sea never settles down but heaves with a heavy swell * * * No sooner does a cyclone brew upon the North Atlantic in such a season than the wind in the righthand, rear quadrant of the depression travelling towards Europe immediately steepens this swell into great storm-waves, as happened in the Bay of Biscay on December 21st, 1911 * * *” (Cornish, 1934, p. 29). Discussion in the literature of the relationship between wind and waves leads to the very important conclusion (borne out by a great number of observations at sea) that waves do not continue to gain in height indefinitely under a given wind, but that there is a limit to their final heights, no matter how long the wind may have been blowing. Moreover the waves grow much more rapidly at first than later, and when a wave has attained about 75 to 80 percent of the maximum height, for a given wind (see table 7), its further growth is very slow. We should caution the reader here that the word “fetch,” as applied to the development of ocean waves, does not mean simply “sea room,” as one might gather from a cursory reading of writings on the subject, 226794 O - 53 - 3 20 WAVE DIMENSIONS but refers to the extent of ocean over which the wind has been blowing in a comparatively uniform direction, strongly enough to have pro- duced the waves in question. TABLE 7.—Mazimum wave heights theoretically possible with various wind strengths, and the fetches and durations required to produce waves 75 percent as high as the maximum with each wind velocity Fetch for Maximum | 75percentof | 75 percent tor 1 coneute Wind velocity (nautical miles per hour) bai paen eee ie rarer of mneiaiand ee leig ee eight (nau- : tical miles) | beight (hours) Chee eS pe ed nes Se eS 2.6 2.0 10 5 2. Eee = Nak ae ai Sa eer ee Bis ae ee Fetes 10.6 8.0 90 16 ig, a SS Re is en a ee pee ee Oe 25 ee ee 23.7 17.8 260 28 FN Re eS a ce ee 42.5 31.9 400 34 eae oe ee oP ee ee oe eee 66. 2 49.7 740 48 The proverbial rapidity with which the waves rise when a violent squall strikes is not a guide to the rate at which the heights of the waves in question have actually increased, because the squall may have been acting on them for many hours during its advance before reaching the observer. Such no doubt was the case in one recorded instance in the North Atlantic on the 22d of December 1906, when a violent squall, lasting only 4 minutes, resulted in an apparent increase of 7 feet in the height of the waves (Cornish, 1934, p. 9.) ; and in a second, off Cape Horn on the 23d of January 1926, when an increase in the strength of the wind from four on the Beaufort Scale (23 miles per hour) to about nine (56 miles per hour) between early morning and midafternoon, was accompanied by an increase in the heights of the largest waves from about 2 or 3 feet to about 26 feet.? Waves generated by storms have risen close to their maximum heights by the time they have travelled 600 to 700 miles from the place where they were generated. And a fetch of 900 miles probably is sufficient for the development of the largest of storm waves that have been reliably reported anywhere, no matter how strong the wind. Thus the waves may be nearly 30 feet high during the most severe blows in the Gulf of Lyons on the south coast of France, where the fetch is only about 400 nautical miles; 29 to 30-foot waves, and higher, have been recorded south of Newfoundland, where the fetch (upwind) was about 600 miles; and 40-foot waves in a heavy swell in the north- eastern Atlantic, west of Ireland, where the distance upwind was about 1,100 sea miles to Greenland, or about 1,200 sea miles to the Newfound- land Banks, though the effective fetch may not have been as long as this. Observations made many years ago on the west coast of Scotland, where the contour of the coast with its off-lying islands makes it fea- * Schumacher, Arnold. 1928. Die stereogrammetrische wellenaufnahmen der Deutschen Atlantischen Expedition. Z. Ges. erdk. ergiinz. vol. 3, pp. 117-119, figs. 52, 54. HEIGHT Zi sible to determine the effective fetch with some accuracy, also led to the conclusion that the waves caused by ordinary winter gales averaged about 1.5 times as high (in feet) as the square root of the fetch (in nautical miles) for distances up to 300 to 400 miles (Stevenson, 1874, pp. 23-26). And the heights derived by this formula, which has been accepted in many of the more recent discussions, correspend fairly well with the heights of waves that have been measured elsewhere in storms or ordinary intensity. Waves, for example, 22 to 23 feet high have been recorded in the Duluth Canal on Lake Superior, where the fetch is 259 nautical miles (Gaillard, 1904, p. 69), as compared with 24.1 feet, according to the formula; and a 30-mile wind has been observed to produce 22-foot waves in the western Meriterranean, where the fetch from the windward shore was about 260 nautical miles, i. e., where 24-foot waves might be expected (Cornish, 1910, pp. 36-40). It is obvious, however, that since this formula takes no account of the strength of the wind, it cannot be invoked indiscriminately, else serious errors will result. Thus a 20-mile wind, which should produce a 7.5-foot wave with a fetch of 25 miles according to the formula, and one of 15 feet with a fetch of 100 miles, would actually produce waves of only about 6 feet and of 8 feet, respectively, at these distances. The average heights of waves.—The accounts of the early voyagers of the last part of the eighteenth century and of the first quarter of the nineteenth contain many reports of mountainous waves—especially in the stormy Southern Ocean. But it has long been known that their reports were greatly exaggerated. While waves up to 40 to 50 feet high, or even higher, do occur, as described below (p. 23), during severe and prolonged gales, the common run of waves are very much smaller, even in the most tempestuous regions (See table 8.). TABLE 8.—Relative frequency of waves of different heights in different regions [Adapted from a chart, based on 40,164 extracts from sailing ships’ log books, in Schumacher, 1939] Height of waves in feet Region SS — So pre 0-3 344 4-7 7-12 12-20 >20 North Atlantic, between Newfoundland | Percent | Percent | Percent | Percent | Percent | Percent 10 15 pact lore vit | So ae ee a 20 20 20 15 Mid-equatorial Atlantic______--______--_- 20 30 25 15 5 5 South Atlantic, latitude of southern AMICI Ts ek SO ER Sie 10 20 20 20 15 10 North Pacific, latitude of Oregon and south of Alaskan Peninsula_____----___- 25 20 20 15 10 10 Mastiequatorial Pacific...» -_..-_._-._.- 25 35 25 10 5 5 West Wind Belt of South Pacific, latitude DiEOntneMn Cie: <2 ie eee 5 20 20 20 15 15 fe =e Ocean, Northeast monsdon Pe Re ee ani 55 25 10 5 0 0 North ; nated Ocean, Southwest monsoon Caro 25 Se a ae ee 15 15 25 20 15 10 Southern Indian Ocean between Mada- est Wind Belt of southern Indian Ocean on route between Cape of Good Hope ascar and northern Australia___________ 35 25 20 15 5 5 and southern Australia_-.........----_- 10 20 | 8 8 & 22 WAVE DIMENSIONS The wave heights listed in table 8 mark the North Indian Ocean during the season of the Northeast Monsoon as the quietest extensive region, the waves there being less than 4 feet high for more than four-fifths of the time, less than 7 feet high nearly 95 percent of the time, very rarely as much as 12 feet high, and practically never so much as 20 feet high. The equatorial belts of the eastern Pacific and of the Atlantic oceans are the next quietest, with waves less than 4 feet high for two-thirds of the time and one-half of the time respectively ; less than 7 feet high for four-fifths and three-fourths of the time, more than 12 feet for only some 10 percent of the time, and rarely as high as 20 feet. The waves, too, are at least no higher than 4 feet for nearly one-half the time, even in the West Wind Belts of the Northern Hemisphere, whether Atlantic or Pacific, with waves less than 7 feet high for nearly two-thirds of the time; they are less than 4 feet high for roughly one-third to one-fourth of the time, and less than 7 feet high for roughly one-half of the time, in the West Wind Belt of the Southern Hemisphere, whether Indian or Pacific, though this is the most turbulent part of the ocean. The relative frequency with which waves of different heights have been observed at South Beach, Martha’s Vineyard (table 9) with the corresponding tabulation of the height of the surf for points on Long Island, in New Jersey, and in North Carolina (see table 34, p. 151), il- lustrates the great preponderance of the smaller waves (less than 5 feet high) along the middle Atlantic coast of the United States. TABLE 9.—Frequency distribution of waves of different heights at South Beach, Marthas Vineyard, from observations made between November 1943 and April 1944. Each case is the mean of 20 consecutive waves Mean height in feet a. Monthly SSS SSS eee Eee ta. mean Month o NOS |) Te) Gere ee |S | ee rE || Ce |e | Qe |) “SS helene Th PO NG OZ || EO WI OPA 0 | 9.0 | 10.0 ee INOVEMDEES 2 8s 2a ees 2 1 1 Hl ees So a ee eee 8 (eee | Pe ee ea ye eee oe ee December--_-_-___---- i 3 1b aa Pam [RSPR I a 5 See | (eee by else S\icGon ees : January ee = 8 8 22 13 3 1 2 1 1% eee 1 52 7B February.________-- 4 26 10 6 3 ri aes Se [a yi Pe ee 52 2.4 Marche 22 So 5] 20 13 9 3 2 ia) ae ae ee eee 53 2.4 1 oe 1 20 10 9 2 42 2.3 Total cases.__.| 22} 93| 48| 28 9 5 2 1 2 1 7 gl Pees Frequency (percent) ___] 10.4 | 44.1 | 22:7] 13.3 | 4.3) 24] 0:0} O55 | 0.9") 0:6?) eee eee The vast majority of waves, in short, are considerably lower than 12 to 15 feet, and waves much higher than 20 to 25 feet are not usual anywhere. Thus the highest measured wave observed on the cruise of the French frigate Venus around the world in 1836 to 1839 was about 25 feet, in a case where 2 waves had joined, and otherwise only about 23 feet; these were in the vicinity of Cape Horn. (So far as HEIGHT 2 we can learn these measurements, made according to the method pro- posed by Arago [see p. 61] and reported by him,’ were the first that were ever reported of waves at sea measured by any dependable method.) Similarly, the largest waves observed from H. M. S. Challenger during her historic scientific crifise around the world, 1873-75, were only 18 to 22 feet high (southern Indian Ocean between Crozet Island and Kerguelen),? while the maximum height reported by United States naval officers from any part of the ocean during the three years, 1883-86, was 25 feet (Gaillard, 1904, p. 76). The maximum heights of storm waves.—The heights of the largest waves that ships encounter at sea during severe storms is a matter of perennial interest, and published statements have varied widely. We have just pointed out that the vast majority of waves are less than 12 feet high in all parts of the ocean, and that waves higher than 25 feet are not common. But it is well established that waves may grow to 40 or 50 feet—or even higher when a really severe gale extends over an area great enough to have an effective fetch of 600 to 800 miles. The earliest definite measurements by a dependable method of storm waves of that general order of magnitude, with which we are ac- quainted, were made in February 1841 near the Azores by Lt. de Missiessy, during a violent gale of 2 weeks’ duration; he reported wave heights of 43 to 49 feet.* More recent reports of waves higher than 35 feet out at sea (mostly from Gaillard, 1904, and Cornish, 1910 and 1934) are listed below. North Atlantic: Waves with average heights of approximately 30 feet, the largest (about one in every six) about 43 feet high, observed by Dr. Scoresby midway between Newfoundland and Ireland (lat. 51° N., long. 38°50’ W.) on March 5, 1848. A maximum height of about 35 feet observed at Peterhead, Scot- land, in February 1900. Waves of at least 40 feet which forced the Vormania to put back to New York from halfway across the Atlantic, because of the damage done to her upper works, in January 1894. Waves commonly 29 feet high, but some of them 43 feet high, en- countered by the /vernia off the west coast of Scotland on Decem- ber 7, 1900. A huge swell, with many waves up to 41 feet high, encountered by the Minnehaha, eastbound from New York to Southampton, in latitude 48°54’ N., longitude 18°20’ W., on February 9, 1907. 2 Arago, D. F. J. 1841. Plus grande hauteur des vagues. C. R. Acad. sci. Paris. vol. 11, p. 326. 3Tizzard, T. H., and others. 1885. Rep. sci. res. * * * H. M. S. Challenger. vol. 1. Narrative, pt. 1, p. 330. * Arago, D. F. J. 1857. Oeuvres complétes. Paris. vol. 9, p. 550. 24 WAVE DIMENSIONS Waves of about 40 feet encountered by the Egypt and measured by Cornish off the Bay of Biscay in December 1911. A colossal sea apparently with wave heights of at least 60 feet, as calculated by Cornish from data supplied by the ship’s officers, en- countered by the Majestic southwest of Ireland on February 20, 1923. A wave of very irregular shape with multiple peaks rising a little above 36 feet, as calculated from stereophotograms taken from the liner Deutschland, south of Newfoundland on March 15, 1929 (Schu- macher, 1939, atlas, insert chart 29). North Pacific: A single wave of at least 57 feet, as calculated from a photograph taken from the United States Fisheries’ steamer Albatross, off the northwest coast of the United States. Waves estimated by the commanding officer to be at least 70 feet high, encountered during a prolonged gale of hurricane force by the S. S. Ascanius on the run from Yokohama to Puget Sound. An enormous wave, the highest that has ever been reliably reported, with an estimated height of about 112 feet, encountered during a prolonged period of stormy weather by the U. S. S. Ramapo in the central part of the North Pacific on February 7, 1933. ° Southern Ocean—West Wind Belt: Waves of about 30 feet encountered by the Novara expedition in the southern Indian Ocean in November 1857. Waves commonly 30 feet high, with a maximum of 42 feet, near Cape Horn in 1880. Heights of 21 to 46 feet encountered on the run from New Zealand to Cape Horn in 1885. A miximum of 37.5 feet reported by Lieutenant Paris in the south- ern Indian Ocean, between the Cape of Good Hope and St. Paul Is- land, in 1891, Waves up to 39.4 feet measured by Dr. G. Schott from a sailing ship in the South Atlantic, also in 1891. Waves 33 to 36 feet high measured by Captain Chiiden in the South Pacific. Heights of 38 to 45 feet, measured from the Corinthic in the south- ern Indian Ocean in August 1907. Waves at least 45 feet high, measured from the Owestry Grange between St. Paul Island and Kerguelen, also in August, 1907. Additional instances of very high breakers on one coast or another are given on page 119. 5 Whitemarsh, R. P. 1934. Great sea waves. Proc. nay. inst. vol. 60, p. 1100. As this is the highest wave on record, we should point out that the method by which it was measured appears to have been reliable, and that the observer discusses the possibilities of error. HEIGHT 25 The stormier latitudes of all oceans experience about equally severe gales at one time or another; hence it is not astonishing to find that the largest storm waves that have actually been measured so far have been of about the same heights in the North Atlantic as in the South Atlantic and in the Southern Ocean. Single high waves and groups of high waves.—Successive waves al- ways differ considerably in height, whether the general run is high or low at the time, and from time to time a wave comes that is con- siderably higher than the common run. Thus a 6- to 8-foot wave is not unusual when the common run is only 4 or 5 feet, nor are storm waves more than 30 feet high uncommon, even when the average is only 18 to 20 feet while occasional single waves of 50 feet, or even higher, have been observed not uncommonly, as just noted. This is partly because longer and hence faster running waves are constantly overtaking and combining with the slower running ones. This hap- pens when there are two series of waves present, and the phenomenon is called interference. And the chief source for outsize waves of this sort is the union of those that advance from different directions, a frequent event in stormy weather. When this happens, the joint waves may be much higher than those that precede them or that follow them; and there is no way to predict the coming of a wave of this sort. Likewise, when a trough of one series of waves coincides with the crest of another, the resulting wave is considerably lower than most. During a gale, a ship may also encounter groups of waves, from time to time, that are much larger than the usual run; these may be the product of the more violent squalls with which every gale is punctuated. During the early stages of a blow, when the waves are still so steep that the sea is breaking, a sharp squall often lowers the heights of the waves by temporarily cutting off their tops bodily, as noted elsewhere (p. 19). But the effect of a squall later in the gale, when the waves are relatively longer, is to increase the size of the particular group on which it acts. And, since every gale of any severity is interspersed at irregular intervals by squalls of brief duration, the wave pattern is correspondingly interspersed by groups of considerably larger crests. Cases frequently quoted are a 4-minute squall during a moderate gale in the North Atlantic that was accom- panied by waves about 7 feet higher than the ordinary run (p. 20) ; and another 3 minutes in duration with waves 6 feet higher. The number of individual waves that may combine to form a train of this sort depends on the area covered by the squall responsible for them and on the rate at which it is advancing as a whole, not on the velocity of the wind within it. A squall, for example, advancing at a rate of 20 nautical miles per hour and occupying 4 minutes in its passage (a 26 WAVE DIMENSIONS common case) would be about 114 nautical miles from front to rear. If the waves averaged, say, 800 feet from crest to crest at the time the squall first developed, it would act on only about 10 of them; it would influence a proportionately greater number if it developed earlier in the gale while the waves were shorter, or a smaller number if it devel- oped after a really long sea was already running. And squalls of wider extent would act upon a correspondingly larger number of waves. A case of this sort is on record for the south coast of England, when a train of 139 large breakers was observed, the product of a single violent squall, with periods so long (average 19 seconds) that the group as a whole must have extended over a distance of 49 miles while they were still out in deep water. This group occupied three-quarters of an hour and it was preceded by five groups, each of four to seven still larger breakers, with average periods of 20 seconds. These groups, occupying one to two minutes had, no doubt, been engendered by a series of 1- to 2-minute gusts, and had outrun the more extensive group produced by the three-quarters of an hour squall. But the still fiercer gusts, lasting only a few seconds, which, in turn, punctuate every squall, extend over such short distances that they affect only part of one of the individual waves, if the latter have advanced beyond the very earliest stages in their development. Conse- quently, the sizes of the largest waves produced by a squall correspond to the average velocity of the wind within the latter, not to the very highest velocities to which the wind may rise momentarily. When we remember that individual squalls travelling at rates of 20 to 40 miles per hour have been shown by self-registering instru- ments at meteorological stations to have advanced unbroken for dis- tances up to 1,000 miles or more, there is nothing astonishing in the well-established fact that the trains of very large waves that they produce may do the same. THE LENGTHS OF WAVES Anyone who has seen ripples grow to whitecaps under a rising wind and who has watched whitecaps develop into a sea knows that the waves grow longer as they gain in height. And the linear distance from crest to crest increases much more rapidly than does the absolute height of the waves, provided the shape of the latter (i. e., the ratio between its length and its height) continues approximately the same, for waves are invariably many times as long as they are high. If a 5-foot wave, 100 feet long (a common proportion of height to length), doubles in size, for example, its length increases by 20 times as much (by 100 feet) as its height (by only 5 feet). And this in- ®Cornish, Vaughan. 1929. Waves of the sea, Encyclopedia Brittanica, 14th ed. vol. 23, p. 442. LENGTH 27 crease in the length of the wave continues not only as long as its height is increasing rapidly, but even after it has attained the maxi- mum height to which the particular wind in question can raise it. Table 10, abbreviated from one already published, gives at least a rough picture of the average lengths of the waves to be expected out at sea with winds of different strengths. TABLE 10.—Average lengths of waves, observed at sea, according to the strength of the wind [Adapted from Kriimmel]] Wind Waves, res average rene eee vate | Tengen eaufort scale escription miles per feet hour Jiecee ee eS ee ee eee ight )breezec-- --— 11 52 i eS ee as ee 2 ee Moderate breeze____________ 20 124 ee Pe we wea be Sos Sete SY HTC 0) 96/0) b= a UR al 30 261 Piper tie ae pet eS as es SE a eee is Moderate gale__-__-_----___- 42 383 UD ee te oe SS ee ee ee eee ee CLONE Palpees esa 56 827 The averages presented in table 10, which were based on a large number of observations made in different regions, show that ocean waves are usually more than 100 feet long from crest to crest, unless the wind is very light. A similar tabulation (table 11), based on other published measurements of waves from 4 to 46 feet high and more than 60 feet long, also shows that storm waves are not ordi- narily longer than 450 to 550 feet in the North Atlantic or North Pacific, and perhaps a little longer, though not averaging so, in high latitudes in the South Atlantic and South Pacific. To find really long storm seas, we must turn to the so-called “Southern Ocean,” on the route from South Africa to Australia, where the seas are com- monly as much as 600 to 800 feet long in heavy gales. An average of 775 feet has, in fact, been recorded there for an entire day, with occational waves 1,200 to 1,300 feet long. The lengths just quoted are for waves either still gaining height or at least near the maximum heights to which the wind in ques- tion can be expected to raise them. Old swells may be much longer still. And the North Atlantic yields nothing, in this respect, even to the Southern Ocean. Swells as long as 1,520 feet (calculated from their periods, as explained on page 35) have, for example, been ob- -served by French officers in the Bay of Biscay; swells 866 to 1,481 feet long on the west coast to Ireland; others averaging 1,850 feet, and with a maximum of 2,594 feet (by similar calculations), on the south coast of England following a severe Atlantic gale; and still others with a length of 1,914 feet off the Cape of Good Hope many years ago. Swells of 2,719 feet, reported for the equatorial Atlantic, 28 WAVE DIMENSIONS are the longest yet on record (Kriimmel, 1911, p. 49, and Cornish, 1910, p- 92). TABLE 11.—Lengths of storm waves observed in different oceans {Adapted from Gaillard] Wave length in feet Number of Ocean area cases Maximum Minimum Average North Atlantie_.___- eee eee Sa 5 REE ae oe 559 115 303 15 BOUtBVA tIATINIC lias kk Soe ee ae 701 82 226 32 |i Oa Ae ee ee SS eT 765 80 242 14 SHLEMn Pe MCIan sete ee ss ee” toe 1,121 108 360 23 COUT TE YS i ee ne epee ae Bias i Re 261 160 197 3 Information as to the lengths of waves is scant for narrower seas. S They appear to average somewhat shorter in the China Sea than in the eS open ocean under similar conditions of wind and weather. And this probably applies also to the Mediterranean, where the longest waves yet recorded in print were of about 328 feet, although higher and hence probably somewhat longer waves have been reported in winter gales. THE STEEPNESS OF WAVES The lengths of waves concern the seaman in two ways chiefly : first, as governing the number of individual crests and troughs across which a ship of a given length will extend in different conditions of wind and weather, and second, and more especially, because the length of a wave combined with its height determines its steepness. Steepness may be expressed in two ways, as the ratio of height to length, or as the ratio of length to height. Both methods of expression are used here. The steepness of waves is a matter of very direct concern, if one’s vessel is heading into a sea of any considerable size, or if she is run- ning in the trough of the sea. It is a matter of common knowledge that waves average steeper in the earlier stages of a blow than they do later on (i. e., that they are “choppier”). And theory is in accord with observation in this respect, as appears from table 12. This tabulation is in line with observations at sea. Off the Cape of Good Hope, for example, a wind blowing for 4 days in a uniform di- rection has been reported as lifting the average heights of the waves only from 20 to 23 feet on one occasion, though their average lengths increased from 3870 to 770 feet (observations by Lieutenant Paris, cited from Kriimmel, 1911, p. 64). In another published in- stance for the Atlantic Trade Wind Belt near the equator, when the largest waves grew from about 5 or 6 feet high to about 10 feet in height, their average lengths increased from about 33 feet to more than 100 feet, i. e., tripled (Kriimmel, 1911, p. 64). STEEPNESS 29 TABLE 12.—The average steepness of waves, expressed as the ratios of their lengths to their heights (boldface, to nearest whole number) and of their heights to their lengths (italics), for winds of different strengths and durations [Based on tables 4 and 15] Duration of wind in hours Wind velocity (nautical miles per hour) 5 10 15 20 30 40 I... ---+. eb See ee eee ee 11:1 1 26:1 A hel | 52:1 59:1 0.089 0. 043 0.038 0.027 0.019 0.017 UL 1 eee eee 12:1 20 21Gi) 23 Pl | 0. 087 0. 057 0.050 0. O44 0.031 0.025 pe se ck sk ana ckene 11 14:1 ie (ei | 27:1 31:1 0.090 0.071 0.060 0. 046 0. 037 0.032 cH eres = Sone Pee se oe Soe cs 11:1 12:1 14:1 16:1 25:1 0.095 | 0.081 | 0.069 | 0.062 0.049 0.040 Ww. so- s+ ee See ee 11:1 1 14 17:1 0.097 0.091 0.078 0. 069 0.058 0. O48 Observations taken at sea cannot be expected to yield any general rule for the ratio of the lengths of ocean waves to their heights, be- cause low waves may either still be very young—hence, relatively short and steep—or they may represent very old swells, in which case they may be many times as long, relative to their heights. The ratios of length to height among the 2- to 5-foot waves, for example, that are listed in one of the most extensive tabulations yet published (Gaillard, 1904, p. 79), ranges from 10:1 to 125:1 (steepness 0.1 to 0.008). In the case of very high waves, however, the ratio of length to height is never as great as this last, for the fact that they still continue rela- tively high shows that their proportions have not altered very greatly since the wind commenced to die down. Thus, the largest ratio of length to height for waves of 15 feet and higher (34 cases) that is in- cluded in the tabulation cited is 45.6: 1 (steepness 0.022). And while the smallest ratio there listed is 10:1 (steepness 0.1), it is certain that waves sometimes ave as steep as 7:1, when they become unstable. Since it is among old—but low—waves that the lengths are greatest relative to the heights, the ratio of length to height would average somewhat greater for low waves than for high, if waves of all stages of growths were combined. But an average of this sort is meaningless in the case of low waves, for the reason just stated, unless indeed the cases that represent waves still in the process of growth can be segre- gated in some way from those that represent old swells. The need for this precaution has been emphasized before, but no attempt to do this appears ever to have been made for any extensive series of data. And the most that we dare offer in this connection is that the ratio of length to height is usually less than 25: 1 (steepness 0.040) for waves that are still growing in height, or of such as have only recently attained their maximum heights, as appears from the following tabulation for 68 published cases falling in this category from different oceans (table 13). 30 WAVE DIMENSIONS If moderately high swells are included under the heading of “storm waves,” as they should be since rough seas are so often running on top of swells, the average ratio is not far from 26:1 (steepness 0.038). When seas have altered into swells as described on page 63, they are often as much as 40 to 100 times as long as high, and swells so old and low that they are recognizable only when they develop into surf along some coastline may even be 1,000 times as long as high. Storm seas and swells varying in steepness from 0.013 to 0.001 have in fact been observed on the south shore of Martha’s Vineyard, and probably could be on any other exposed beach to which old swells commonly run. TABLE 13.—Mazimum, minimum, and mean steepness of waves of different heights expressed as the ratios of their lengths to their heights (boldface) and of their heights to their lengths (italics) [Adapted from Gaillard] Steepness i SA a pe Number Wave height in feet of cases Maximum | Minimum | Average Gee he Dine le io da” ea eS ek aay Sa Ph 1 kel Be 24:1 13:1 17:1 23 0. 042 0.077 0. 059 NPE ea oe: Be eee ee eee Seca ens eee Me 24:1 10:1 18. 6:1 12 0.042 0.10 0. 954 71072) NOE PE LSS aes SEE EE ae Bee Oe AWE an, AGT 23:1 13:1 15. 5:1 5 0. 043 0.077 0. 065 3 Re sored 20 pees a INE Ses: Si ae 2 18:1 11:1 14:1 11 0. 056 0.091 0. 071 7 Ndi | ene ee aah he RRS SF oe ete eee 16:1 14:1 15:1 2 0. 062 0. 071 0. 067 A further illustration of this general rule is that the average ratios of length to height, among 179 published French observations, were 17:1 for waves shorter than 100 feet, hence still comparatively young; 21:1 for those of 100 to 200 feet, hence older; 25:1 for those of 200 to 300 feet; and 27:1 for those of 300 to 400 feet. Since, as the waves grow, length and height increase ,at different relative rates, the steepness of growing waves is a measure of their development, for younger waves are steeper than older ones. It has also been found that the age of a wave that is growing under the influence of the wind may be satisfactorily expressed as the ratio of wave velocity to wind velocity. The relationship between wave age and wave steepness for growing waves is shown in table 14. The relationship between the heights of waves and their lengths, whether arrived at from measurements at sea or from a theoretical analysis, fails in one very striking respect, for neither method of calculation would suggest that waves are ever less than about 10 times as long as high (steepness 0.1), whereas it is certain that at least the tops of their crests frequently rise to the angle of instability (steepness 0.14), else waves would not break as they so commonly do in windy weather. The discrepancy arises from the fact that the theoretical treatment concerns an average condition. VELOCITY AND PERIOD 31 TaBLE 14.—Correlation between the age and the steepness of growing waves [Derived from an average curve fitted toempirical data, in astudy by Sverdrup and Munk, Scripps Institu- tion of Oceanography} Steepness Steepness Age of wave, expressed as SLMEYE, Age of wave, expressed as cE vee: wind velocity/wave velocity height/wave wind velocity/wave velocity height/wave length H length (lat itie. 2222 ee 2 ee ees SOR 01 ah Oe ee ee ee a 0. 039 (oS Sa ee . 080 ee se Se SE oe ee . 033 Jie. 362.323 UGS Al | plea sae a a ee ee . 028 Seisy 2s Be ee . 054 1h Se See ee ae ee > oye . 025 JUL... 2d eee . 045 Doe See = Jere ee Ee oe . 023 A given wave may repeatedly break; anyone can satisfy himself on this point by looking out over the water when a brisk breeze is blowing, for it is often possible to watch an individual crest steepen until it breaks with a consequent decrease in its height and steepness, then builds up to the breaking point for a second time or sometimes even for a third time before it is lost to view among the neighboring waves. And we have no doubt that every individual wave of a stormy sea breaks in this same way time after time. Thus the history of the compound wave is one of constant alterations in its steepness, altera- tions of which the theoretical calculations of height and length give no hint and on which no information is available from observations. THE VELOCITIES AND PERIODS OF WAVES The fact that is perhaps the most difficult for the layman to accept, when first he observes waves at sea, is that it is not the direct push of the wind against their backs that causes the waves to advance, but that once a wave of oscillation has been set in motion, it will continue to run across the surface of the sea, even in a flat calm. This fact is easily demonstrated; if one drops a stone onto a calm water surface, it is easy to see that the resultant wavelets run out in all directions, far beyond the site of the original disturbance. Perhaps the most striking illustration of the rule that wave forms may continue to advance long after the disturbance immediately responsible for them has ceased, is afforded by the bow waves that a steamer sets up in her passage through the water. These may run so far, that, in thick weather, the first notice a watcher on the land may have that a ship is passing offshore comes when the waves she has set up break on the beach. Theoretically, the velocity of a freely running wave in deep water is determined chiefly by its length, the rule being that the longer the wave, the higher its velocity. And while the relative steepness of a wave does have some theoretical effect on its velocity, this effect is so small that it can be ignored for all practical purposes. Consequently, an old swell, long but now low, travels at least as fast as the much higher 32 WAVE DIMENSIONS seas from which it has been derived, or even faster if its length has increased during the period of time since it altered from sea into swell; and there are reasons for thinking that this may happen (p. 66). It is commonly stated that the velocity of a free wave (i. e., of one that is kept advancing by gravity alone) is proportional to the square root of its length,’ with the velocity in knots equal to about 1.3 times the square root of the length in feet. And observations on waves at sea agree closely enough with this to show that the formula is a close approximation for waves of ordinary shape. Actually the velocity depends somewhat on the steepness of a wave, as well, in that higher waves of a given length run a little faster than lower. But this effect is so small that it can be ignored for ordinary waves unless in shoal water (p. 104). (For the complete equation, taking account of steepness, see O’Brien and others, 1942, p. 21, equation 19.) The facts that the velocity of a wave in deep water is chiefly depend- ent upon its length, but hardly at all upon its height, and that swells reminiscent of previous storms run at the greatest velocities of all, because of their great lengths (p. 66), make it as misleading to corre- late the velocities of waves as a whole with the strength of the wind as it is to attempt similar correlations for their steepness (p. 29), unless their stage of development is known. Any such correlation must therefore take account of the length of time during which the waves in question have been subject to a wind of any given strength if they are to be of any significance whatever. This has been at- tempted in the following table, adapted and simplified from a recent theoretical analysis of the subject. TABLE 15.—Theoretical wave periods (italic), in seconds, and wave velocities (bold- face), in knots, in relation to the strength and duration of the wind! [Based on H. O. Pub. No. 604] Duration of wind in hours Wind velocity, nautical miles per hour 10 20 30 40 50 1 Whe a ge RR te I Mah I Baek hen tel sete PAE ty hte Pe 2 3.0 3.8 4.6 4.8 4.8 9.1 11.5 13,6 14,5 14,5 7 | 2 As ot Saal enna S BO cAI eh gst PB), vps te ay 5.8 6.7 7.4 8.0 13.3 17.6 20.3 22.4 24,2 11S oe Seer PERE inter ied ons. 5.6 Ts 8.5 9.5 10.4 17.0 22.1 25.8 28.8 31.5 Lian 2S woes Guha pra Bye ct lent arbeled Rang, 8 «ey oh 6.7 8.8 10.2 11.4 12.4 20.3 26.7 30.9 34.5 37.6 1 The theoretical relationships between velocity, period, and length, for waves of small steepness, is ex- pressed in the basic equations T= J coy) c=) = L,and L=£ T°, where Tis the period, C the velocity, L is i g the acceleration of gravity, and x the constant 3.14 (Kriimmel, 1911, and various subsequent authors). 7 According to a simplified equation C= J Z L, where Cis the velocity, g the acceleration of gravity, x the relation between the circumference of a circle and its diameter (approximately 3.14), and L the length; or, taking the average value of g as 32.172 feet per second, C (in knots) equals about 1.34 -~Z. Seealso Foot- note to Table 15. VELOCITY AND PERIOD 33 It is evident from table 15 that the relationship between the strength of the wind and the velocity of the waves is not a constant one through- out the development of the latter. Thus the statement sometimes made that the velocities of storm waves average about 0.8 as great as that of the wind would apply, theoretically, to a 20-mile wind only while the waves were about 15 hours old; to a 30-mile wind only when they were about 25 hours old; to a 40-mile wind only while they were about 35 hours old. The calculations summarized in table 15 also show the velocities of the waves produced by a uniform wind of any given strength as rising somewhat higher, eventually, than the velocity of the wind. But the few observers who have measured the velocities of storm waves at sea, in relation to the wind, have reported that the advance of the waves is usually somewhat lower than the velocity of the wind as long as the latter is still rising, or as long as it is still blowing at its peak strength. Thus Schott reported the velocity of the wind as varying between 1.17 times and 1.51 times (average 1.52 times) as great as that of the waves, on ten occasions when the waves were measured and the strength of the wind estimated every 2 hours by the Beaufort Scale. Similarly, Lieutenant Paris, of the French Navy, found the velocity of the wind to average about 1.4 to 1.7 times as great as that of the waves in stormy weather when a heavy sea was running.® Again, Capt. H. F. David, of the S. S. Corinthie, estimated the average length of the waves in August 1907 in the south- ern Indian Ocean between Kerguelen and St. Paul Island as about 675 feet, corresponding to an average velocity of 40 statute miles per hour, when the wind was logged as 9, Beaufort, or about 44 statute miles per hour (Cornish, 1910, p. 112). Cornish has reported wave periods corresponding to velocities of about 41 knots in the Bay of Biscay during a very strong gale, when the ship’s officers estimated the strength of the wind as somewhat greater than 9, Beaufort, or something like 52 knots (Cornish, 1934, p. 4). And waves advancing at 48 to 55 knots (as calculated from their estimated lengths and meas- ured periods) were observed from the U.S. S. Ramapo, in the central part of the North Pacific during a February gale when the average velocity of the wind was 60 knots as recorded by anemometer."’ Zimmerman, however, reports several cases of storm waves running faster than the wind.” The explanation for the greater frequency of waves running more slowly than the wind probably lies in the fact that most observations § Schott, Gerhard. 1893. Uber die Dimensionen der Meereswellen. Festschrift Ferdi- nind Freiherrn von Richtofen zum 60. Geburtstag. Berlin. p. 255. “Paris, A. 1871. Observations sur letat de la mer recueillies a bord du Dupleie et de la Minerre. Rev. marit. colon, vol. 31, p. 121. 10 Whitemarsh, R. P. 1934. Great sea waves. Proc nay. inst. vol. 60, p. 1100. 1 Zimmerman, BE, 1920. Aufsuchung von Mittelwerten fiir die Formen ausgewachsener Meereswellen auf Grund alter and neuer Beobachtungen. Schiffbau. vol. 21, pp. 666—668. 34 WAVE DIMENSIONS are made on smaller, hence younger, waves, and that gales so com- monly change direction before the velocities of the waves they produce have risen as high as that of the wind. And it has long been known that as soon as the wind does slacken, the waves outstrip it in their continued advance, so much so, that the waves of an old swell often run at velocities as high as 30 to 40 knots, and sometimes even as high as 60 knots (as indicated by their periods) even during a flat calm. The nearest approach to a working rule that we dare offer for the velocities of waves, as compared to that of the wind, is the following: Storm seas that have risen nearly, but not quite, to their maximum heights for the wind in question, are usually traveling at a velocity a little lower than that of the wind, if the latter is still blowing strongly ; waves may outstrip the wind slightly, even while the latter is near its peak strength, if it has been acting on them for a long period; and the waves invariably run faster than a dying wind. The waves, produced by a storm in the offing, often give warning of its approach before the wind has begun to blow up where the observer is stationed. The reason is that atmospheric disturbances often advance at rates much lower than the velocities of the winds within them, or than the rates at which the resulting waves advance, as is illustrated by the fact that only 60 out of a group of 264 gales were found to have traveled faster than about 31 knots from the Atlantic toward the coasts of Great Britain (Cornish, 1934, p. 28). The coastwise inhabitants of many parts of the world are, in fact, well acquainted with large waves as forerunners of storms—they were known at one time (perhaps locally) as “death waves” on the west coast of Ireland, and perhaps still are (Kriimmel, 1911, p. 92). This general phenomenon is of practical importance in those parts of the world, in particular, where tropical cyclones are to be expected during the “hurricane” or “typhoon” season, for when heavy swells develop there, for which the wind then blowing is not responsible, the chances are that they are coming from an atmospheric disturbance of this sort. This applies in the West Indian-Gulf of Mexico region and off the southeast coast of the United States from July through Octo- ber; in the southwestern tropical Pacific from December through March and into April; in the Philippine region and the China Sea from June through October; in the Arabian Sea from March through June and from September through December; in the Bay of Bengal from May through December; and in the southern Indian Ocean from November through May. These are the months when hurricanes or typhoons occur most often, not the extreme dates for them. We have seen it stated that the velocities of these forerunning swells, as calculated from their periods or from their lengths, give the velocities of the winds within the approaching hurricanes, on the VELOCITY AND PERIOD 35 principle that large waves run with velocities not very different from those of winds that produce them. But this is not a safe rule for reasons stated previously, and because the effective fetch within storms of this sort usually is not great enough for the waves produced there to grow to the maximum dimensions theoretically possible for the winds of such high velocities. For example, a wind of only 60 knots (and hurricane winds often blow from 80 to 100 knots) requires a fetch of something like 1,300 to 1,400 miles to produce waves long enough to be advancing at velocities of 50 knots. Since the period, length, and velocity of a wave are interrelated, the velocities of waves can be calculated from their periods, wherever it happens to be easier to record the period than the length, the working rule being that multiplication of the period in seconds by 3 gives the velocity in knots.2 A large number of calculations of this sort have been made in many parts of the world, both for storm waves measured on shipboard and for surf breaking on the shore. At first sight, the rule that waves moving at the highest velocities have the longest periods might seem contradictory to everyday experience. The reason it applies is that a wave travelling at high velocity is so much longer from crest to crest than is a wave of lower velocity that it occupies a longer period of time in passing any given point. Measurements of the periods of waves can likewise be converted into terms of length (since length is the feature of a wave that chiefly governs its velocity) according to the formula that length, in feet, is equal to the square of the period of the wave, in seconds, multiplied by the factor 5.12. The relationship between the lengths and velocities of waves and their periods is summarized in table 16, and in figure 5. TABLE 16.—Theorelical values of velocity (to nearest knot) and length (to nearest foot) for waves of different periods in deep water ee Velocity | Length ane e% E Velocity Length Period (seconds) | (knots) | ifcet) Period (seconds) | (knots) | (fect) ie | 6 POE is; a aes Tap Sete wl a 42 | 1, 004 La ee 12 BING cee Howe sah eee 48 | 1,311 Ne = Shia 5 Se ee See 18 | tere]; take Ae eas ee aS el 55 | 1, 659 fio 3 ese ee Se ee eee 24 328 || 20.5 ee ee 61 2, 048 iQ: 3-3-4528 ee eee 30 | 512 \| 728 Soe Ee eee ae es | 67 | 2,478 P42 ah 5 SSS Se eee 36 | SUM ea ee ee eS eee 73 2, 949 i The theoretical values given in table 16, and presented in graphical form in figure 5, agree quite closely with the relationship that has been observed at sea, in different parts of the ocean, as illustrated in table 17. The agreement between the theoretical and the observed values is in fact good enough to show that, for this relationship, the 2 Actually the equation is C=3.037 where C=the velocity of the wave in knots, and T its period, in seconds. This is a simplification of the formula given on page 382. 226794 O - 53 - 4 36 WAVE DIMENSIONS former is the more reliable of the two, for it is difficult to take exact measurements of waves at sea oe Pe et Gi i el ate - oar | 8 co boa 3 ! “| 1 Peay | ee VELOCITY (C), KNOTS 200 800 1000 1200 1400 1600 1800 LENGTH (L), FEET FieurE 5.—Graphical presentation of the theoretical relationship between wave lengths, velocities, and periods in deep water. TABLE 17.—The lengths of waves (as observed and as computed from the observed pertods) and the wave pertods (as observed and as computed from the observed lengths) in different parts of the oceans {Adapted from Kriimmel and from Sverdrup, Johnson, and Fleming] Length in feet Period in seconds Region Observed | Computed | Observed | Computed ACIANUICRFaQCS iso ee hh eae 213 200 5.8 6.0 ridianOcesibrades san ee eee eee 315 341 7.6 7.3 South Atlantic Westerlies_____ Tree Be Sn ee 436 535 9.5 8.6 Recht CCR OV CSLOBUGS so o-oo oe oe ae ee 374 341 7.6 8.0 @himsaihes=s oo oe FR ee eee ee 259 282 6.9 6.6 NVESLOINE ECGs = a eee eee ee eee ioe 335 397 8.2 7.5 Incidentally, 26 seconds (reported from the south coast of England) is the longest period yet recorded in print for any wave, though we are informed that waves with periods as long as 30 seconds have been observed at Long Beach, Calif. And velocities of about 79 knots and of about 91 knots that correspond, respectively, to the periods just quoted are the highest that have ever been reported for wind waves at sea. But even these are insignificant as compared with the speeds at which the waves travel from severe earthquakes, such as that of 1868, when the resultant waves in the Pacific had estimated velocities of 300 to 400 knots; or the wave from the Straits of Sunda, or Krakatoa quake of 1883, which must have advanced at a rate nearly Mir ai, © DIRECTION OF ADVANCE at or quite as high, for it is known to have crossed the entire breadth of the Pacific Ocean in 12 hours, while a secondary wave produced by it in the Atlantic Ocean, was recorded on the tide gage at Rochefort on the coast of France, 2 days later (Gaillard, 1904, p. 108, and Berget, 1923, p. 53). The earthquake waves that did severe damage in the Hawaiian Islands on April 1, 1946, offer a more recent illustration. In deep water (16,800 feet) these waves theoretically were advancing at about 430 knots, which agrees fairly well with the recorded interval of 4 hours and 34 minutes occupied by the first of them in travelling the distance of 1,946 nautical miles from their point of origin south of the Aleutian Isiands. The waves arrived at average intervals of 15 to 17 minutes, indicating that their lengths in deep water had been about 100 nautical miles. Waves of this sort are so long relative to their heights, i. e., their slopes are so gentle, that they cannot possibly be recognized by ships that meet them out at sea. At first thought, one might expect that the velocity with which a group of waves advances as a whole would be the same as the velocities of the individual waves that make up the group. And this is true of waves that are still being built up by the wind. In the cases, however, of old swells that continue to run on, as explained on page 34, either after the wind has died down or after they have advanced beyond the limits of the wind system that produced them, the leading waves tend to die out, chiefly because their energy is expended in setting un- disturbed water in motion, but partly because of the resistance of the air that the wave crests must displace in their advance. The next wave then takes the lead, and this process of replacement continues progressively. Each wave then takes up energy that was left behind by its predecessor, and, in turn, leaves some of its own’ energy to be taken up by the next wave. And new waves are formed, successively, in the rear of the preexisting group, so that the position occupied by the latter as a whole, as existing at any given moment, is not as far advanced as it would be if it still consisted of the same individual waves of which it was originally composed. Theoretically, the veloc- — ity of such a group of swells is only one-half as great as that of its component waves, individually, if the depth of water is greater than the lengths of the waves, as it actually is over the oceans as a whole. THE DIRECTIONS IN WHICH WIND WAVES ADVANCE Wind waves advance at right angles to the sidewise extension of their crests, or at right angles to the chords or tangents of the latter, if the crests are wide enough transversely to show a measurable cur- vature. When the wind is rising, the waves that it generates run with it, and they continue to advance in the same direction as the wind, so long as 38 WAVE DIMENSIONS the latter blows in the original direction. But an alteration in the di- rection of the wind does not cause waves that are already in motion to diverge at all from their original lines of advance, though it may widely alter their surface contours, as described below (p. 51). It is only when a wave encounters some obstacle, or comes into shoaling water at an angle with the coast line, that the line of advance of any part of its crest or trough is diverted, as described below (p. 155). The tracks along which wave forms progress also differ in another very important respect from those along which the winds blow, for they are not deflected measurably from their original courses by the effects of the rotation of the earth, whereas winds, unless at the Equator, are thus deflected, to the right in the Northern Hemisphere, to the left in the Southern, so widely that they actually blow at only a very small angle with the isobars (or lines of equal pressure) in the atmospheric disturbances that gave rise to them.* The reason for this difference is that the net advance of the water particles of which a wave is com- posed is so small as to be negligible in this connection, whereas the masses of air that compose the winds do advance bodily. The end result of the contrast, outlined above, between the directions of waves and of winds is that the former parallel the latter, wherever and whenever the isobars follow straight lines, or curves of very long radius as is characteristic of the winter gales of the West Wind Belts (fig.6). But the isobars often follow curves of shorter radius. Under such conditions, the directions of advance of the waves, that are gen- erated at successive points along the isobars, diverge from the latter, whereas the winds blow along the isobars so that they veer away more or less sharply from the lines of advance of the waves. The difference in this respect, that may exist in different parts of an atmospheric dis- turbance, is illustrated diagrammatically in figure 7, where the wave direction would parallel the wind direction within the area between the lines AB and A’B’, because the isobars there are nearly straight. And the waves generated there would be the largest, because it is there that the effective fetch would be the longest. But the winds in other sectors of the disturbance would veer away from the waves because of the curvature of the isobars, so that a very complex series of cross seas, of different generations and running in different directions, would result. It is not known precisely how much the wind must deviate from its original direction to give rise to a distinct new train of waves. As a rule, too, an atmospheric disturbance does not long remain stationary over the ocean, but advances in one direction or in another, 13 The direction of the wind averages about 10° to the left of the isobars in the Northern Hemisphere, 10° to the right of the isobars in the Southern Hemisphere. For a readable explanation of the deflective effects of earth rotation, see Pettersen, Sverre. 1941. Intro- duction to Meteorology. New York. p. 100. DIRECTION OF ADVANCE 39 Figure 6.—Simplified chart showing the isobaric distribution over the North Atlantic at 1300, Greenwich mean time, September 19, 1938. so that the relationship between wind direction and wave direction to be expected with the approach of a disturbance depends not only on the shapes of the isobars within the latter, but also on the position of the observer relative to its line of advance. The winds of tropical hurricanes afford a classic example of this. In one such example in the tropical North Atlantic (Tannehill, 1936, pp. 231-238), the direc- tion of the wind is known to have deviated by as much as 60° from that of the waves in the two front quadrants of the cyclonic disturb- ance, and by as much as 90° to 100° in the left rear quadrant whereas 40 WAVE DIMENSIONS the direction of the winds of the right rear quadrant nearly paralleled that of the waves that spread thence (fig. 8). Figure 7.—Diagram showing the relative directions of advance of the waves (broken arrows) and of the winds by which they are generated (solid arrows), according to the degree of curvature of the isobars around different parts of a barometric depression. Fieure 8.—Differences in directions between winds (solid arrows) and waves (broken arrows) in different parts of a tropical Atlantic hurricane. (After Tannehill. ) DIRECTION OF ADVANCE 41 The persistence of the waves in their original courses, contrasted with the fact that the wind may either blow in a uniform direction across the surface of the ocean for hundreds of miles, be veering in character, or shift abruptly, makes the relationship between the direc- tions of the one and of the other extremely complex. The case is still further confused by the fact that while the velocity of the wind usually does not differ greatly from that of the waves if the weather is stormy, the rate of advance of a wind system as a whole is usually considerably slower than for the winds within it, or for the waves produced by it, so that the waves generated by one system very commonly run to regions that are dominated by a different barometric distribution where the wind blows from some other direction. Thus the possible range between the directions of waves and of winds cannot be reduced to any one simple rule. ¥ , aie a % _ . eter oe. af tle te) A ain he Lr) jepady ys? a’ Di ery ‘i ee Chapter 3 THE CONTOURS OF WAVES; THE EFFECTS OF CURRENTS AND OF SHOAL WATER; THE MEASUREMENT OF WAVES The Profiles and Surface Contours of Waves The theoretical profile of a free surface wave of oscillation (1. e., of one that is no longer being driven by the wind but is running on its own momentum, p. 69) is very nearly the shape of a trochoid. That is to say, it follows the curve that would be outlined by the motion of a point within a disc, if the disc were rolled along the underside of a level surface (fig. 9). In a curve of this kind the crest is slightly FieukE 9.—Profile of a wave of trochoid form 20 times as long from crest to crest as it is high from crest to trough. steeper and narrower than the trough, i. e., the mean level of the water is a little lower than midway between crest and trough, a phenomenon which has some importance in relation to harbor con- struction but is not of practical interest in relation to ocean waves. Storm waves still being built up by the wind are usually between 14 times and 24 times as long (from crest to crest) as they are high, so that their average slopes from crest to trough would range from 1 in 7 (8°) to 1 in 12 (5°) if the profile of the wave from trough to crest were a straight line. But it is actually concave in the trough and convex on the crest, so that the slope is somewhat steeper near the top of the latter. In the case of comparatively long waves, this curvature is so gentle that its effect is very small. If, for example, a wave were 100 feet long and 5 feet high (a common ratio of length to height), its slope would average only about 7° to 8°, along a distance of 15 feet of the steepest part of the actual curve, contrasted with about 5° (or 1 in 10) along a direct line from the bottom of the trough to the top of the 43 44 WAVES crest. But the angle along 15 feet of the steepest part of the curve of a wave of this same height only 50 feet long would average about 20°, contrasted with about 12° on a direct line from bottom of trough to top of crest (fig. 10). 10 to 1 wave (BC = 1/5AC ) Angle BAC = about 12° Angle BAC = about 20° vow 2° SB _ ony 1 —— eine —4e aS Ficure 10.—Profile of a wave of trochoid form, 10 feet high and 100 feet long from crest to crest, to show the angle at which a boat, 30 feet long, would be pitched upward on the steepest part of the crest. Thus, a small boat would be pitched upward at about three times as steep an angle as it mounted the crest of the shorter wave than of the longer, whereas the slope would be only twice as steep in the one case as in the other if it depended solely on the linear dimensions of the wave. It is largely because of this relationship between length, curvature, and slope that relatively short waves—even if well-rounded —may cause small craft to pitch so sharply, and that a “chop” is so proverbially uncomfortable for small-boat navigation. A trochoid approaches a sine curve in shape if its height is small relative to its length. But the crests become narrower and the troughs relatively longer if the height is large, relative to the length (i. e., if the wave is steeper). If the ratio of length to height decreases to as little as about 7:1 (steepness about 0.014) so that the angle at the crest increases to about 120°, the wave becomes unstable (fig.11). And FicurE 11.—Theoretical profile of steepest possible wave, according to Stokes and Michell. (After Sverdrup, Johnson, and Fleming.) when the crests approach this angle of instability, they tend to be- come cycloid in form and therefore very much steeper toward the top, as anyone can see who watches the seas in stormy weather. Waves cannot continue to advance in this shape, but break at the crests, thus losing in height and consequently in steepness as described on page 19. Very few actual measurements have been made of the profiles of waves. But considerable material is available for such, from pub- lished stereophotograms. And these show that the crests of high, wm . PROFILES AND SURFACE CONTOURS 45 short storm waves are very much steeper than those of relatively longer ones. In one case that has been frequently reproduced (fig. 12), the difference in level between the highest and the lowest points was between 26 and 27 feet in a horizontal distance of only about 190 feet, or a ratio of length to height of only a very little more than 7:1. This crest was thus on the point of breaking, and waves of this shape are very commonly seen in stormy weather. 10 10 15 10 HEIGHT DIFFERENCES IN FEET yey ND WD a oO oO = ° fo) 100 200 300 400 500 HORIZONTAL DISTANCES IN FEET FIGuRE 12.—Profiles of waves of different degrees of steepness, based on stereo- photogrammetric pictures. The vertical scale is five times the horizontal scale. (Adapted from Schumacher.) Instability of this same sort can also develop in very small waves as well as in large, whenever the wave is growing rapidly in height, as is usually the case with a rising wind of any considerable strength. The “whitecaps” that develop when a brisk breeze blows up are familiar examples. The seas may continue to break even after they have ceased to increase in height, if the wind continues strong, because the pressure of a high wind is so much stronger on the back of the crest (its windward side) than on its front (lee side) that its crest is 46 WAVES forced forward and falls into the trough ahead. A very strong wind may even blow the water bodily ahead from the crests in sheets of foam or spray, so that waves may not reach their maximum heights until the wind has slackened somewhat (p. 19). In small bodies of water, indeed, severe squalls or winds of hurricane force may lift sheets of spray bodily from the surface in this way, even when the waves are very small, as we have seen ourselves. And the violent squalls that are a usual feature of full gales, when the average velocity of the wind may be 50 to 60 miles an hour, or even higher, often raise the breaking crests so high above the general wave level that if these masses of water chance to fall on deck, lifeboats are often stove in, stanchions carried away, etc. In short, the old rule still holds and always will, that it is the waves of a storm, not its winds, that the mariner has to fear; also that a high and heavily breaking sea is a dangerous one, whenever and wherever it is encountered. Lest anyone should think that danger of serious damage by waves to well-found steamers is a thing of the past, we cite the cases of the U.S. heavy cruiser Pittsburgh, 100 feet of the bow of which was torn away bodily by an enormous sea during a typhoon in the western Pacific, June 5, 1945, and of three United States destroyers that were lost during a similar cyclonic storm between the Philippines and the Marianas on the eighteenth of the previous December. The foregoing discussion of the dimensions and profiles of waves has been oversimplified intentionally, by the tacit assumption that waves are more or less regular in shape and that they are distinct, one from the next; also, that their crests extend sidewise for indefinite distances. But this is never the case in reality, for the topography of the surface of the sea is always extremely complex and irregular. Whenever the wind is high, waves of all sizes, from the very smallest up to the highest that have yet developed are intermingled, with neighboring waves differing in shape from comparatively low and long to so short and sharp that they are breaking, or about to do so. Secondary ridges, peaks, and valleys are also to be seen, running on top of what may be called the primary series (figs. 13 and 14), which, in turn, may or may not run in the direction of the wind. Also, it is only when the “seas” have been transformed into “swells” as described below (p. 63) that the individual crests extend far widewise. In stormy weather, on the contrary, their lateral breadth may not be more than three to five times as far as it is from one crest to the next, and sometimes no farther than it is from crest to crest, with their ends merging into the valleys in a wholly irregular pattern. The result is that any profile, transverse to the general trend of the waves, is always a very irregular one, so long as the wind is blowing strongly. 47 PROFILES AND SURFACE CONTOURS San0}W09 a -aq] PaVnyy) JSBOH B IBY] BBIB] OS [JAMS ABP[O UR AB ? 3 M Jo Aj xe]duI0d ay} a} BAIYSNITIT 03 ‘ (ydt s]se 103) 1s0j0yd paeny Is g iI JO uo puryeq Jo do} uo Sutuuna— Hye) MOT oO ‘SO [BDWO) “rey vaM ApurA ut pajoedxa A Uo TF Po Ba0U0D ATASAB] SI JAOISG JaLOAjs SUIY BAI U9] JO 9UIOS—SBARA\ JaT[VUIG— “ET ce vata) AC f WAVES 48 (Cydrasojoyd £aen ‘Ss ‘9 ‘S.1NOJUOD DAB BIBISNI[T 0} ONULTPV GJAON oy} ul vas AAvoY {Jo} RAIBpONT Y— FT aM oT PROFILES AND SURFACE CONTOURS 49 A striking example of such irregularities is to be seen in figure 15, in which the successive contours reveal the presence of several much smaller wave forms running upon the front of a single larger wave that was 18 to 19 feet high from trough to crest. Neither does any one wave reproduce another, as is evident from comparison of the wave represented in figure 15 with the 27-foot wave, the contours of which are laid down in figure 16. And while the topography of the Figure 15.—Surface configuration of the front of a wave about 19 feet high, during a rough sea, based on stereophotogrammetric pictures taken off Cape Horn on the morning of January 23, 1926. Contour lines are in feet. (Adapted from Schumacher. ) 50 WAVES sea surface is strongest and most complex with high winds and a rough sea, anyone looking out over the water can soon convince him- self that the wave pattern is not only irregular, but always constantly changing, even when sea and wind are moderate. It is only in cases of old developed swells and in moderately calm weather that wave crests are well-rounded and that they tend to extend far side- wise across the surface of the sea. And even then, other waves of Figure 16.—Surface configuration of the back of a storm wave 27 feet high, based on stereophotogrammetric pictures taken on the afternoon of the same day, and at about the same locality, as those on which figure 15 is based. Contour lines are in feet. (Adapted from Schumacher.) CURRENT EFFECTS od various sizes, smaller or larger, will be running across the older swells in one direction or another if the wind is strong enough at the time to produce a wave pattern (fig. 13). In any case, when twe separate trains of waves are present, travelling in different directions, the result of the interference will be a series of peaks rather than ridges, (See Sverdrup, Johnson, and Fleming, 1942, p. 531, fig. 133.) The most obvious cause for these irregularities is that whenever the wind changes in direction, or when a new wind springs up from a new direction after a calm, a cross sea develops on top of whatever ylder waves may already be in existence. But irregularities also de- velop from the immediate effects of a freshening wind, because the latter is never steady, but comes in gusts that vary so widely in strength (also in direction) that every fresh gust sets up a new set of short- crested wavelets on the backs of the older waves. This is true, even in the Trade Wind Belts where the wind is more nearly constant in strength and in direction than it is anywhere else. And it is largely because the new wave systems set up by a dying wind are progressively smaller and smaller that old swells are so much more even in contour than storm waves are (p. 45). During storms, the contour is still further complicated by the fact that peaks occasionally shoot up to great heights when two waves come together from different directions, as illustrated on a small scale in figure 17. Reports have it, in fact, that the most tumultuous and dangerous seas of all are those that develop in the area of calm air at the “eye” of a tropical hurricane as a result of the interference between the wave trains that meet there. Nautical periodicals contain repeated accounts of the damage done even to well-found ships, steam as well as sail, by the masses of water that may fall on board when such seas break; of decks swept clean of boats and houses, of bulwarks carried away, and of hatches stove in by the mere weight of water. Many a ship has been lost with all hands under such circumstances. If a strong head wind blows up suddenly, or if the wind suddenly shifts while still blowing strongly, the waves—even very small ones— often break backwards, so that their crests are driven over into the troughs behind. Similarly, a short steep sea, and often a very tumul- tuous and irregularly breaking one, tends to develop if waves are run- ning against a strong tide or current, since the effect of the latter in such cases is to increase the heights of the oncoming waves, but at the same time to decrease their lengths and thus to render them steeper, as is described more fully on page 53. THE EFFECTS OF CURRENTS ON THE DIMENSIONS OF WAVES The preceding pages have taken no account of the possibility that the surface stratum of the sea may be moving in one direction or 226794 O - 53 - 5 WAVES 52 Cydeasojoyd XAUN *y 1) [RDYO) “AOL ITV ISI] V Jo osussed ay} Aq WOTOU UT JOS SOABA PUL SSOUYSUOT 9] Le POUT JO LOS VB UsdAJaq dUaleJte}UL ay} AQ Padojerep syveag— IT auaowy CURRENT EFFECTS ne another, independent of the motion of the wave forms across it. Actually, however, this is the normal state of the sea, except for very brief periods of time and over very small areas, water being the most mobile of common substances next to air. Therefore, the effects that currents may have on wave motion deserve consideration. The prob- lem, reduced to its simplest terms, is one of the effects on waves of currents that are either contrary or are following, because it is the contrary or the following component of motion that comes into con- sideration in the cases of currents that are flowing at an angle with the run of the waves. Briefly, the effect of a contrary current is to decrease the lengths and hence to increase the heights of waves, since the amount of energy is unchanged, thus rendering them steeper. But it does not alter their periods, because it decreases their velocities in the same proportion that it decreases their lengths. The effects of following currents are the reverse, i. e., they increase the lengths of waves and decrease their heights so that the waves are rendered less steep, though again with- out altering their periods. The degree to which a wave is altered by a current depends on the ratio between the velocity of the wave while in still water and the velocity of the current it encounters, the latter being regarded as positive if it is in the same direction as the wave, negative if it runs against the wave (table 18). TABLE 18.—Ratios between the heights, lengths, and steepness of waves in still water and in currents of different relative velocities [Based on a theoretical study made at the Scripps Institution of Oceanography] Ratio between current velocity and wave velocity in still water BAO be ween Wate aS SS SSS eet Contrary currents Following currents water — ec = —0,25 | —0.20 | —0.15 | —0.10 | —0.05 | +0.05 | +0.10 | +0.15 | +0. 20 +0. 25 a 2 peels ae q = | eee EUV Ni i= Se hepeiees 2.00 ey 1.39 Tet 108 0. 93 0. 87 0. 82 0.79 0. 76 Wenethie-Ast 9822. 2 43 Noe . 67 | .79 | . 90 1.08 1.19 1.26 | 1.36 1. 43 Steepness. = 1-2... 5.49 3.40 2.07 | 1. 53 | ibe . 86 73 65 . 58 . 53 The general rule is, the stronger the current, the greater its effects upon the waves that may be advancing either with it or against it. According to table 18, if a wave that has a period of 4.2 seconds, hence is 100 feet long in deep water and is travelling at the rate of 13.4 knots, encounters a current flowing in the opposite direction at 2 knots (ratio of current velocity to wave velocity of —0.15), the height of the wave should theoretically be increased by a factor of 1.89 by the time a steady state was reached, but its length would be decreased to 67 feet. The alterations would be smaller in both these respects. if the current were flowing more slowly, larger if it were flowing more rapidly. If the wave in question ran inte a following current of the 54 WAVES same velocity, its height would be 0.82 as great as previously and its length 1.28 as great. Thus a contrary current affects the heights of waves much more in proportion than a following current does, a matter of importance in connection with tide rips. For example, the steepness of the 100-foot wave would very shortly be increased by about 2.07 if it ran into a contrary current of 2 knots, and by 1.35 if it ran into a contrary current of only 1 knot. The result is that when moderately steep waves run into contrary currents, the increase in their heights, combined with the decrease in their lengths, may ren- der them so much steeper still as to cause a violently breaking sea. Thus, a head current of 2.2 knots would soon cause a wave that was 5 feet high and 100 feet long, to start with, to steepen to the breaking point. The effects of currents on the heights of waves are the greater, the shorter the waves and the lower the wave velocities, because the dif- ference between the speed of the current and the original velocities of the waves is less then. If, for example, the wave just men- tioned, as encountering a head current of 2 knots, were only 50 feet long, the ratio of velocity of current to that of the wave would be, about 0.21, in which case the effect of the current would be to increase the height of the wave by about 1.9 or nearly to double it, if the wave did not break. And for the same reason, the decrease in height in a following current is greater for a short wave of low velocity than for a long one. The surface currents that are of concern to the seaman, as they affect the shapes of waves, may be classified as “wind drifts,” as “ocean currents,” and as “tidal currents.” It is not necessary for our present purposes to discuss the basic causes for larger ocean currents. The frictional drag of a wind blowing in a constant direction for more than a brief period soon sets a wind drift in motion, the velocity of which varies according to the strength and duration of the wind, entirely apart from any velocity of mass transport by the waves (p. 6). And drifts of this sort are often so strong that they must be taken seriously into account in navigation, especially in coastwise waters where a slight error in one’s dead reckoning may have serious results. In most cases, however, the velocities of wind drifts average only about 1.5 to 2 percent as great as that of the wind,'* which is not enough for them to have any great effect on the shapes of the waves that may be running either with them, or even against them. The drift, for example, set up by a 20-mile wind would average only about 0.3 to 0.4 knot, which is only about 0.03 of the velocity of the waves that winds of that same strength should, theoretically, generate after blow- ing for a period of 10 hours. Even if the current were directly con- 14 Based on a very large number of observations by the U. S. Coast and Geodetic Survey. CURRENT EFFECTS 55 trary in such a case, the heights of the waves would be increased by only about 1.06 times. And even in the rare cases when wind drifts do flow at velocities so great that they would steepen the waves meas- urably if they were contrary, it almost always happens that the waves are running with the drift, because both the waves and the drift are generated by the same wind system. The wind drifts with velocities as high as 1.4 to 1.9 knots with 25 to 55-mile winds, that have been reported at Diamond Shoal Lightship, about 15 miles out from the land southeast of Cape Hatteras, are cases in point.’® Tidal currents, like wind drifts, are seldom strong enough out over the ocean basins to cause any noticeable alterations in the shapes of the waves; but they do often run so strongly in continental waters that their effects are notorious for steepening any waves that may be running against them there, and this is true even well out from the land in many localities. Thus the tides run at velocities up to 1 to 1.6 knots on the shoaler parts of Georges Bank, which forms the off- shore rim of the Gulf of Maine, while tidal velocities as high as 1.3 knots have also been recorded at Nantucket Lightship, which is sta- tioned at the 30-fathom contour, 41 miles out from the land. And the tides run even more strongly still around many a jutting headland, as it also does in its passage up funnel-shaped bays or through narrow channels and sounds. Tidal velocities at strength up to 1.8 knots round the tip of Cape Cod, up to 2.5 to 3 knots in the Grand Manan Channel at the entrance of the Bay of Fundy, up to 3 to 4 knots in the Golden Gate (entrance to San Francisco Bay), up to 8 to 10 knots in Seymour Narrows, British Columbia, and as high as 9 to 11 knots in the narrow waters between Scotland and the Orkney Islands are well known illustrations.” In cases as extreme as these, a very moderate sea, indeed, may be transformed very abruptly into one that is very dangerous to small craft, upon the advance of the waves into the tideway, if the latter is running against them. And many points, shoals, and bars in various parts of the world owe their local names to this fact; “Pollock Rip” at the entrance to Nantucket Sound, the “Rips” on Nantucket Shoals, “Race Point” at the tip of Cape Cod are familiar examples on the east coast of the United States. Steep, tumultuous waves also characterize the more swiftly flowing parts of the major ocean currents, whenever the waves there are run- 1% Yor tabulations of wind currents with different winds, at Diamond Shoal Lightship and at other lightships along the Atlantic coast of the United States, see Haight, F. J. 1942. Coastal currents along the Atlantic coast of the United States. Spec. pub. U. S. Coast and geodetic survey, No. 230, pp. 55—70, tables 12-15. 16These velocities are cited from: Stevenson, 1874, p. 65; Kriimmel, 1911, p. 104; Marmer, H. A., 1926, The Tide, New York, p. 99; Bigelow, H. B., 1927, Physical oceano- graphy of the Gulf of Maine, Bull. U. S. Bur. Fish., vol. 40, pt. 2, p. 856 ; and from various publications of the U. S. Coast and Geodetic Survey. 56 WAVES ning against the current. The proverbially choppy and irregular vaves of the Gulf Stream—especially when a northeast wind is blow- ing against the current—have this source; so, too, the high seas that develop along the easterly edge of the Grand Banks of Newfoundland when southerly winds combat the Labrador Current coming from the north; also off Cape Agulhas, South Africa, with westerly winds, dur- ing the season of the year when the Agulhas Current is flowing west- ward. And many other like cases might be cited in other parts of the ocean where current and wind are opposed. Another phenomenon of practical importance is that when waves, running against a tide rip or other contrary current, pass out of the latter, they lose height and become smoother with astonishing abrupt- ness, for they then shrink almost instantaneously to the heights at which the winds blowing at the time would have maintained them in still water, while their lengths increase at the same time. Likewise, storm waves may be entirely knocked down if they strike a strongly running tidal current at right angles, perhaps because of the eddies that are set up along the zone of conflict between the current and the less rapidly moving water outside its influence. The narrow waters between the Shetland Islands and around them afford classic examples of this. But, for some reason, it appears that ocean currents do not have a quieting effect of this sort on wave trains that run transverse to them, for swells originating from storms in the Gulf Stream region of the northwestern Atlantic are sometimes known to run as far as St. Helena in the South Atlantic, which involves the crossing of the North Equatorial Current, of the Equatorial Counter- current, and of the South Equatorial Current. ALTERATIONS IN THE DIMENSIONS OF WAVES OVER A SHOALING BOTTOM Waves that are generated out at sea are not interfered with by the proximity of the bottom, for this happens, in measurable degree, only where the depth of water is less than one-half as great as the lengths of the waves (or than the lengths to which these would have grown, if unhampered) ; and storm seas are seldom more than 600 to 800 feet long, whereas the break in slope at the margin of the Con- tinental Shelf lies at a depth of about 600 feet in most parts of the world. But when waves run in from the open sea toward the coast, their lengths are altered as they advance over the shoaling bottom, and often to such a degree as to be of considerable importance from the seaman’s standpoint. This phenomenon bears so directly on the development of surf that it is discussed in more detail in relation to the latter (p. 102). It is enough here to point out that waves decreases progressively in length, as the water shoals, according to the relation- on ALTERATIONS DUE TO SHOALING 57 ship explained on page 103, and illustrated in figure 21. At the same time, they first decrease slightly in height, then may increase. But they lose less than one-tenth in height at most by this initial decrease, a loss that is far outbalanced by the decrease that takes place simul- taneously in their lengths, even if their heights do not increase subse- quently, as may or may not happen, for the lengths have decreased by about one-third by the time the wave has reached the point where the depth of water is one-tenth as great as the initial length of the wave, and by nearly one-half when it reaches the point where the depth is only one-twentieth that great. And the steepness of the wave increases accordingly. The lengths of the waves offshore and the angle of slope of the bottom together determine the precise distance from shore at which these stages will be reached, in the alteration of any wave, the rule being, that the longer the wave is in deep water, the farther out from the land will it begin to steepen noticeably. Waves, for example, 120 feet long, would not be noticeably steeper until they reached, say, the 2-fathom line, although their lengths would begin to decrease measurably from the time they advanced beyond, say, the 4-fathom line, however far out thai might be from the land. But a 240-foot wave would have steepened noticeably when it reached the 8-fathom line, a 500-foot wave when it reached the 15-fathom line; and waves much longer than 240 feet are common. Waves averaging about 9 seconds in period, and hence about 415 feet in length offshore, that have been recorded at South Beach, Martha’s Vineyard (p. 106), should thus have begun to feel the bottom and hence to steepen when they reached the 30 to 35-fathom (180 to 210-foot) line, which lies about 40 miles out off this part of the coast. By the time they reached the 7-fathom line, they should, theoretically, have been only about three-fourths as long as they were while out in deep water, and one-half as long, but correspondingly steeper, by the time they reached the 3-fathom line. A more striking case is illus- trated by a group of very heavy breakers observed on the south coast of England in winter, the lengths of which (as calculated from their periods) averaged about 1,185 feet while they were out in deep water, so that they had begun no doubt to shorten at about the 100-fathom line, on the upper part of the continental slope off the mouth of the English Channel, at least 275 miles out to seaward from the place where they were recorded on the coast (Cornish, 1910, p. 88). And additional illustrations of the same sort, if less extreme, might be cited for other parts of the world. The southern part of the North Sea affords an interesting example of the steepening effect of a shoaling bottom on the waves in the downwind parts of partially enclosed waters of broad extent. Strong 58 WAVES gales from the southwest and west are common here during the winter, and the effective fetch of something like 300 miles from the English to the Danish coast (depending on the precise locality) is theoretically sufficient for a 30-mile wind to generate waves 330 to 340 feet long, or waves 115 to 125 feet long with a 20-mile wind. But the water is less than 131 feet (40 meters) deep for a distance of 60 to 70 miles out from Denmark, and less than 65 feet deep for miles, so that the waves would begin to “feel the bottom” when they still were 60 to 70 miles out from the Danish side during a 30-mile gale blowing across from the English shore. And by the time they reached the 5-fathom line, the ratios between their lengths and their heights would be only about 0.7 as great as it had been before their deformation commenced. Tt is no wonder, then, that the waves of the eastern side of the North Sea are proverbially steep and dangerous for small craft in westerly gales, as are those in the western part of the English Channel also whenever storm seas are heaving into it from the open Atlantic. But is is only while the wind is blowing strongly onshore, or fol- lowing an onshore gale, that areas of shoaling bottom (even if exten- sive) are plagued in this way by the development of steep seas of troublesome size. The submarine shelf that fronts the southwest coast of Florida is worth citing in this connection, for while the 30 to 35-fathom contour lies 70 to 120 miles out from the land there, and even the 10-fathom contour is 25 to 40 miles out, the wind is most com- monly offshore, at all seasons of the year, or blows along the shore. When it does blow onshore, it is shown on the monthly Pilot Charts as seldom stronger than about 15 nautical miles per hour (No. 3 Beaufort). Consequently, smooth seas prevail there the year round, except on rare occasions, as when a winter norther develops. THE SIZES OF WAVES THAT ARE DEVELOPED IN SHALLOW WATER The shapes and heights of the waves that are produced where strong winds blow across extensive stretches of shoal water are a matter of concern to the operators of small craft, both in enclosed sounds and estuaries, as well as along open coasts fronted by a gently sloping bottom during periods when strong winds blow parallel to the general trend of the shoreline. In situations of this sort, the depth of the water may directly limit the heights of waves if it is less than say 10 to 12 feet, for waves begin breaking when they grow to the point where their heights are approximately equal to the depth below undisturbed sea level.7 But while the development of breakers usually results in the total extinction of the wave forms upon the shore, waves that grow 17 Waves generated in shallow water in tank experiments broke where the depth was equal to 0.8 times the wave height. SIZE IN SHALLOW WATER 59 in shoal water until they are about as high as the water is deep often continue to travel onward thereafter over a comparatively level bottom for considerable distances. In this case, the intermittent spilling along the tops of their crests prevents any further increase in their heights either until their prog- ress brings them into deepening water or until more active breaking de- creases their heights to accord with the smaller depth, if their advance carries them across some still shoaler bar. Shoal water also seems to limit the sizes of waves in some other way, for often they are not as high there as the water is deep, even in situations where the wind strength and the fetch are enough for this. The distance, for example, in Pamlico Sound, N. C., is long enough from shore to shore (40 to 45 miles) for the waves produced by the strong southwesterly winds of summer to rise to 9 or 10 feet towards the end of their run, where the water is 2 to 3 feet deeper than that over a considerable area. But the local boatmen have informed us that the waves seldom, if ever, are higher there than perhaps 6 to 7 feet, no matter how strong the wind. And Pamlico Sound appears to be typical of similar situations else- where in this respect. The explanation for this failure of the waves to rise higher in shallow sounds lies, we believe, in the effect that shoal water has on the lengths of the waves. Unfortunately, it is not yet known whether the relationship between wave length and depth of water follows the same curve for waves that are developed over shoal bottoms as it does for those that advance from deep water into shoal. But it is at least of the same order; i. e., waves in such situations grow more slowly in length than they would in deep water, hence they are steeper, so that they may commence to break sooner than they would otherwise. Esti- mations of the waves to be expected in enclosed sounds under any par- ticular combination of wind, fetch, and depth, must await theoretical analysis of the subject, but the following rules appear to apply: (a) the waves in such situations will never be much higher than the water is deep and very likely will be considerably lower; (6) they will be steep and will break along their-crests throughout the greater part of their runs, if the wind is strong. The preceding discussion of the waves in shallow sounds applies equally to the inshore ends of the wave trains that are generated by strong winds blowing parallel to open coasts in regions where the slope of the bottom is more than usually gentle. The strong “Northers” that sometimes strike the southwest coast of Florida illustrate this, for while the fetch is long enough, theoretically, for a 30-mile wind to produce waves 18 feet high by the time they have advanced the length of the Peninsula from the offing of Apalachicola to the offing of Key West, they cannot be more than 12 feet high, anywhere along the 2- 60 WAVES fathom contour. And the growth of their inshore ends is still further hindered by the effects of refraction, as explained on page 155. The end result is that, while waves generated by winds blowing parallel with the coast are only a little lower near the land than they are farther out during the first stages in their development, the difference in height between the inshore and offshore sectors becomes progres- sively greater as they continue to advance, depending on the strength and direction of the wind, on the length of the fetch, and on the angle of slope of the bottom. METHODS OF MEASURING WAVES The lengths and periods of waves can be estimated from shipboard with little difficulty and with a fair degree of accuracy, if the waves are upwards of 20 feet or so long. A great number of measurements of this sort have been taken in various parts of the world. The simplest way to measure the lengths of waves is with an old- fashioned chip log. If this is payed out over the taffrail until the chip is at the crest of one wave when the stern of the ship is on the crest of the next, the length of line outboard is equal to the length of the wave, provided the ship is running at right angles with the crests. If she is not, the angle of her course can easily be allowed for by the traverse tables that are included in every navigational handbook. Another method is to record the frequency with which the waves overtake the ship, and the time required for each crest to run her whole length from bow to stern. If, for example, it takes a wave 10 seconds to run from the stern to the bow of a vessel 300 feet long, running in the direction of the waves, and if the waves overtake the ship every 18 seconds, it means that the ship is only ten-eighteenths as long as the waves, i. e., that the length of the wave equals 300x18 or 540 feet." But an allow- 10 ance must be made, in this case also, if the ship is running at an angle with the waves. Measurements, from shipboard, of the velocities of waves demand a knowledge of the speed of the ship through the water. If she is lying motionless at anchor, and the time is recorded for the crest of a wave to run along her side for a known distance, the velocity of the wave is equal to the distance divided by the time. If, for example, observers 100 feet apart were to note that it required 5 seconds for a wave crest to advance from opposite the one to opposite the other, its velocity would be 100/5 or 20 feet per second, corresponding to 11.8 knots. If the ship is running with the waves, the velocity of the latter is equal to the distance divided by the time, plus the speed of the ship. If she is running against the waves, the velocity of the latter is equal to the 18 Adapted from Marmer, H. A., 1930, The Sea, New York, p. 182. MEASURING 61 distance divided by the time, minus the speed of the ship. To obtain the wave velocity in feet per second, it is necessary to state the speed of the ship in the same units, a value obtained by multiplying her speed in knots by the factor 1.69. It is also necessary, when attempt- ing to make allowance for the speed of the ship to remember that this _may be greatest, temporarily, if she is sliding down the front of a wave crest that is advancing in the same direction, and least if she is meeting a crest advancing from a direction opposite to her own. Proper allowance must also be made for the ship’s course if this is at an angle with the line of advance of the waves. A single observer can calculate the velocities of waves if these are running with the ship, by paying a chip log out astern for a known distance and then recording the time interval between the instants when the chip is at the top of a crest, and when the latter reaches the ship, again with proper allowance for the speed of the ship through the water, and for her course relative to that of the waves.” The velocities of waves can also be calculated from their lengths, as measured above, or from their periods. If the ship is at anchor, the time occupied in the passage of two suc- cessive crests past any fixed point on board gives the period of the wave direct. If she is under way, the simplest method of measuring the periods of the waves is to record on a stop watch the interval, in seconds, between the time when a patch of foam or other flotsam is at the top of one crest, and the time when it is at the top of the next crest—always with due regard to the likelihood that the wind may be blowing the foam ahead over the surface of the water (first proposed by Cornish, 1934, p. 38). It is not easy to make accurate measurements of the heights of waves at sea, and rough estimates are notoriously unreliable in this respect. In most cases, the only practical method is to find some place on board from which the crests of the waves appear to be level with the horizon when the ship is in the trough of a wave and on an even keel, i. e., when she is neither pitching nor rolling at the moment. The heights of the waves are then equal to the height of the observer’s eye above the water line." But the heights measured in this way are only approxi- mate at best, because it is difficult to pick a moment when the ship is actually on an even keel, and neither rising nor falling fast, and also because successive waves vary so greatly in height that it is often » This method was described by the famous physicist and astronomer, D. F. J. Arago, 1857, Oeuvres complétes, Paris, vol. 9, p. 550. “This simple method seems first to have been described by Arago, in the Instructions for Scientific Observations, prepared by the French Academy of Sciences for the Command- ing Officer of the Corvette La Bonite for her voyage of exploration in 1836 and 1837 (Arago, D, F. J., 1835, Hauteur vagues, C. R. Acad. sci., Paris, vol. 1, pp. 403-404). 62 WAVES difficult to find an appropriate point from which to make the observa- tions. The heights of waves have also been estimated by the alteration that takes place in the readings of an aneroid barometer as the ship rises from trough to crest and then sinks again from crest to trough. But this method is liable to errors, the magnitude of which it is difficult to . estimate; hence, it is not of much practical value under ordinary cir- cumstances. Waves and breakers may be most easily measured from piers with an ordinary sounding line. The lead is allowed to rest on the bottom and the line held taut, when the extent of the rise and fall of the water can then be measured on it. Or the difference in the elevation of the crests and troughs, relative to a fixed point such as the railing of the pier, may be measured by raising and lowering the lead with the sur- face of the water, as the latter rises and falls. Another simple method is to attach a scale of feet and inches to one of the piles of a pier, or to a pound net stake, and to read the rise and fall of the surface of the water from this, with the passage of successive crests and troughs, using a field glass or telescope if it is necessary to take the readings from a distance on the beach. Waves can also be measured from the shore by means of an anchored float which bears a vertical mast with cross arms at intervals of, say one foot, the float being observed with a transit, as the rise and fall of the water surface causes the arms to pass the cross hair in the instrument. And sighting devices of various other kinds have been devised for the purpose. Recording meters have also been used in which a small float, rising and falling with the waves along a vertical rod, operates a pen writing on arotating drum or on a moving tape, but these, and recording meters working on other principles, have not as yet come into general use, although they may be expected to prove useful. Chapter 4 SEAS AND SWELLS The characteristics of storm waves that most impress the observer are their irregularity and steepness, also their great heights in many cases, and the frequency with which their crests break, all of which may be summed up in the term “fierceness” (figs. 18 and 19). As long as waves are still in this stage of development, the combined pheno- menon is known as a “sea”; one speaks of a “high sea,” of a “low sea,” of a “rough sea,” of a “smooth sea,” as the case may be. But the shapes of the waves undergo wide alterations when the wind dies down, or when the waves produced by a given wind system advance to regions outside the latter, as very commonly happens. The wave train in question is then known as a “swell,” and the individual waves as in- dividual “swells.” The outstanding characteristics of a swell, as contrasted with a sea, are its low, rounded crests, the comparative smoothness of its surface contours, its great length from crest to crest, and the broad sidewise expanse of its individual crests; its gentleness, in a word, contrasted with the fierceness of the waves that composed the storm sea from which it has developed. There is nothing astonishing to the observer in the fact that rough seas are the usual accompaniment of stormy weather, for the power of the wind forces itself on the attention of anyone who has to walk against it. But the succession of low ridges, separated one from the next by distances that may be as long as 800 to 1,000 feet, or even longer, that disturb the glassy surfaces of the.open sea on a calm day is a phenomenon that must almost be seen to be believed, because the observer neither sees nor feels any immediate cause for their existence. ALTERATION OF SEAS INTO SWELLS The reason that a sea alters into a swell when the wind dies is that the waves then begin to loose energy, the shorter ones with the least energy becoming lower and disappearing first, so that the longer ones alone are left. At the same time, the sharp peaks so frequent during a rough sea subside; the irregularities of the surface tend to smooth out; any cross seas that may have been running upon the pri- mary wave pattern either die down also, or are absorbed by the latter; and the remaining crests decrease progressively in height and become more rounded. The end result is that the waves tend to approach the 63 AS AND SWELLS ~ u SE 64 ysvoD “§ “1 PWO) (ydeasojyoyd parney ‘Ig}ND parny ysROD ‘Ss ‘“ 1 WO, PeMOIA SV ‘OS SuLyVotq Puvw YSty ATO] BApoUt ¥— St AMAT] 65 SEAS CHANGING TO SWELLS (ydeasojoyd pavny ISBOD "SD [RIOWO) “Ysno1] Sulpaadons vy} OUT Surpuadseap st MOq Jay SB ‘19}]ND Pareny JsSBOH ‘S “O B Wody POMOIA ‘OAV UII0}S SULYvaIq puL YSty AIBA BV JO JSa10 ay} JO yovgd MO L—6L anor 66 SEAS AND SWELLS trochoid profile characteristic of the so-called free wave ” of theory. Meantime, the individual wave crests, that are seldom more than a few times as broad transversely as the wave is long during windy weather, tend to expand farther and farther sidewise, while the nar- rowest of them seem also to be obliterated in some way, until finally a crest that was only 500 feet or so wide, while the gale was still blow- ing, may expand toa breadth of 1,500 to 2,000 feet or even more. We have ourselves observed swells that were well over one-half mile wide just before they broke upon the shore. But the variations in the lengths of successive members of a given train of swells persists as the swell proceeds. Among 139 nearly consecutive breakers, for ex- ample, the periods of which were timed on the south coast of England after a heavy gale, the shortest, with a period of 10 seconds, was only 0.385 as long as the longest, with a period of 26 seconds (Cornish, 1910, p. 89). : Theories have been developed according to which the lengths of waves from crest to crest, and hence their velocities and also their periods, should increase after a sea has been transformed into a swell, contradictory though this might seem at first sight, when we remember that it is from the wind that the waves have derived their whole energy in the first place (Sverdrup, Johnson, and Fleming, 1942, p. 5384). This is supported by the fact that swells of very long periods reach the Californian coast (p.36) and also the Moroccan coast (p. 69), more frequently than would be expected from the frequency of storms in the North Pacific and the northwest Atlantic, severe enough to pro- duce such long waves. And while it has been questioned whether the periods recorded for any particular series of breakers have been longer in any known case than might possibly have accorded with the maximum strength of the fiercest squalls during the gales that had set them running,” we believe the view is correct, that swells do gain in length, and in velocity and probably period as well, as they advance farther and farther from the regions of their birth. The alteration of seas into swells is a progressive event; hence, it is never possible to pick a precise moment prior to which the waves are of the former character, and subsequent to which they are purely of 2 A “free wave’’ may be defined as one that is set in motion by a sudden impulse acting once and for all and that owes its continued existence solely to the force of gravity. *3' The offshore velocity (67.5 knots, or 78.5 statute miles per hour) deducible from the longest periods yet recorded for any group of breakers on any coast (average, 22.5 seconds for 12 successive breakers on the south coast of England) was about 11 statute miles per hour lower than the probable maximum velocity, in gusts, of the wind during the particular Atlantic gale that generated them. Wind velocities, in gusts, of 80 to 90 statute miles per hour were, in fact, recorded (by anemometer) during the preceding month over southern England, during several gusts, with a maximum of 101 miles per hour, briefly. (Cornish, 1910, pp. 118-120, and 1934, pp. 11-14.) But it is a question whether squalls as violent as these last long enough, or extend over areas large enough, for the generation of waves as long as those of the group of swells in question. This matter of squalls is also discussed on pages 20 and 26. : DIRECTION OF SWELL 67 the latter. But the transformation is often very rapid when the wind dies down, as every mariner knows. On a recent occasion, we. noted that a low, but rough, sea about 2 to 3 feet high had become trans- formed into a swell, though still nearly as complex in pattern, during a period of about 2 hours, as the breeze slackened ; the smaller wavelets were almost entirely absorbed into the higher and longer ones during the ensuing half hour, by which time the wind had entirely died out. And the alteration in character from sea to swell may be as rapid for larger waves as for small ones if the wind falls flat, though the in- corporation of the younger waves into the older and longer ones on which they are running requires a longer time when the parent seas are large than when they are small. Very few observations have been made as to how rapidly the height of a swell decreases in calm weather. In one published instance, the heights of swells running from the West Wind Belt in the southern Indian Ocean were described as decreasing by about one-half in a distance of 350 miles. And we have ourselves seen a small swell of about 2 feet fall to about 3 inches in a little less than one hour during a flat calm. THE DIRECTIONS OF SWELLS The directions in which swells advance are reminiscent not of the winds at the time of observation, but either of winds that blew pre- viously or of wind systems at a distance. Consequently, the swell that is encountered at sea on any given occasion may be coming with the wind; it may run against the wind (if the latter is not strong enough to have flattened the waves down) ; it may run at any angle with the wind; or it may run ahead of the wind so that a ship in the path of an oncoming storm may find herself plunging into swells so heavy that she takes water over the bow, even if the weather is perfectly calm for the time being. But the direction of advance of a swell, if reversed, leads back toward the place where its parent waves were produced, because waves once set in motion continue to progress in their original direction for as long as they continue in deep water, regardless of any subsequent changes in the direction of the wind (fig. 20). If the swell continues to come from the same direction, it may be assumed that the storm area as a whole is either advancing directly toward the observer, that it is receding directly away from him, or that it is stationary for the time being. If, however, the swells are coming from a storm that is passing by, their direction of advance will change as illustrated in figure 20. Thus the sudden development of a heavy swell at sea, or of a surf upon the coast, may give warning in this way of the approach of a 226794 O - 53 - 6 68 SEAS AND SWELLS storm; and the length of the warning will depend on the rate at which the waves outstrip the storm. Swells, for example, with an average period of 10 seconds, coming from a tropical hurricane 600 miles off shore would reach the coast about 24 hours in advance of the storm itself, if the latter were advancing at the rate of 10 knots. But 12- second swells would precede the storm by about 9 hours only, if it were advancing at 15 knots. And we must caution the reader that the approach of a hurricane is not always heralded in this way by swells coming in advance of it. Position of Observer Figure 20.—Diagram to show the changes in directions from which swells come, With the advance of the storm center that produces them. The direction from which swells come, from hour to hour, may also give some clue to the direction in which the storm center is moving. But the application of this principle is complicated by the fact that the directions of the waves within tropical hurricanes may diverge considerably from the direction of the wind there, as described on page 40, because the latter circles so sharply along the atmospheric pressure gradients in storms of this type, to the left (counterclock- wise) in the Northern Hemisphere and to the right (clockwise) in the Southern Hemisphere, according to the “Law of Storms,” with which every navigator is familiar. And while the direction of the swell, in reverse, as observed out in deep water, points toward the storm area, oa SWELL PERSISTENCE 69 it may no longer do so by the time the swells reach the coast, because of the refraction to which they are subject as they advance over a shoaling bottom (p. 155). Perhaps it is hardly necessary to caution the reader that the familiar phenomenon of a swell reaching the coast ahead of a storm has no bearing on the question whether the velocities of the swells are higher than that of their parent seas and winds, but simply means that the swells often outrun the storm centers, or wind systems as a whole, even when these are moving in the same direction. In fact, swells often reach the coast from storms that pass by offshore, altogether. THE PERSISTENCE OF SWELLS The identification of the regions from which swells originated, through the study of synoptic weather maps, combined with vessels’ log books, has proven in many instances that swells may run for hundreds, or even for thousands, of miles, unless they are beaten down by contrary winds. Thus, a swell from the northwest, originat- ing from severe gales in the Gulf Stream region south of the New- foundland Banks, has been reported not only in the Trade Wind Belt at a distance of 1,500 miles, but even within 270 sea miles of the coast of Sierre Leone, i. e., at a distance of at least 2,500 miles from its birth- place. Very heavy swells have, again, been experienced on the south coast of England at a distance of at least 1,680 sea miles from the storm center that almost certainly gave them birth, while in December 1880 the whole eastern half of the northeast Atlantic experienced a swell, spreading from an area west of the Azores, following winds of hurricane force that had blown there 2 days before (Kriimmel, 1911, pp. 87, 88, fig.21). It has also been known for many years that swells from the winter gales of the West Wind Belts of high latitudes, north and south, are common in the equatorial belt of the Atlantic. Indeed, they reach the coast of Morocco so regularly from barometric depres- sions between Ireland and Iceland, some 1,600 miles away, that swells of 3 feet (1 meter) or higher were recorded at Casablanca and at Rabat on every day when observations were made, from January 1943 to April 1945. Their average heights ranged from a little more than 3 feet (1.2 to 1.3 meters) during July and August to about 10 feet (3.1 to 3.2 meters) in January, with a maximum of about 26 feet (recorded for March) ,* while their recorded periods ranged up to 17 seconds as they approach the shore. And the French Department of Public Works of the Moroccan Protectorate of Rabat has found it possible to predict their arrival about 70 percent of the time.*? They 24 Observations by Institut Scientifique Cherifien, French Morocco, received through Commander C. J. Fish, U. 8S. N. R. 2% Cited from Marmer, H. A., 1930, The Sea, New York, p. 189. 70 SEAS AND SWELLS often cause a violent surf even on the islands of Ascension and of St. Helena in the South Atlantic (in latitudes of about 8° S. and 15° S., respectively) from December to April; and, in the same way, heavy swells from the storms of the Westerlies in high latitudes of the South Pacific run to the island shores of the Paumotos Group, so that they may be expected finally to intermingle with the swells that are gen- erated by the Southeast Trades. A swell would eventually be extinguished by the internal friction of the water and by the resistance of the air that it displaces in its advance, if the ocean were of unlimited extent. But this friction is so small that swells actually tend to run until they strike some coast- Jine, or until they are beaten down by an opposing wind, which may happen so rapidly that a fresh trade wind has frequently been seen wholly to smooth out a moderate swell under the eye of an observer. And the effect of floating ice is still more spectacular in this regard, as described below (p. 147). FORECASTING SEA AND SWELL The prediction of the swell and state of the sea a day or more in advance can be accomplished by the proper use of the relationships summarized in tables 4 and 5, provided sufficient data on wind con- ditions are available. The details of the operations necessary to make a forecast are given in Wind waves and swell; principles in forecast- ing published by the United States Hydrographic Office. Such pre- dictions have been found very useful during wartime unloading opera- tions off open beaches, as during the allied invasion of Europe. For practical purposes, it is important to know the size of the largest waves rather than merely the mean of the entire set, and the pre- dictions give approximately the mean of the highest third of the waves. * Superseded by H. O. Pub. No. 604, Techniques for Forecasting Wind Waves and Swell. Chapter 5 THE FREQUENCY OF HIGH AND LOW SEAS AND SWELLS IN DIFFERENT REGIONS It is not possible, as yet, to picture the average condition of sea or swell for any part of the world in more than a very rough way, for while great numbers of reports of the heights of waves have been received at the Hydrographic Offices of the maritime nations, these have not only been concentrated chiefly along the more travelled routes, but the great majority have been rough estimates only. A criticism, equally serious from the mariner’s standpoint, is that the reports available for this study yield no information whatever as to the frequency with which the sea runs higher than 20 feet, as they often do in the Westerlies of both hemispheres during the stormy season, as well as under the southwest monsoon in the North Indian Ocean. The charts presented here (pls. I to XXIV), with the accompany- ing discussion, are based upon information received and analysed at the United States Navy Hydrographic Office chiefly for the period from 1932 to 1940. The relative frequencies (stated as percentages of all reports received) with which the sea and swell was reported as “calm,” as “low,” as “medium,” and as “high” were calculated for each 5° square, or similar area, and it is from these percentages that the contours were laid down on plates I through XXIV. The cate- gories are based on wave heights which are different for sea and for swell. “Low,” “medium,” and “high” seas indicate waves of 1 to 3 feet, 3 to 8 feet, and 8 feet or higher, respectively, whereas the same cate- gories for swell indicate waves of 1 to 6 feet, 6 to 12 feet, and 12 feet or higher. This distinction between the measurement of sea and swell complicates any comparison between the relative frequencies of low waves of the two classes, but it is still possible to compare high waves in a rough way. Failure to mention “calm” water more than casually in the follow- ing discussion is deliberate, due to the very strong probability that a very old and hence very Jow swell may be overlooked, and that a sea only a few inches high may be reported as “calm.” Actually, it is only when there is no wind at all that there is no sea at all. Likewise, it is unlikely that any considerable part of the open ocean is ever wholly free from a swell, though the latter is often so low and so long that its presence is made visible only if it runs into shoaling water. For these 71 72 FREQUENCY OF WAVE CONDITIONS reasons, the category “low,” as used below and on the charts, includes “calm” unless otherwise noted. The value of presentations of this sort depends chiefly on how far the data on which they are based can be regarded as representative. The percentages have been taken into account only for such of the 5° squares as were the subject of at least 10 reports for the time in question; this minimal number is so small that the contours as laid down on the charts are offered only as the roughest of approximations, except perhaps along the chief steamer lanes, where the picture is more dependable. Where fewer than 10 reports were available for a 5° square, the area has been left untinted. The features of seas and swells of primary and secondary import- ance to the mariner are the frequencies with which these run high and low, respectively, in one part of the ocean or another at different times of the year. It has seemed sufficient to limit the comparison to winter and summer, these being the seasons when the weather is either at its stormiest or the reverse over most parts of the oceans. In the following discussion, “summer” and “winter” refer to those seasons in the Northern Hemisphere. Paucity of data has made it necessary to base each of the seasonal charts for the Indian Ocean, for the South Pacific, and for the South Atlantic on percentages derived from the total observations for two months (July and August representing summer conditions and Janu- ary and February, winter). Winter conditions-in the North Atlantic are also shown by combining the data for January and February, since the percentages derived in this way appear to yield a more representative winter picture for that area. Winter conditions in the North Pacific are based on data for February alone, and summer conditions for both the North Pacific and the North Atlantic are drawn up from August reports only. NORTH ATLANTIC Summer.—The northern part of the North Atlantic is least often rough in July and August for the very obvious reason that winds of gale force (force 6 to 8 Beaufort or stronger) are least frequent then, even in high latitudes. It is only to the northward of the general latitudes of southern Newfoundland, for example, and of southern Britain—locally, too, off the coast of northwest Africa—that seas higher than 8 feet have been reported as often, even, as 10 percent of the time for August; while seas of even that moderate height, in frequency greater than 20 percent, have been reported only for the waters between southern Greenland and Scotland. Elsewhere throughout the North Atlantic the seas of late summer may be characterized as the least often high and as the most often low ee NORTH ATLANTIC 73 in the Equatorial Belt on the African side; considerably less often low along the Northeast Trades; more commonly low, again, in the latitudes of the Variables, as well as along the northeast coast of the United States; but less and less often so to the northward. And the wave pattern, while somewhat skewed, is nearly enough latitudinal for the following table to illustrate the south-to-north gradation in the prevailing heights of the sea, at least in a rough way. TABLE 19.—Mazimum, minimum, and mean percentages of low, medium, and high seas in 5° squares for different latitudinal belts of the North Atlantic in August Low seas Medium seas High seas North latitude - = axi- | Mini- Maxi- | Mini- Maxi- | Mini- mum | mum Mean mum | mum Mean mum | mum | Mean Percent) Percent) Percent) Percent) Percent| Percent| Percent| Percent| Percent 81 17 49 7 19 49 9 2- VSI h 2 i ee a i 0 3 LR?) Ge 75 15 46 70 25 50 19 0 4-5 2 EA ee 82 17 49 78 19 48 14 0 34 6 = eee 78 29 58 64 19 40 7 0 2-3 [Deg oh, See 68 30 48 61 30 45 13 | 2 7 9 21 US) ee 55 14 32 58 29 47 36 | The contours for high seas and for low, in different frequencies, as laid down in plates I and II, are self explanatory in most respects. Attention should, however, be called to the prevailing smoothness of the sea along the northeast bulge of South America in the Doldrum Belt between the southern boundary of the Northeast Trades and the northern boundary of the Southeast Trades, on the one side of the ocean, and along the coast of equatorial West Africa from Cape Palmas to the Gulf of Guinea on the opposite side, i. e., between the Southeast Trades and the land. The increasing frequency with which seas higher than 3 feet (“medium” according to the code adopted), and even higher than 8 feet (2 to 9 percent), are encountered, running out from the African coast into the Southeast Trades (which reach north of the equator in summer ), is in line with common experience. The situation is similar along the axis of the Northeast Trades, from the African coast between latitudes 20° and 35° N., right across to the northern part of the Lesser Antillean chain, where the sea has been reported in August as “medium” for about 65 percent of the time, which accords with an average strength of about 14 to 16 knots for the Trades, where best developed. In fact, the seas are seemingly more uniform in height along this belt than they are anywhere else in the North Atlantic at this season. Even so, the reports for August have shown a considerable gradation from east to west along the Trades, the sea being somewhat more often high (10 to 14 percent) on the African side than to the westward and in the Caribbean (0 to 8 per- 74 FREQUENCY OF WAVE CONDITIONS cent). We cannot offer any explanation for this contrast, since gales are not reported any more often near the African coast at this season than they are farther to the westward ; neither do the Trades commonly blow any more strongly there, nor more constantly in the one direction. The seas average somewhat lower toward either boundary of the Northeast Trades than along the axis of the latter, as might be ex- pected from the character of the wind; this is especially true along the northern Bahamas and toward the coast of southern Florida, where the sea has been described as “low” in 75 to 80 percent of the August reports, and only very seldom as “high”. And this applies equally to the Gulf of Mexico (seas 70 to 80 percent low, 0 to 1 percent high). The Gulf is in fact as smooth as, or perhaps even smoother than any subdivision of the open Atlantic of equal extent at this season. The reader might reasonably object, here, that neither the foregoing account nor the charts (pls. I and II) give any hint of the fact that high and very dangerous seas do accompany the tropical hurricanes that occur from time to time at this season, some of them crossing the Caribbean and the Gulf of Mexico, but others skirting the West Indies, Bahamas, and Florida, either to spend their force inland, or to run parallel to the coast of the United States northward and northeast- ward. The reason they do not more evidently influence the frequency with which “high” seas are reported, is that really severe storms of this nature are rather unusual events, even in the regions where they occur the most commonly in the month in question. Thus the total number of storms of this kind, of hurricane force, that were recorded for August from 1887 to 1936 was only 51 (Tannehill, 1938, p. 113), or about 1 per year, corresponding to which the percentage of severe gales is shown on the Pilot Chart for August as only 0 to 1 for the region in question.” The great frequency with which the seas are low (more than 40 percent) and the infrequent occurrence of high seas (0 to 7 percent) are the outstanding features of the wave pattern of summer along the belt of variable winds in the western half of the ocean, between the northern boundary of the Trades and about latitude 40° N. The scarcity of high seas anywhere along the United States coast as far north as the Grand Banks of Newfoundland (0 to 5 percent) in summer is due to the fact that onshore winds, or longshore winds, strong enough and with a fetch long enough to generate waves of any considerable size are not usual there at this time of year. And it is this prevailing smoothness of the sea, combined with the great num- ber of good harbors, that makes our northeastern coast the summer * The tracks of many of these cyclonic storms are laid down on the U. S. Hydrographic Office Pilot Charts for August and for September, as well as for other months. NORTH ATLANTIC 75 playground that it is for innumerable small-boat sailors. In fact, there is probably no better or safer cruising ground for small yachts anywhere in the world than between New York and Nova Scotia, which would be equally true to the southward were safe anchorages as numerous there and located as close together. The contrast in this respect between the east coast of the United States and the west coast of Europe is considerable, for while the ocean is at its smoothest there, too, in summer, the sea runs high for as much as 12 or 14 percent of the time even then, not only along western Ireland and western Scot- land in the north, but also along the Iberian Peninsula to the south- ward, and 5 to 6 percent of the time in the intervening waters of the Bay of Biscay, as well as off southern Britain. And there is a correspond- ing contrast in the frequency with which the sea is reported as less than 2 to 3 feet high along the United States coast (about 60 to 81 percent), on the one hand, and along the coast of western Europe from Spain to Scotland (about 33 to 55 percent), on the other. In fact, one must sail northward as far as the coast of Newfoundland to find sea conditions on the American side of the Atlantic comparable to those along Spain and Portugal, or in British waters. Yachtsmen, in par- ticular, are well acquainted with this difference in the prevailing state of the sea in the two sides of the North Atlantic in midlatitudes, and so are marine architects, for racing craft must be designed for maxi- mum speed in rougher water in Europe than in the United States. The Gulf of St. Lawrence is of interest in this connection, for while the sea is reported “low” almost as often there (73 percent) as it is even off the northeast coast of South America, seas higher than 8 feet are also comparatively frequent there (9 percent) ; this agrees with com- mon report (with our own experiences, too) that the Gulf in summer is either pleasantly smooth or decidedly rough. The frequency distribution for swells of different heights over the North Atlantic Ocean in summer recalls that for seas. It is only to the northward of about latitude 50° N. that swells higher than 12 feet are reported for August with a frequency as great as 20 percent, while the most extensive area where the swell is described as “low” in more than 60 percent of the reports for that month is along the belt of variable winds in midlatitudes. But the differences in detail between the distribution of swells and of seas are enough to call for some dis- cussion. Thus, a high swell is reported with 9 to 20 percent frequency in August from Newfoundland right across the Atlantic to the coast of Europe (Scotland to southern Spain), where a high sea is decidedly less common; also thence southward in a continuous tongue along the coast of Africa about to the latitude of Cape Verde, where high seas in equal frequency are confined to a much less extensive pool between the vicinity of the Canary Islands and the vicinity of Cape Blanco. 76 FREQUENCY OF WAVE CONDITIONS High swells similarly average about twice as frequent (about 7 percent) as high seas do (about 3 percent) for the North Atlantic in August from latitude 40° N. southward, the contrast in this respect being especially interesting in the downwind parts of the two Trade Belts off South America, where a high swell has been reported locally in August with frequency as high as 19 to 23 percent, but high seas with only 9 percent at most. On the other hand, the mid-latitudinal belt where the waves are reported as “low” more than half the time in summer is much more ex- tensive for swells than for seas (cf. contours for 60 percent low, pls. II and IV), while the swell is also more often low along the West African coast between the offings of Cape Verde and of Cape Palmas during that month (60 to 84 percent) than the sea is (42 to 62 per- cent). The greater frequency with which the category “low” is re- ported for swells than for seas is probably due to the fact that it in- cludes a wider range of heights for the first of these classes of waves than for the second, as explained on page 71. But it is likely that the discrepancies between the frequency distributions for high seas and for high swells chiefly reflect the fact that, while the former are the direct product of whatever wind may be blowing at the time, the swell that is encountered on any given occasion is likely to be the cumulative product of seas generated by stronger winds alternating with weaker winds, or even with calms. We may also point out that high swells are perhaps a better index to the effects of hurricanes in the western side of the Atlantic than high seas are, to judge from the fact that the former are reported de- cidedly more often (6 to 12 percent) than the latter (1 to 3 percent) to the north of the Virgin Islands, as well as in Bahaman waters; high swells are also more frequent (6 to 7 percent) than high seas (1 to 2 percent) out from the coasts of the Carolinas. Closer analysis of the local differences between the frequency dis- tributions of summer swells and seas of different heights over the North Atlantic would require a much more detailed comparison be- tween the waves and the character of the wind, and especially with the frequency of gales, than we have been in a position to undertake. The state of the swell in August may be summarized as follows for enclosed seas on the western side of the Atlantic: a. Gulf of St. Lawrence.—Swell lower than 5 to 6 feet for more than three-fourths of the time (82 percent), and very seldom high (0 per- cent), as might be expected from the fact that the maximum effec- tive fetch within the Gulf is not more than about 180 miles, no matter what the direction of the wind may be. b. Gulf of Mexico—Swells low over the entire area of the Gulf for at least 80 percent of the time, and for more than 90 percent of the es ee NORTH ATLANTIC a time along both its northeastern shore and in its southern side; swells are high for only 0 to 5 percent of the time. e. Caribbean.—Swells low only about 56 percent of the time on the average with 84 percent as a maximum, thus considerably less often than in the Gulf of Mexico. Although high swells are no more fre- quent along the south coast of Cuba (3 percent), or in the shelter of the Antillean chain (1 to 5 percent), where the effective fetch for the Trade Winds is negligible, than they are in the Gulf of Mexico, they are reported with 8 to 12 percent frequency by the time the waves generated by the Trades have reached the downwind parts of the Car- ibbean, off the coasts of Colombia, Costa Rica, and Nicaragua, where the Trades have an effective fetch of something like 350 to 375 miles. The failure of high swells to develop more often than they do in the northern side of the Caribbean, in spite of the tendency for the tropical cyclones that cross the latter to follow this general track, reflects the rarity of such storms there. The pilot chart shows the tracks of 10 only, as following this particular route, for the month of August, over the period from 1901 to 1940. Winter.—The increasingly stormy weather of autumn in high latitudes, with its continuance through the winter, results, as one might expect, in an increase in the average frequency of high seas to 50 to 60 percent and more between Newfoundland, Greenland, and the coasts of northern Europe. This stormyness also causes so wide an expansion, from summer to late winter, in the confines of the region where high seas are encountered for more than a very small part of the time that more than 20 percent of the reports for January and February combined have classed the sea as “high” throughout the whole of the North Atlantic down to latitudes 30° to 35° N., except- ing only along the coasts of southern Spain and of northwest Africa in the one side, and along the northeastern United States in the other. An interesting illustration of the dependence of the height of the sea on the strength of the wind is also to be seen in the fact that the boundaries of the tonguelike extension, southward and westward in midocean, of the area where a high sea is reported more than 40 percent of the time, as shown on plate V, corresponds in gereral with the limits of the region where gales occur in February with frequency greater than 15 percent, as outlined on the Pilot Chart. Another point of interest is that, while in summer the sea is oftener high along the coasts of western Europe than along the eastern United States at corresponding latitudes (p. 75), there is little difference in this respect during the stormy half of the year between the western side of the Atlantic and the eastern. In fact, the sea has been re- ported “high” rather more often from Nova Scotia to the Grand Banks 78 FREQUENCY OF WAVE CONDITIONS of Newfoundland at that time of year (31 to 39 percent) than for the Bay of Biscay, off the mouth of the English Channel, or along the west coast of Ireland (24 to 31 percent). We would leave the reader with only a very pale picture of the actual fierceness of the sea that ships often encounter in high lati- tudes of the North Atlantic, during winter gales, if we were to stop here, for no one, we fancy, who has made many winter crossings during the stormy season would class an 8- or 9-foot sea as a high one at that time for that part of the ocean. Actually, waves of 20 feet or higher have been reported by sailing ships during 13 percent of the time between Newfoundland and England for the year as a whole, for which no doubt the storms of winter are chiefly responsible (p. 77). And waves more than 40 feet high have been reliably reported, not only along this belt where the Westerlies rule, but even as far south as the vicinity of the Azores in the eastern side of the Atlantic, during winter gales of unusual severity, as described above. The data at hand do not afford any further information in this regard, except that it is certainly unusual for the sea to rise much higher than 15 feet or sc anywhere in the western side of the Atlantic south of Newfound- land, unless during exceptionally severe gales. And we might remind the reader that tropical cyclones of hurricane force have never been known to develop in the Atlantic in winter. (See Tannehill, 1938, p. 222.) Corresponding to the general increase in the frequency of high seas in winter, the area in mid-latitudes where a low sea is reported with frequency as great as 40 percent in August (pl. II) contracts between August and January to February, to a much narrower belt north of the Trades between the latitudes of northern Florida and of the northern Antilles (pl. VI); during these months, too, it is less usual to meet a very low sea even there (40 to 54 percent) than it is at the end of the summer (62 to 81 percent). A still more striking alteration of this same order also takes place from summer to winter in the western side of the North Atlantic, along the southern margin of the Trade Wind Belt off South America, where the frequency of seas smaller than 2 or 3 feet falls from 40 to 80 percent in August to only 10 to 35 percent at the end of the winter; this alteration, no doubt, reflects the strengthening through the autumn of the Northeast Trade Wind to a winter average of 14 to 16 knots, or even higher. But the prevailing height of the sea does not alter much from summer to winter in the eastern part of the Trade Belt, between the Cape Verdes, the Canaries, Madeira, and the coast of Africa, where the average strength of the wind does not change much from the one season to the other (average about 12 to 14 knots ae ee NORTH ATLANTIC 79 from December through February as well as from June through August). And the sea ranges low for nearly or quite two-thirds of the time by the end of the winter, not only along equatorial West Africa as is the case in summer, but westward thence, as well, right across to the longitude of eastern Brazil (See the contours for “low seas” with 60 percent frequency, pls. II and VI) following on the autumnal migration southward of the Southeast Trades. We have only one report of the state of the sea in the Gulf of St. Lawrence for January, none for February. And in any case, there is so much drift ice in the Gulf toward the end of the winter that scat- tered data would be of little significance there. High seas are somewhat more frequent in the Caribbean during January and February (2 to 13 percent) than in August (0 to 11 per- cent), corresponding to the fact that the Trades average somewhat stronger there in winter than they do in summer, though the sea is re- ported “low” about as frequently there at the one season as at the other (22 to 51 percent in summer, 21 to 38 percent in winter). The sea, too, is usually much the smoothest close under the shelter of the Lesser Antilles, of the Virgin Islands, of Puerto Rico, of Hispaniola, of Jamaica, and of Cuba, and the roughest off the coasts of Colombia, of Costa Rica, and of Nicaragua, in winter as well as summer, which is to be expected, since the Trades are the governing winds over the Caribbean the year round. The seasonal succession is similar to this in the Gulf of Mexico, where the stronger winds of winter, with occasional gales of moderate strength, generate high seas during 2 to 7 percent of the time and most often in the general vicinity of Tampico, with the corollary result that one is considerably less apt to find the sea low there during the winter (45 to 68 percent) than at the end of the summer (70 to 91 percent). An interesting corollary of the stormy weather of winter is that the swell runs high considerably more often at that season than the sea does, wherever a high sea is a common event. The most striking illustration of this rule is to the northward, as illustrated by the much wider areas enclosed by the successive contours for high swells (pl. VII) than by the corresponding contours for high seas (pl. V). This predominance of high swells over high seas in the stormier latitudes of the North Atlantic probably results from the fact that the swells resulting from the seas raised by one storm are followed so soon by the swells from the next, that the surface of the ocean is never free from them. Similarly, the swell runs high nearly twice as often in winter (20 to 30 percent) as the sea does (13 to 18 percent) in the downwind part of the Northeast Trades, no doubt because seas are so soon transformed into swells, if the wind slackens temporarily. 80 FREQUENCY OF WAVE CONDITIONS The increasing frequency through the autumn of high seas over the northern part of the North Atlantic is further reflected in the fact that most of the area of the latter is disturbed by a swell of 12 feet or higher for more than one-tenth of the time by the last part of the winter. The only exceptions are along the Lesser Antilles, the Bahamas, and northern Cuba in the west, also the subequatorial belt in the east, from equatorial West Africa out to the longitude of eastern Brazil, where a high swell, like a high sea, has not been reported at all in January and February for some of the 5° squares, nor in fre- quencies greater than 6 or 7 percent for any of the others. To the northward, indeed, of the Northeast Trades, it is only off the coasts of Florida, Bahamas, and Cuba that the swell has been reported “low” or altogther absent for as much as 60 percent of the time in late winter ; whereas in August this applies not only to the entire western side of the North Atlantic, west of the longitude of Newfoundland, but also to an extensive area as well in midlatitudes in midocean (pl. IV). A longitudinal contrast, of practical interest in the state of the swells of winter, is that these are considerably less often high along the coast of the northeastern United States and off the coasts of Europe and of northwest Africa than they are in midocean, as is illustrated by table 20. High swells are somewhat more common in the Gulf of Mexico in winter ( 4 to 9 percent) than at the end of the summer (0 to 5 percent) ; likewise, they are considerably more common throughout the Carib- bean as a whole, much as high seas are (p. 79), and with similar gradation, with frequencies from about 5 percent under the immediate shelter of the Antilles in the east but 11 to 20 percent along the coasts of Colombia and of Nicaragua in the west. TABLE 20.—Ranges of percentage frequencies of high swells in unit areas of the North Atlantic in January and February, to show the contrast between the frequency of high swells within approximately 500 miles of the American and European coasts and that in midocean North Off coast of Midocean Off coasts : ; longitude of Europe latitude America 30°-40° N. and Africa Percent 50°—40° 40°-30° 30°-20° SOUTH ATLANTIC Available data suggest that a really high sea is about as common in high latitudes of the one hemisphere as of the other during the stormy OE Ee | ) SOUTH ATLANTIC 81 season, for the frequency with which waves of 20 feet and higher have been reported for the year as a whole is very nearly the same for the South Atlantic, in the latitude of southern Argentina (12 percent), as in the North Atlantic between Newfoundland and England (13 percent. See table 8, p. 21.) On the other hand, the seasonal expansion and contraction of the limits of the area where a high sea is commonly encountered in the Southern Hemisphere is the reverse of that in the Northern, as illus- trated by the fact that while, in the latter, it isin January and February that the contour line for high seas in 10 percent frequency approaches nearest to the equator, it is in August that this happens in the South Atlantic. This difference was of course to be expected from the fact that the northern winter is the stormy season in the Northern Hemis- phere, whereas it is stormiest in the Southern Hemisphere during the northern summer. Correspondingly, it is during the northern winter, when the high and mid-latitudes of the North Atlantic are the most often troubled with high seas, that the sea is the least often rough in the corresponding belt of the South Atlantic. A heavy swell, too, is reported considerably more often throughout all but the subequatorial region of the South Atlantic during the northern summer than it is in the North Atlantic, for this same reason, the opposite being true in northern winter. This again is consistent with the differences in seasons in the two hemispheres. During the stormy half of the year, too (northern summer in this case), a heavy swell has been reported generally throughout low and mid-latitudes of the South Atlantic considerably more often than a high sea has, much as is true of the North Atlantic in the northern winter, and no doubt for similar reasons (p. 78). Although the number of reports received from the South Atlantic is small except along the two coasts, they are enough to show that the frequency distribution of seas of different heights there in the northern summer is roughly a mirror picture of the sea pattern of the North Atlantic; i. e., while a heavy sea is the most common in high latitudes and least so in low, in both oceans, the area where the sea is low for more than half the time extends farthest from the equator in the eastern side in the Southern Hemisphere, but in the western side in the Northern. In northern winter, high seas, and high swells as well, are considerably more common off the coast of Africa at corresponding latitudes, to the southward of about 20° S., than off the coast of South America, which is true of high swells in the northern summer as well. (See tables 21 and 22.) 82 FREQUENCY OF WAVE CONDITIONS TABLE 21.—Average percentage frequencies of low and high seas and swells in the South Atlantic within approximately 300 miles of the coasts of South America and of Africa in July and August Swells South Off South : Off South F latitude America Off Africa ‘America Off Africa Low High ; Low High | Low | High | Low High Percent| Percent | Percent | Percent | Percent | Percent | Percent | Percent 22 8 79 0 41 14 70 2 15 50 17 40 30°-35° 19 30 TABLE 22.—Average percentage frequencies of low and high seas and swells in the South Atlantic within approximately 300 miles of the coasts of South America and of Africa in January and February Swells South Off South A Off South . iatigude Off Africa Off Africa America America Low High Low High Low High Low High Percent| Percent | Percent | Percent | Percent | Percent | Percent | Percent 53 61 5 30°-35° NORTH PACIFIC Summer.—The available data vary even more widely in number from one unit area to the next for the Pacific than for the Atlantic, and they are less numerous for most of the squares, especially along the equatorial belt. There are enough, however, to show that the re- gional variation in the relative frequency with which seas of dif- ferent heights are encountered in summer is fundamentally the same for the one ocean as for the other, as is to be expected from the fact that the wind systems are essentially similar over the two. Thus, it is only to the north of about latitude 50° N. that high seas are reported in August in the Pacific as often as 20 percent of the time. In the Pacific, too, as in the Atlantic, northward from about latitude 35° N., high seas are not only considerably more common near the coast in the east, at that time of year, than in the west, but they are reported about as frequently from southern Alaska to the offing of Los Angeles (5 to 17 percent), as from Ireland southward along Europe and north- west Africa to the vicinity of Cape Verde. Also high seas are about as frequent along the Pacific shores of Japan and of the Kuriles (2 to 7 percent), as along the eastern United States, north of Florida, or along Nova Scotia. Wm one NORTH PACIFIC 83 The area, however, where a high sea has been regularly reported in August during more than 10 percent of the time extends something like 1,200 miles farther southward in midocean in the Pacific (to about latitude 25° N.) than in the Atlantic (to about 45° or 46° N. only; cf. pl. [IX with pl. I). A high sea is also reported about four times as often on the average (8 or 9 percent) from southern Japan southward, past the northern Philippines to the offing of Mindanao in the open Pacific, as well as locally in the northern part of the South China Sea, than it is along the Atlantic seaboard of North America as a whole from Cape Hatteras southward, in the West Indies, in the Gulf of Mexico, or in the Caribbean (average about 1 or 2 percent). This difference between the two oceans may be partially due to the fact that the prevailing winds of summer are somewhat weaker along the south- eastern United States and in the Gulf of Mexico at that season than in the western side of the Pacific at corresponding latitudes, where they average 12 to 14 knots. But it is also likely that the dangerous waves raised by tropical hurricanes have been included more often in the reports of the state of the sea in the western tropical Pacific for the late summer than they have in the Atlantic, for the typhoon season is not only at its height then, but dangerous storms of this nature cross the East and South China Seas much more often than they do the western tropical Atlantic, the Caribbean, or the Gulf of Mexico. The Pilot Charts for August, for example, show the tracks of 169 for that general part of the Pacific for the 25-year period from 1921 to 1945, but only 36 for the western tropical Atlantic for the 39- year period from 1901 to 1940. Neither are there any apparent counterparts in the North Atlantic to the “pools,” so to speak, in mid-Pacific, the one extending south- easterly from the Hawaiian Islands, the other lying farther south- eastward in the equatorial belt, where high seas are reported in sum- mer in frequency as great as 10 percent. No doubt the Northeast Trades are responsible in the first case, for it is about here that they average their strongest in summer, and the Southeast Trades for the second. On the other hand, a high sea is reported considerably less often along the coasts of Central America and of Lower California in the eastern tropical Pacific in August (0 to 2 percent) than it is in the corresponding latitudinal belt of the eastern Atlantic from Gibraltar to Cape Verde (7 to 14 percent). At the same time, what may be named the “east-tropical smooth” (outlined on the charts by the con- tours for 60 percent low) extends some 1,500 miles farther northward in the eastern side of the Pacific, where it reaches to southern Califor- nia, than in the eastern side of the Atlantic. The smoothness of the sea in this part of the Pacific no doubt reflects the fact that the inshore 226794 O-53 -7 84 FREQUENCY OF WAVE CONDITIONS boundary of the Trade Wind Belt is separated from the coasts of southern and of Lower California by a belt some 300 miles wide at its narrowest, with the coasts of Central America fronting on the Dol- drum Belt, where the winds are not only variable, but as a rule weak. Available information for summer also makes it likely that a smooth sea is equally characteristic along the equatorial belt in the western half of the Pacific, though the reports received thence were not numerous enough to have much statistical value. And more fre- quest reports of low seas westward along the Northeast Trades from about the longitude of Wake Island and of the Marshalls, than eastward, accord with the wind distribution at this season. It is doubtful, however, whether there is any clear parallel in the North Pacific to the smooth belt along the belt of Variables that is so con- spicuous a feature of the sea pattern of summer in the North Atlantic (p. 74). Perhaps as good an illustration as any of the contrast be- tween the summer seas of the two oceans in this last respect, is that the general August average between latitudes 25° and 35° N. is about 52 percent low and about 8 percent high for the North Pacific west of the longitude of western Alaska, but about 67 percent low and only 0 to 4 percent high for the North Atlantic west of about longitude 35° W. Ten of the 19 reports received from the southern part of the Sea of Okhotsk for July and August (we have no information from its northern part) described the sea as “low,” none of them as “high,” which is in agreement with the fact that gales of force 8 or stronger are so uncommon, at that time of year, over the waters between Kamchatka and the Asiatic coast that their percentage is shown as zero there on the Pilot Chart for August. The summer seas run low rather more commonly in the Sea of Japan (41 to 80 percent according to locality) than in the Sea of Okhotsk, nor is a high sea reported at all there in August and only occasionally (0 to 5 percent) in July. And the state of the sea is much the same as this in the Yellow Sea. It rises high rather more often, however, in summer in the South China Sea (0 to 14 percent frequency), due to the gales that sometimes blow there and to the occasional typhoons that cross its northern half; the Hydrographic Office Pilot Chart for August gives frequencies of 1 to 4 percent for gales for the South China Sea as a whole and shows the tracks of 4 typhoons crossing its northeastern part. But the sea has been classed as “low” in 94 to 100 percent of the August reports from the waters between the southern Philippines, Borneo, and Celebes, nor do they mention a high sea at all, ordinary gales and typhoons alike being unknown there. In a general way, the summer swell is most often high in the parts of the North Pacific where the sea is most often high, and low where NORTH PACIFIC 85 the sea is most often low; this is, in fact, the general rule for all parts of the ocean at all seasons. Thus, a high swell is reported locally south of Japan, across the mouth of Bering Sea, and off the Alaskan bight as often as one-fifth of the time in August, much as is true of the sea. Similarly, a heavy swell is encountered somewhat more often in the coastal belt off southern California, and off southern Alaska, than it is in the intervening regions, while the irregular area along the Trades, eastward and westward from the Hawaiian islands, outlined in plates IX and XI by the contours for 10 percent “high,” is much more exten- sive for swells than for the seas of which they are reminiscent; a dis- crepancy of this sort has already been discussed for the Atlantic (p. 76). The regions in the western side of the Pacific in mid-lati- tudes, where swells and seas run high more than 10 percent of the time likewise correspond, in general, one with the other, though their pre- cise boundaries differ considerably for any particular frequency that might be selected ; this is due partly, no doubt, because the term “high” has a different meaning in the one case (12 feet and over for swells) than in the other (8 feet and over for seas), but chiefly because waves that have lost the characteristics of a sea so commonly continue to ad- vance for long distances as a swell. The swell, also like the sea, runs high considerably more often in summer in the waters between Japan, the China coast and the Philip- pines in the one side of the Pacific than it does along the coasts of Cen- tral America and of Lower California in the other. The consequence is that vessels crossing in summer from Canadian and Californian ports to Japan and to China may expect to find the swell low during more than half of the time until they cross longitude 180°, beyond which the swell is likely to be low somewhat less often, and high somewhat more so (10 percent or more). But the swells, encountered by ships crossing from San Francisco or Los Angeles to the Hawaiian Islands, are likely to be rather heavy for something like one-tenth of the time during the entire voyage, and low considerably less than one- half of the time. At the other extreme, the swell is so seldom heavy enough to be of any practical account along the western sector of the equatorial belt of the North Pacific that such of the August reports as mention it at all there class it as “low” more than 80 percent of the time, all along from about the longitude of the Gilbert group westward to the Mo- luccas and to the southern Philippines; nor do any of the August re- ports mention a high swell at all within this general region. And since the August sea also is reported “low” there, for 63 to 93 percent of the time, and never “high,” the region bounded in plate XII by the con- tour for 80 percent low, may be named the most pacific pait of the ocean of that name of any considerable extent north of the Equator. 86 FREQUENCY OF WAVE CONDITIONS Agreement between the two classes of waves is also close in the east- ern side of the tropical Pacific, from the Equator northward coastwise to southern California. Perhaps the difference chiefly deserving of emphasis between the August picture for swells for the North Pacific and that for seas (since it might not appear from a cursory survey of the respective charts) is that a high swell has been reported more than 10 percent (locally as often as 38 percent) of the time, between the Equator and latitude 5° N., westward from the Galapagos Islands, where a high sea has not been reported at all in any of the returns for the month. The swell is reported as more commonly high in the southern part of the Sea of Okhotsk (20 percent) than the sea is (0 percent high) and less commonly low there. A high swell is also reported somewhat more often (11 to 19 percent) than a high sea (9 to 13 percent) in the eastern and southeastern parts of the South China Sea. But there is no great difference in the frequencies with which high swells and seas are reported near the Asiatic mainland in this region (0 to 10 percent for swells, 1 to 14 percent for seas). Neither is there any greater difference in the relative prevalence of low swells in summer, as compared with low seas, either for the South China Sea or for the Japan Sea, than can be charged to the fact that this category includes a much wider height range for swells than for seas (p. 71). Winter.—The sea is much more commonly rough in middle and high latitudes of the North Pacific in winter than it is in summer, as might be expected from the stormier weather; in fact, it has been described as “high” in 40 to 60 percent of the late winter reports that have been received, not only across the Alaskan bight, but throughout most of the northwest part of the Pacific down to latitude about 30° N., ex- cept along the Japanese island chain, where it is high rather less often even at this time of the year (12 to 36 percent). Ships crossing from Yokohama to Seattle or Vancouver may thus expect a rough sea some- thing like half of the time, except, perhaps, as the American coast is neared, and even higher than 20 feet during winter gales, according to evidence from other sources.” And winter crossings from Japan to San Francisco are also likely to be rough, after the first couple of hundred miles and until the longitude of the eastern Aleutians has been left behind, after which it is likely to be smoother, especially nearing the California coast, where a high sea has been reported only about 10 to 14 percent of the time, even in winter. The most widespread evidence, however, of the increasing rough- ness of the North Pacific, through the autumn, is that the boundaries 7 The reported frequency of 10 percent, for seas higher than 20 feet, south of the Alaskan Peninsula in the latitude of Oregon (p. 21), is for the year as a whole; actually, however, So heavy a sea is encountered much more often in high latitudes of the Pacific in winter than in summer, just as it is in the Atlantic. NORTH PACIFIC 87 within which a high sea is reported during more than 20 percent of the time expand, by February, to include the whole vast area south- ward to the latitude of southern Japan in the west and to that of Lower California in the east (to about latitude 25° N.), excepting only for the smoother tongue that still intervenes between it and the United States coast, in the east, as just noted. The southern limit of this tumultuous region does not differ much in position anywhere across the Pacific from the corresponding boundary of the area where severe winter gales have been reported on more than 5 days out of 100 during past years. Indeed, it is only where the frequency of gales of force 8 is greater than 10 percent that consistent reports have been received of high seas with frequency greater than 35 percent from any part of the North Pacific at any time of year. The autumnal roughening of the ocean is also accompanied by a reversal in the relative frequencies with which the sea runs high in the coastal belts of the two sides of the Pacific in mid-latitudes ; in summer, this happens more often along the California coast than along the Japanese (pl. IX), whereas in February the reverse is true (12 to 31 percent high along the Japanese islands, 3 to 14 percent high from southern California to Puget Sound). The greater frequency of high seas in the waters between Japan, Korea, the China coast, and the Philippines in February (0 to 28 percent) than in August (0 to 13 percent) reflects the general increase that takes place there through the autumn in the average strength of the wind, rather than the effects of typhoons, for these seldom develop there in winter. The expansion that takes place from summer to winter of the area within the Northeast Trade Wind Belt, where a 9-foot sea is more than an exceptional event (see the contours for 10 percent “high,” pls. [TX and XIIT), has a similar cause. And gales of moderate strength (force 7 or higher) blowing more commonly in winter (up to 10 percent) off southern Mexico, than in summer, are no doubt responsible for the fact that high seas are reported a little more often off the Central American coast from Costa Rica northward (up to 7 percent) in February than in summer (1 to3 percent). Well- known examples are the rough seas generated in the Gulf of Tehuan- tepec by the gales, known locally as “Tehuantepecers,’ that blow out from the land there in late autumn and winter at times when cold air masses are flowing in sufficient strength southward from the North American continent, and along the western side of the Gulf of Mexico, to be funneled, as it were, across the Isthmus of Tehuantepec.” The 28 See Hurd, 1929, Monthly Weather Review, vol. 57, No. 5, p. 192, for a readable account of these ‘‘Tehuantepecers.” 88 FREQUENCY OF WAVE CONDITIONS swells generated in this way are sometimes reported southward as far as the northern coasts of the Galapagos Islands. It also seems likely that the 20-foot seas, or higher, that are reported for the equatorial belt southeastward from the Hawaiian Islands, with 4 percent frequency for the year as a whole (p. 21, table 8), actually develop there most often either in September or in February, these being the only months when gales of even moderate intensity (force 7 or stronger) are reported there, other than on the rarest of occasions. The reported frequencies, however, of high seas in low and mid- latitudes in the eastern half of the North Pacific in midocean give no hint of the severe cyclonic storms that occasionally blow there in winter; the Pilot Chart shows the tracks of three such that developed to the north of the Hawaiian Islands in the month of February, during the period from 1922 to 1936. A corollary of the increasing frequency with which high seas are reported in the northern Pacific, through the autumn, is that the only regions where a low sea is reported as often as 40 percent of the time by February are an isolated pool in the latitude of the northern Philip- pines, of Formosa, and of southern Japan in the west, and the general offing of the American coast, southward from middle California, in the east. This last is also the only extensive area in the North Pacific where a perfectly smooth sea has been reported in winter during so much as one-twentieth of the time, though the few reports received suggest that this may likewise apply along the equatorial belt in the western side of the Pacific, where calm weather is equally common. Reports from the Sea of Okhotsk for January or February were not numerous enough to be considered representative. The northern and eastern parts of the Japan Sea are, however, much rougher in winter (high sea 14 to 20 percent) than in summer, as is also the northern part of the South China Sea (high 9 to 15 percent). The sea is, however, as constantly smooth at the entrance to the Gulf of Tonkin in winter as it is in summer, which applies equally along the Bornean coast to the southward, as well as to the waters between the southern Philippines and Celebes. The question, “How does the North Pacific compare for roughness in winter with the North Atlantic?” is one often asked. During severe winter gales the sea may be expected to rise about as high in the one ocean as in the other; seas, however, more than 20 feet high have been reported considerably more often along the northern routes in the North Atlantic for the year as a whole (13 percent) than for the North Pacific (9 percent), the gales of winter being chiefly responsible in each case. On the other hand, the area where high winter seas have been consistently reported dtiring more than one-fifth of the time extends something like 300 miles further southward in the Pacific in NORTH PACIFIC 89 the late winter (to about latitude 30° N.) than in the Atlantic (only to about latitude 35° N.). ‘High seas are also considerably more fre- quent in middle and low latitudes in the western side of the Pacific, from southern Japan to the northern Philippines (5 to 28 percent) than they are in the corresponding belt in that side of the open North Atlantic, i. e., from northern Florida to French Guiana (2 to 11 per- cent). Other than this, however, the winter seas of the Northeast Trades average high about equally often in the one ocean as in the other, except that the east-west gradation is, of course, condensed within a much shorter distance in the North Atlantic than it is in the North Pacific ; and the Doldrum Belt is smooth about as constantly in the one ocean, off equatorial West Africa, as it is in the other, of Central America. The increase that takes place in the frequency of high seas, through the autumn in middle and high northern latitudes is mirrored so closely in the swell that by midwinter the latter runs high during 40 to 60 percent of the time throughout the north central portion of the Pacific as a whole. Indeed, the only extensive regions where the swell has not been definitely reported “high” during at least 10 per- cent of the time, for the open North Pacific in February, are in its western side from southern Japan southward along the Philippines, and in the general offing of the American coast in the east, from south- ern California to the equator. It is probable, however, that this also applies to the equatorial belt, westward from about longitude 180°, for a high swell was reported in only 1 out of 62 returns that were received thence for January and February. Corresponding to this greater frequency of high swells, low swells are encountered considerably less often over the Pacific as a whole, southward to the latitude of middle Japan in the one side and to that of middle California in the other, in February (9 to 44 percent) than in August (34 to 80 percent) ; this applies also in the Trades, and along the equatorial belt in the west, wherever, a significant number of reports have been received. On the other hand, the smooth area in the American side of the equatorial Pacific, where the swell is low during more than four-fifths of the time, is much more extensive in winter than in summer (con- tours for 80 percent low swells, pls. XII and XVI). A.swell, larger or smaller, is, however, mentioned in 70 to 90 percent of the winter returns, except along Japan, as well as here and there perhaps in the ‘quatorial belt in the west, and locally in the Panamanian region in che east. Hence it appears that no considerable part of the open Pacific is ever wholly free from a swell at this time of year, a low one being so inconspicuous a phenomenon that it is apt to be ignored, 90 FREQUENCY OF WAVE CONDITIONS especially if a sea of any considerable size is running upon it, as so commonly happens. No reports of swell were received for the Sea of Okhotsk for Jan- uary or February. In the Japan Sea, a high swell is more common in winter (0 to 10 percent) than at the end of the summer (0 percent). Little change take place, however, in this respect, from summer to winter at the mouth of the Yellow Sea, while the most noticeable alter- ation, in the swell pattern of the South China Sea, from the one sea- son to the other, is that the belt where a high swell is the most com- mon (upwards of 10 percent) withdraws northward, away from the coasts of Borneo and of Palawan. And the frequency with which the surface has been reported as wholly free from swell, alters but little from summer to winter in any partially enclosed seas of eastern Asia (table 23). TaBLE 23.—Percentage frequency with which unit areas of the Japan and South China Seas have been reported wholly free from swell in summer and winter Percentage frequency of no swell Area Maximum Minimum Average August | February August | February August February ———— —— Percent Percent Percent 36 Percent Percent Percent 22 32 50 30 0 US Se ee ee 0 33 21 South China Sea_-_-.___.-_-__-- | 50 SOUTH PACIFIC The reports from the South Pacific were so few in number that it is doubtful whether such month-to-month differences as they indicate are of much significance, while large areas are necessarily left blank on the charts (pls. IX to XVI). Combination, however, of the reports for July with those for August, yields a pattern consistent enough to be accepted as representative of the late summer state. Features of the July-August charts (pls. IX and X) of special interest are: (a) the demonstration that the west equatorial smooth belt (contour for 60 percent “low” seas) is confined even more closely to the vicinity of the equator in the Southern Hemisphere than in the Northern; (6) the delineation of the approximate boundaries of the midequatorial “pool” where high seas are reported during more than 10 percent of the time at that season of the year, with waves even as large as 20 feet occasionally (p. 88); and (c) the illustration of the pre- vailing roughness, in general, of the southern half of the South Pacific during the months in question, when winds averaging up to 16 to 18 miles per hour in velocity, northward as far as about latitude 30° S., generate high waves more than one-fifth of the time, equatorward past SOUTH PACIFIC 9] northern New Zealand and as far as about latitude 20° S. in the mid- longitudinal belt of the ocean. It is much to be regretted that the data are not sufficient to extend the July-August survey farther southward for the mid-Pacific. Con- ditions, however, along the Chilean coast (table 24) suggest that seas higher than 8 feet are to be expected during at least 40 percent of the time, during these months, to the southward of the latitude of the Straits of Magellan, generally. TaBLeE 24.— Average percentage frequencies of high seas and swells within approzi- mately 300 miles of the west coast of South America July-August January-February South we Res latitude Percent | Percent | Percent | Percent 0 6 0 1 15 23 28 53 42 The seasonal character of the weather also makes it likely that the waves of 20 feet and higher, that have been reported 15 percent of the time for the year as a whole (table 8, p. 21) in mid-Pacific in the latitude of southern Chile, actually develop there rather more often during the northern summer than during the northern winter. Other aspects of the South Pacific sea pattern of northern summer deserving attention are that high seas running out from the coasts of Peru and of northern Chile are increasingly frequent, as the average strength of the Southeast Trades increases out from the land, and that the sea is high less often between Australia and the North Island of New Zealand than it is eastward from the latter. The most interesting aspect of the South Pacific swells of northern summer is that these have been reported “high” considerably more often than the sea has throughout the region of the Southeast Trades, as illustrated by the fact that the average frequency for this category between the equator and latitude 20° S., in July and August, is about 13 percent for swells, but only about 5 percent for seas, with the con- trast in this respect between the two classes of waves nearly as wide close in to the South American coast as it is out in midocean. “Rolling down the Trades,” an old expression from sailing-ship days, is thus much more than a figure of speech when applied to the South Pacific Trades in northern summer. The fact that the northern summer swell runs high northeastward from New Zealand on the one side (45 to 91 percent), as well as along South America at corresponding latitudes on the other (20 to 42 per- 92 FREQUENCY OF WAVE CONDITIONS cent), considerably more often than the sea does, suggests that this would prove equally true right across the ocean in this belt, as well as tothesouthward. And this is certainly the case between New Zealand and Australia, where an average July-August frequency of about 30 percent for high swells, but of only about 15 percent for high seas, af- fords still another illustration of the general rule that wherever the sea runs high for any considerable proportion of the time, the swell may be expected to do so even more frequently. In fact the only areas in the South Pacific of any considerable extent, where a high swell has not been reported in frequency as great as 10 percent, for July and August combined, are off the tropical American Coast in the east, along the equatorial belt in the west, and under the close shelter of the more extensive island groups, such as the Fijis and the Ellices. The Trades, however, raise a sea higher than 8 feet so much less often in the South Pacific during the northern winter than during the northern summer that the average frequency of the category “high” is less than 1 percent (stated as 0 on the chart), for January and February at 71 out of the 104 squares between the equator and latitude 25° §., from which a significant number of returns were re- ceived. Indeed, the maximum reported frequency for high seas for this season, along all this belt, is only 11 to 14 percent (off Australia). The prevailing smoothness of the South Pacific is especially striking at this season off South America, when it is necessary to proceed some- thing like 1,000 miles offshore to find high seas in reported frequency as great even as 3 to 11 percent at any individual square, anywhere to the northward of the latitude of northern Chile (lat. 25° S.). Simi- larly, the swell is heavy enough to be reported as “high” only about one-third as often in January and February, as in July and August, throughout the Trade Wind Belt of the South Pacific in general, all of which is in line with common experience. And the seasonal contrast is of this same order for seas in the mid- latitudinal belt as well, for even there the January-February chart fails to show a frequency greater than 20 percent for high seas any- where to the northward of the latitude of northern New Zealand on the one side of the South Pacific, or of central Chile on the other. And while a high swell is reported rather more frequently in northern winter from eastern Australia out past New Zealand (9 to 35 percent ) than a high sea—as is indeed the usual rule—the seasonal alteration from summer to winter is of the same order for high swells as for high seas throughout such other parts of the South Pacific as the reports cover, as illustrated by the smaller areas enclosed by the con- tours for high swells in 10 percent and in 20 percent frequency in January and February (pl. XV) than in July and August (pl. XI). Corresponding, too, to this decrease from July-August to January- NORTH INDIAN OCEAN 93 February in the frequency of high waves of either category, the east- tropical smooth area, as defined on the charts by the contours for “low” in 60 percent frequency, extends tongue-like, something like 1,800 miles farther out along the equator from the American coast in northern winter than 4n northern summer for seas, and apparently as far as the longitude of the Marquesas and of the Paumotos (about long. 140° W.) for swells, to judge from such scattered information as is at hand. And a corresponding expansion of the equatorial- American region, where swells and seas alike are low for more than 80 percent of the time, takes place from northern summer to winter. Ships crossing the northwestern part of the South Pacific in north- ern winter, or in early spring, must however take account of the pos- sibility that they may encounter the dangerous seas that are generated by tropical hurricanes, for these develop most often there from De- cember to March. Such of these storms as originate in the Coral Sea usually move either toward New Caledonia, or past New Guinea, or— more rarely—southward paralleling Australia; others of great sever- ity occur from time to time in the neighborhood of the Fijian and Samoan Island groups. NORTH INDIAN OCEAN Summer.—The chief causes for high seas in the Indian Ocean north of the equator are the winds of the Southwest Monsoon, which blow strongest, and with frequent squalls and gales, from June through August. High seas, therefore, are the most frequent there in summer or just when they are least so in the northern parts of the Atlantic and of the Pacific. Regional differences in the frequency with which a high sea is to be expected during the monsoon season (pl. XVII) are also clearly governed by the prevailing strength of the wind. Thus the region in the Bay of Bengal where 8-foot seas, and higher, are reported during more than one-tenth of the time during July and August, corresponds closely with that where the summer monsoon averages stronger than 16 miles per hour. And the limits between India, Arabia, and Africa, within which a high sea has been reported in frequencies greater than 20 percent, and than 40 percent, for July and August combined, coincide almost exactly with those within which the monsoon averages stronger than 16 and 20 miles per hour, respectively, and where gales of force 7, or stronger, are then the most frequent. High seas, indeed, are reported locally in frequencies about as great (maximum 74 percent) within this general region, during the monsoon season, as they are anywhere in the world; and they rise there to heights of 20 feet or more during about 10 percent of the time (table 8, p. 21). Corresponding to this, we read of the western coasts of Hindustan that all small craft near Bombay are laid up from the 94 FREQUENCY OF WAVE CONDITIONS end of May until early in August, when the more venturesome put to sea again.” The sea is also higher than 2 or 3 feet more constantly (more than 80 percent) in this part of the Arabian Sea, during the height of the Southwest Monsoon, than happens at any season any- where else in the Indian Ocean, except in the western part of the South- east Trades Belt, off Madagascar. The violent winds of the tropical cyclones that develop from time to time in the Arabian Sea, and in the southern or central parts of the Bay of Bengal, are a second potential source of high and dangerous seas in the northern part of the Indian Ocean. In the Arabian Sea these occur most often during the period of transition between the two monsoons, June through July and October.through November, but they are infrequent even then. And while they cross the Bay of Bengal most often from June through November, this does not happen frequently enough to have any appreciable effect on the frequency with which high seas have been reported there; the total number of tropical cyclones reported for the Bay of Bengal in July and August was only 92, for a 25-year period, according to a recent tabulation.” Transition is abrupt, in summer, from the stormy waters of the Arabian Sea through the Gulf of Aden, into the Red Sea, to which the monsoon does not extend, and where the winds of summer average so light (8 to 10 miles per hour)—and with gales practically unknown —that the sea rises only occasionally there to 9 feet. A high sea has, however, been reported rather more often in summer in the Persian Gulf (7 to 8 percent in July and August), for what reason is not apparent, since the wind averages no stronger (less than 10 knots) and gales are no more frequent there in summer than in the Red Sea. A high swell is reported at least as often as a high sea throughout the North Indian Ocean as a whole during the Southwest Monsoon season, excepting only along the Burmese coast of the Bay of Bengal (pl. XTX). The contrast in frequency between the two classes of waves is par- ticularly instructive in the northern part of the Arabian Sea, where the high seas generated to the southward, where the monsoon average strongest, assume the characteristics of swells so soon, as they spread, that the latter are reported “high” considerably more often along the coasts of northwestern Hindustan, of Beluchistan, and of Arabia in July and August average about 40 percent) than the sea is (average about 20 percent). Similarly, the swells of summer run high about twice as often in the western side of the Bay of Bengal, northward from Ceylon (average about 18 percent) as the sea does (average 2 British Admiralty, West Coast of Hindustan Pilot, 4th Edit., 1898, p. 38. 3° Doraiswamy Iyer, V. 1936. Typhoons and Indian weather. Mem. India. Meteorological dept. vol. 26, p. 97. NORTH INDIAN OCEAN 95 about 7 percent) ; so, too, in the equatorial belt (lat. 0° to 5° N.) clear across from the African coast to the offing of Sumatra (average about 17 percent for high swells, about 7 percent for high seas). On the other hand, it is no more common, in summer, for the swell to run high than for the sea in the Red Sea, in the Gulf of Aden, or in the Gulf of Oman. And the boundaries of the areas within which the summer swell is reported “low” in any chosen frequency differ from those for low seas no more widely than can be charged to the nature of the information from which they have been derived (pls. XVIII and XX). Winter.—The alteration that takes place, from summer to winter, in the state of the sea in the northern Indian Ocean, with the change of the monsoons, can fairly be described as “spectacular.” Thus the northeast winds of January and February average so much weaker than the southwest winds of summer—and with gales so unusual— that a high sea was not reported at all, for January or February, for about one-half of the unit areas (pl. X XI) and the maximum fre- quency was only 4 percent at any of them, except in the general offing of the Gulf of Aden, where an average wind velocity of 12 to 14 knots, December through February, generates 9-foot seas a little more often (5 to 7 percent). It is also perhaps characteristic that a high sea is reported in 4 percent frequency, in winter, between Ceylon and the northern atolls of the Maldive Group, where we ourselves met a sharp gale in January 1902. It is not astonishing, with high seas so unusual, that the frequency of “low,” in late winter, should be more than 40 percent throughout the entire extent of the North Indian Ocean, except for a circumscribed tongue off the East African coast, and more than 60 percent, except in the southwestern part of the Arabian Sea, locally in the offing of the Gulf of Oman, and southwest of Ceylon (pl. X XII). The following summary (table 25) illustrates how much smoother during the winter than during the summer (both as to seas and as to swells) those parts of the North Indian Ocean are, where the heights of the waves are ruled by the monsoon wind. TABLE 25.—Average percentage frequencies of low and high seas and swells in the Arabian Sea and in the Bay of Bengal in winter and summer Arabian Sea Bay of Bengal Season Seas Swells Low | High | Low | High | Low | High | Low | High January-February (Northeast Mon- | Percent Bate Percent | Percent | Percent| Percent| Percent | Percent EGG) seat ee ee 60 75 3 76 1 89 1 July-August (Southwest Monsoon) - 23 oA 25 33 37 9 44 16 a Ne ES) (ON MORO 96 FREQUENCY OF WAVE CONDITIONS SOUTH INDIAN OCEAN The seasonal alternation in the prevailing state of the sea is of the same order in the South Indian Ocean as in the North, i. e., it is high the oftenest in northern summer, when the northern boundaries of the Southeast Trade Wind Belt and of the Westerlies have both reached their most northerly limits for the year; when the average velocities of both these wind systems are at their highest; and when gales of force 7, or stronger, are the most common in high latitudes. The sea pattern (pl. XVII) exhibits a rather definite north-south alternation in midocean at this time of year. In the equatorial belt of calms, the sea is high for generally less than 5 percent of the time; in the axis of the Southeast Trades Belt, a high sea is reported in frequency greater than 10 percent (greater than 20 percent of the time where the Trades blow the strongest) and 20-foot waves have been reported 3 percent of the time for the year as a whole (table 8, p. 21) ; in the Variables, the frequency of high seas averages somewhat less, though varying widely as reported from square to square; and finally, along the northern edge of the Westerlies, the sea has been classed as “high” in 20 to 50 percent of the reports for July and August, together. It is also likely that the sea runs higher than-8 feet for more than half the time along the main sweep of the Westerlies, right across the southern Indian Ocean, from the offing of South Africa, past south- ern Australia and Tasmania; waves of 20 feet, and higher, have been reported from another source (table 8, p. 21) in 17 percent frequency, for the year as a whole on the route between the Cape of Good Hope and southern Australia. The chief departures from this fundamentally latitudinal pattern are: (a) the sea is much less often high (only occasionally so reported) and much more often low (54 to 90 percent, pl. XVIII) in the waters between northwestern Australia and the East Indian island chain to the north than it is farther westward in this same latitudinal belt, where the Trades are better developed; and (6) neither of the two relatively smooth belts—the equatorial and that of the Variables— extends westward as far as the African coast, though high seas are hardly more common there than they are in midocean, at correspond- ing latitudes. The swell runs high much more often in northern summer than the sea does, throughout the South Indian Ocean as a whole, notably along the Southeast Trades from the approximate longitude of northern Sumatra (95° E.) to Madagascar (overage 37 percent for high swells, and about 18 percent for high seas) ; this is no doubt due to the same reason that the Trades swells are high more often than the Trades seas in other parts of the oceans (pp. 79 and 85). And a high swell often ERS Ot hg ia I ee Be SOUTH INDIAN OCEAN Q7 spreads (locally up to 73 percent frequency) northward from the stormy Westerlies to the more placid Variables, where high seas, lo- cally generated, are much less frequent. The slackening of the Southeast Trades that takes place in northern autumn, during their migration southward, is accompanied by a cor- responding alteration in the prevailing state of the sea, so general that the regions, within the Trades, where a high sea is reported in frequency as great as 10 percent, are not only much less extensive in January and February than in July and August, but appear to be confined then to discontinuous pools. A high sea has, however, been reported considerably more often in January and February (22 to 33 percent) than in July and August (10 to 24 percent) off the north- western bulge of West Australia, where the winds of northern winter average somewhat stronger (14 to 16 knots) than those of summer (less than 12 knots). The period from January to March is also the chief season of tropical cyclones in the South Indian Ocean. Storms of this character then develop most commonly southward and eastward from the Seychelles in about latitude 10° S., and follow a southerly course, most of them passing east of Madagascar, but a few crossing the island, or following the Mozambique Channel. This is illustrated by the storm tracks laid down on the Pilot Charts for January and February. Tropical cyclones may be responsible, at least in part, for the rather large frequencies in which high seas are reported in winter southward and eastward from Madagascar (10 to 16 percent). But the chance of encountering the heavy seas they generate on any given voyage is small, judging from the fact that only 139 of a dangerous character, or about 3 per year, were reported for these months during the period from 1848 to 1891. Unfortunately, the winter reports from the northern edge of the West Wind Belt have not been numerous enough, nor distributed evenly enough, to be of much significance. But gales are so much less frequent there in northern winter than in summer as to suggest that 20-foot seas are not to be expected more than half as often from Decem- ber through February, as in June, July, or August, along the steamer route between South Africa and South Australia, where their reported frequency is 17 percent for the year asa whole (table 8, p. 21). It seems further that a heavy swell is not as common along the northern edge of the Westerlies in northern winter as it is in sum- mer for the available percentages, derived from scattered data along the route between South Africa and southern Australia, locate the northern boundary of the area where a high swell is to be expected as often as 40 percent or more of the time, in January and February, as lying to the southward of latitude 40° S., except off South Africa and 98 FREQUENCY OF WAVE CONDITIONS off South Australia, or something like 300 miles farther south there than in July and August. The alteration that takes place in northern autumn in the prevailing state of the swell is, however, so much smaller in the southern Indian Ocean than it is in the northern, that the winter gradation, along any longitudinal belt that might be chosen, is regularly from a small- er frequency of high swells and larger frequency of low, in the north, to a greater frequency of high, and a smaller frequency of low in the south. In northern summer, by contrast, a high swell is most com- mon in the extreme northern part of the Indian Ocean, on the one hand, and in high southern latitudes on the other, and least common (and with the swell most often low) along the equatorial belt in general and, locally, in the Mozambique Channel. The seasonal alteration, from northern summer to winter, in the state of the swell relative to that of the sea, is summarized in table 26 for the relatively calm belt between the equator and latitude about 5° S., as well as for the axis of the Southeast Trades which, roughly speaking, are the best developed between about latitudes 10° S. and about 20° §. in northern summer, but between about 15° S. and about 25° S. in winter. TABLE 26.—Average percentage frequencies of low and high seas and swells in the South Indian Ocean, along the equatorial belt and along the axis of the Southeast Trades, in northern winter and summer Equatorial Belt Southeast Trades Season Seas Swells Seas Swells Low High Low High Low High Low High Percent) Percent| Percent) Percent| Percent| Percent) Percent) Percent 73 1 78 42 8 47 18 14 29 16 32 31 January-February ----_---.---------- Ey ANS ee eee 57 1 55 ‘RIBP JUDLINSUT YIM vsot} oan IHURYVW Go, vy) Ul pure ysnsny ur oyurpy 00d rue) 00d is Pr Vv SRaIv poJUyUuQ Ysnsuy pure Ayne ut WION OY} Ul Sves YSIY JO UOT|NGLUSI—'] "Id oO 009 ‘008 oOOT / q a rs 3 0Z eee 00 sas fe) = er O << Re A a 5 OZ 4 ae od = ea Ov = has A ° ) i bug * ei 0oOV ae ol ae a4 gual Et 2 o> ) ee é pave ies ms 009 : aa 0 O09 002 ale 00g oOVv 009 008 oOOT 226794 O - 53 - 8 “RIVP JUSLIJNSUT YL asoyj a8 Stade paJUyUQ “Jsnsny pure Ane ul ONULPY Wnog ay] ur pue ysnsny UL oVUNpY GON oy] Ul Svos Mol Jo UONNGLUSIG— TT eld oOv 009 008 oOOT Ze) 002 ~ or Ps = is oOV ‘RIBP JUILUJNSUL IIA vSOU} of SRate payuyU.) 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Any type of wave that moves shoreward, or even parallel with the shore line, may produce a surf; whether it will actually do so, in any given case, depends on various factors to be discussed below. In considering surf, it is therefore necessary to include storm waves that may be generated by high winds blowing at the time and place, and also swells that may have come from a long distance, for it is not unusual to encounter a heavy surf in calm weather as well as in stormy. An observer standing on the shore is in an excellent position to judge the state of the breakers, and most of the published discussions of surf have been from the standpoint of the landsman in relation to engineering problems, such as the construction of breakwaters and sea walls, for example, or in relation to the erosion of coast lines: In the following account we attempt to present the matter from the standpoint of the man at sea, who may have occasion to bring landing craft in to the beach through the surf, or out again through it. THE IMPORTANCE OF SURF Breakers, when seen from the seaward, never seem as dangerous as they really are, because a view of their backs gives a very inadequate idea of their heights or steepness; what appears to be a mere swash on the beach, when seen from offshore, may actually be a very dangerous surf indeed. (This point is emphasized in Knight’s Modern Seaman- ship,” a book with which every ship’s officer ought to be familiar.) A heavy surf also carries an enormous power of destruction; any sea- man knows that no one can hold his footing on the deck if it be swept by heavy breakers. A general knowledge of the characteristics of surf, and especially an ability to forecast its height, is therefore of great importance in *t Knight, A. M. 1945. Modern Seamanship. 11th ed. New York. p. 388. 226794 O - 53 - 10 99 100 BREAKERS AND SURF landing operations, for to attempt to bring a boat in through heavy breakers may well be fatal. Surf is also one of the chief factors that must always be taken into account in the construction of breakwaters, of sea walls. of piers, or of other installations on shore lines that are exposed to it. The planning of these structures to withstand the force of the breakers taxes the resources of engineering to the utmost; and even so, severe damage may occur. The energy of a wave is of a twofold nature: (a) “dynamic,” or “kinetic,” whichever term may be preferred, resulting from the com- bined momentum of the innumerable water particles of which it is composed, and (6) “static,” or “potential,” due to the elevation of the center of gravity of the wave crest above sea level—to its “head,” in other words. Half its energy is dynamic, the other half static, with its total energy proportional to its length and to the square of its height.” The total energy, for example, of a wave 500 feet long and 10 feet high is 400,000 foot-pounds per linear foot of its crest; and a wave 200 feet long and 6 feet high would carry an energy of 57,600 foot-pounds per foot at its crest. The total energy of a wave is slightly lessened when it comes into water shoal enough to alter its form. On the other hand, a consid- erably greater proportion of its total energy then hes above stiil water level and moves forward with the wave form; it is largely for this reason that the destructive power of breakers is so great. (For fur- ther discussion, see Gaillard, 1904, pp. 45 and 135-186, pl. 5.) Many measurements have been made with dynamometers, of one sort or another, in the breaker zone along different coasts; these may be typified by the following readings, taken at Skerryvore Rocks, and at Tyree Island, off the west coast of Scotland, in 1845 (table 27). (For a general discussion of the pressures exerted by breakers, see Gaillard, 1904, pp. 124-134 and 145-211.) During the two previous years, the readings averaged 2,086 pounds per square foot in winter, 611 pounds per square foot in summer, a difference that obviously re- flects the seasonal difference in the sizes of waves there. The observed values summarized in table 28, for Florida and for Lake Superior, are a further example of the relationship between the dimensions of breakers and the pressures they have been found to exert. Further- more, dynamometers of the types used in the foregoing experiments measure only the dynamic pressures of the breakers, not the static, 1. e., they record only a part of their energy. % According to the equation E=% WLh?, where E is the total energy in foot-pounds per unit width of the crest in one wave length, W is the weight of 1 cubic foot of sea water, L is the wave length in deep water, and h is the wave height. For an extensive table, giving the force exerted by deepwater waves of different sizes and shapes, see Gaillard, 1904, p. 41 and O’Brien 1942, p. 14. IMPORTANCE OF SURF 101 TABLE 27.—Pressures of breakers on west coast of Scotland, in 1845, as recorded by spring dynamometers {From Gaillard, after Stevenson] Dynamometer sie sas readings Supposed height of waves (feet) Conditions of sea (pounds/square feet) inner ee ea USE er yk el NS Swell@s2 hk ae eee 3,041 Ue eae seh ES eee A ee eee Groundiswelle2 25.) ee 3, C41 ee en eee A ee A a See e Le j22i STs ie Heavyisca. ae). Se Ete 4, 562 Fe a ee ee ne Se ee EL wed ne EB ee Strong gale, heavy sea ______ 6, 083 TABLE 28.—Pressures recorded on spring dynamometers by waves of different dimensions. The first three wave heights (2 to 6 feet) were for the breaker zone at St. Augustine, Fla.; the last three (12 to 18 feet) were for Duluth Canal, Lake Superior, where readings were taken at two different levels relative to the mean level of the lake at the time {Adapted from Gaillard] Length Maximum : par ie pressure Height of wave (feet) eae + (pounds/square feet) | 148 406 667 | 250-1, 150 1, 335-1, 755 2, 195-2, 370 ‘The force with which a breaker will strike any given object does not necessarily correspond to its total energy; it may, in fact, be very much less, for while the energy of a wave depends solely on its shape and size, the force that it may exert on any obstacle depends on the shape of the object struck, i. e., on how nearly streamline the latter may be, as well as on its size. Thus, a breaker 12 feet high and 200 feet long, which would exert a pressure of 1,600 pounds per square foot on a vertical object lying squarely stransverse to its path, such as a barge lying stranded, side on, in the surf zone, would affect the same barge much less, proprtionately, if she were lying bow on. The obstacles on which waves may beat vary so infinitely in their contours that it is not practical to make exact mathematical calucula- tions of wave force for given cases unless their shapes are very simple. But pressures, such as those tabulated above for St. Augustine, are ample to account for the displacement of concrete blocks weighing 3,600 to 21,600 pounds that actually occurred there during the period of ob- servation, even after due allowance has been made for the shapes of the blocks. And in view of the much higher pressures that have been recorded elsewhere, it is not astonishing that many cases are on record where blocks of stone or cement, or masses of concrete used in break- waters, have been shifted from their beds for longer or shorter dis- 102 BREAKERS AND SURF tances, even up to the almost incredible weight of 2,600 tons, though anchored or fastened in various ways with iron rods. Striking ex- amples, often quoted, are: a concrete block of 20 tons lifted vertically toa height of 12 feet and landed on top of a pier 4 feet, 10 inches above high water mark at the entrance to the canal to Amsterdam Harbor; stones weighing up to nearly 7,000 pounds thrown over a wall 20 feet high at Cherbourg on the southern shore of the English Channel; and —most famous case of all—an enormous mass of large stones set in cement, and bound together with iron rods, the whole weighing 1,350 tons, broken loose and moved bodily at Wick Breakwater, Scotland. (For more extensive discussions of the subject, see Gaillard, 1904, pp. 125-134 and 137-144, and Johnson, 1919.) Engineers concerned with the design of breakwaters, and so forth, find it necessary to reckon with presures up to 2,280 pounds per square foot in the Baltic; 3,450 pounds per square foot in the North Sea; and 4,120 pounds per square foot in the Bay of Biscay (Kriimmel, 1911, p. 118). THE CAUSES OF SURF The underlying cause for the development of breakers and surf is the alteration that takes place in the shapes of waves as these move in shoreward over a shoaling bottom, after they have reached the point where the depth is less than one-half their own initial lengths. This alteration, as summarized on p. 56, consists in a decrease in their lengths, often combined with an increase in their heights, by which their crests are progressively steepened until they break. And waves running toward the shore so commonly advance into water shallow enough to transform them into breakers, that one is apt to forget that the water may continue so deep, right up to the strand, that the drag, so to say, of the waves on the bottom may not be sufficient to steepen them to the breaking point before they actually arrive at the barrier of the shore line. Thus, waves advancing against a steep promontory, or cliff, that rises from water, say, twice as deep as the wave heights, may simply surge up and down against the barrier, breaking not at all or only in a confused manner, unless they strike a part of the barrier where irregularities in its face cause them to do so. It is often easy to observe this phenomenon when small waves are running against a stone or steel pier with sheer walls, and we read that it is sometimes taken advantage of in the construction of break- waters. Surf breaks heavily, however, against sea walls, etc., if the water is made relatively more shallow by the accumulation of sand or gravel at their bases, as commonly happens after a time; in such cases the incoming waves are altered into breakers by the sloping bottom that they meet there. CAUSES OF SURF 103 The refiection back of storm seas from a cliff or breakwater against the next incoming waves may so increase the heights and steepness of the latter as to cause them to break heavily, some distance out from the barrier. But the counterwaves may prevent heavy breakers from developing there at all, if the weather is moderate or the wind off- shore. It has been stated that small boats can lie in safety in the zone of confused but low wave action that results next to the shore line under these circumstances. We can only comment, in this regard, that we have never seen a situation of this sort, except on a very minor scale and when the waves were so small that they were not dangerous in any case. Alteration in length and in velocity over a shoaling bottom.—A wave first begins to show measurable deformation when it reaches by Le b ~ N HEIGHT RELATIVE TO HEIGHT IN DEEP WATER fall ae ITY ee zecined: Vor G WAN ” i) “1.1 1.0 (ees Saale ee eee. ae GE: oa bee ea ead: oe et aoe, anes RES a= ae sere) ee °o 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 DEPTH, RELATIVE TO LENGTH OF WAVE IN DEEP WATER Ficure 21.—Theoretical alteration in the dimensions of waves as they advance over a Shoaling bottom. a point over a shoaling bottom where the depth of the water (measured below undisturbed sea level) is about one-half the wave length from crest to crest. It has long been known that the lengths of waves are progressively reduced in their further progress from this point on- ward, so that they are telescoped together, as it were, as they near the shore. The reduction that takes place in the lengths and in the velocities of waves over a shoaling bottom is usually given as proportional to the square root of the depth of water. Recent observational as well as theoretical studies, however, have shown that the situation is much more complex than this, and especially that the decrease in the length of a wave, and hence the increase in its steepness, is much more abrupt as the wave approaches the shore line than was held by the older 104 BREAKERS AND SURF view. It is perhaps of equal interest that the relationship between lengths and velocities that applies to waves in deep water is altered as they run in over a shoaling bottom, with the result that waves that differ widely in length tend to run at similar velocities as they near the breaker line. This is illustrated in figure 21, from which the pro- portional alteration in length and in velocity of a wave can be read directly at different points in its advance over shoaling bottom. The relationship is also summarized in table 29. TABLE 29.— Decrease in lengths and velocities of waves of different dimensions as they advance over a shoaling bottom Waves Depth of water ex l 7 (feet) Length | Velocity | Length | Velocity | Length | Velocity | Length | Velocity (feet) (knots) (feet) (knots) (feet) (knots) (feet) (knots) 1, 000 42.5 500 30.0 250 2122 100 13.4 1, 000 42.5 500 30.0 250 PAL 100 13.4 710 30. 2 445 26.7 248 21.0 100 13.4 635 27.0 410 24.6 240 20.3 100 13.4 530 22. 5 355 PN bss 222 18.9 99 13.3 380 16. 2 2ii5 15.9 178 15.0 93 12.5 240 10. 2 170 10.2 120 10. 2 71 9.5 Perhaps the most interesting rule illustrated by table 29 is that longer waves are slowed much more, relatively, as they advance shore- ward, than shorter ones are, by the time they reach the surf zone. If, for example, this zone were along the 5- or 6-foot contour, as it often is in moderate weather, waves 50 feet long would be still advancing at about 70 percent of their original velocity when they broke, but waves 200 feet long at only about one-fourth the initial velocity, i. e., at about 5 knots. It is for this reason that breakers, caused by a long swell, so often seem to hang almost stationary for the few instants before their crests fall forward. The fact that waves are slowed down by the effect of the bottom can be used to great advantage in determining water depths off an in- accessible coast. Overlapping aerial photographs are taken at short, accurately known intervals of time. From these, the rate of advance, or velocity, of several wave crests is measured. By applying the rela- tionships between wave velocity, period, and depth of water, the depth is then found. It is pointed out, on page 32, that the simple relationship between velocity, length, and period holds only for waves that are very low, relative to their lengths, and that steep waves travel a little faster than would be indicated by the simplified equation (See footnote 7, p. 32.) When waves run into shoaling water and steepen further, the increase in their heights seems to oppose their tendency to shorten, the result CAUSES OF SURV 105 being that they run a little faster than might be expected of lower waves of the same length. In extreme cases their velocities may increase in this way by as much as 10 percent, but usually the effect is much less than this. It is commonly stated that the periods of breakers on the shore are the same as those of the waves out in deeper water, since the reduction in the velocities and in lengths of the latter, over the shoaling bottom, are in at least approximately the same ratio. Any other condition would require either the development of entirely new waves or an accumulation of waves, or the complete disappearance of some of the waves during the last part of their advance shoreward. On the other hand, it has recently been reported, from observations taken with a special wave meter, working semiautomatically, that the periods of waves advancing over a shoaling bottom usually increase— and by a maximum of 25 percent—but with some of the readings showing a small decrease.* Similarly, the average periods of the waves a short distance offshore were reported shorter by about one-half’second than those of the breakers 34 percent of the time, but larger 22 percent of the time, dur- Ing a series of 38 observations off the island of Martha’s Vineyard. And the periods of small breakers, watched by us on another recent occasion, averaged 3 to 4 seconds when the waves half a mile out from the land had averaged only about 25 feet long shortly previous, which corresponds to an average period there of only about 2.25 seconds. We believe, however, that an explanation for these discrepancies can be found in the conditions under which observations are likely to be made. When there is an old swell, with younger and shorter waves running on top of it, as is often the case, the breakers from the larger waves may swamp out or obscure the smaller ones before these reach the point where they would break. In such cases, the periods would average longer for the breakers than for the waves farther out. On the other hand, when the sea is irregular and confused, some of the waves are likely to be overlooked offshore, even if they do not differ greatly in size; but since they, too, would develop nonetheless into definite breakers, the periods for the latter would be shorter than the apparent periods of the waves farther out. The individual periods of any given run of breakers always differ considerably from one to the next, as do those of the waves offshore, because of the variation in length among the latter. The following tabulation of observations, made recently at South Beach, Martha’s Vineyard, may serve as an indication of monthly variations for the northeastern coast of the United States. % Tvanov, A. A. 1938. On the propagation of waves near the coastline. (In Russian.) English summary. Izv. Akad. nauk. ser. geogr. geofiz. pp. 490-491. 106 BREAKERS AND SURF Irregularities, however, of the sorts just cited, do not vitiate the underlying rule that the periods of waves that preserve their identity are at least approximately the same when they break as when they are farther out. Consequently, if one times the intervals between suc- cessive breakers, as can easily be done on any ordinary watch that has a second hand, one can at least roughly calculate the lengths that these same waves had while they were still out in deep water or vice versa, and many calculations of this sort have been published for various parts of the world. Average periods, for example, of 8 to 12 seconds, for the waves included in table 30, correspond to lengths of about 328 feet to about 737 feet offshore, and an average of 10 seconds between breakers timed by us on the southwest coast of Ceylon, January 1902, corresponds to an average wave length offshore of about 512 feet. TaBLE 30.—Freyguency distribution of waves of different periods at South Beach, Marthas Vineyard, from observations made between January and April 1944. Each case is the mean of 20 consecutive waves Mean period in seconds Monthly Month mean RNUARY = a oSanas~ == 2 2 15 13 7 11 7 tl eee tia) eee 1 9.4 Mebruary...2--s=== 2624 |p = 2 3 6 5 13 12 7 2 3) |-aae52 Eee 10.4 AVhay Ghose eee a a 5 12 9 12 7 1 1 a fees 9.8 INDrile acs sao eee 1 6 16 13 10 2 e322. |2 2S eee eee 8.7 Totalcases..----=---=- 3 16 49 40 42 32 16 3 5 2 tNB) eee 2 Frequency (percent) - 1 8 24 19 20 15 8 1 3 1 1 il] Ses eee Se It is fortunate for anyone planning to land through the surf that the period of a wave does not alter as it nears the land (unless by its union with another), for thanks to this fact, measurements of the pe- riods of waves offshore, which are comparatively easy to make (p. 61), give at least a rough indication of the periods between breakers on a neighboring beach. And this is a matter of some practical im- portance, for the longer the time interval is between successive break- ers, the easier it is to bring a boat in through them, or to go out again from the shore. Alteration in height over a shoaling bottom.—The most important feature of breakers to anyone who has to land through them is their height. And it has been known to seafarers, doubtless since the days of the Phoenicians, that swells often grow considerably higher just before they break. The most noticeable alteration in their heights as they move in over a shoaling bottom is thus the reverse of what occurs for their lengths and their velocities. It is not so generally known, because only recently discovered, that this increase in height is preceded by a very small initial decrease, which begins when the depth is about one-half as great as the length CAUSES OF SURF 107 the wave had offshore. The wave regains its initial height when it reaches the point where the depth is about 0.06 as great as its own initial length, after which it becomes higher than the height offshore (fig. 21). It is the initial length of the wave and not its height that determines at what depth, i. e., at what point over the bottom slope, its shape be- gins to change. A relatively long wave suffers greater deformation than a relatively short one, because the alteration continues through a greater range of depth in the first case than in the second. Conse- quently, it is the initial steepness of the wave (i. e., the ratio between its length and its height while still out in deep water) that determines whether the increase in height that follows the initial decrease will more than counterbalance the latter or not and, hence, whether the wave will be appreciably higher at the time it breaks than it was originally. Under most conditions on open coasts, breakers are high- er than the waves. The following example may help to make this clear. Assume two series of waves, both of them 2 feet high out in deep water, but one series 500 feet long, the other only 100 feet. Measurable deformation of the longer waves would commence when they reached a point where the water was still about 250 feet deep. As they advanced shoreward, their heights (after the slight initial decrease) would theoretically increase to 2.1 feet by the time they reached the 20—foot belt, to 2.7 feet by the time they reached a point where the water was about 7 feet deep, and to 3.5 feet at the 5.5-foot line, where a wave of this initial steepness might be expected to break. The shorter waves, however, would continue their progress unaltered until they reached a point where the depth was 40 feet, would decrease to a height of only about 1.8 feet by the time they reached the 15-foot line, would then build up again to the original height of 2 feet by the time they reached the 5-foot line, and to 2.3 feet at the 3-foot line, where they might be expected to break. 34 The change in wave height is brought about by two opposing actions which may be ba ZC. where H is the height at the selected point in shallow water, H, is the height in deep water, C and C, are corresponding values of wave velocity, and n is a complicated function of depth and wave length: (4) 1 oe a Nh E d sinh (4 ¢) where d is the depth of water, and L is the wave length in deep water. The first action tends to decrease the wave height by making the value of n increase. But meantime the wave velocity and hence wave length is decreasing, which causes the crests to peak up. As shown in the equation, when C/C, decreases the relative wave height must increase. The resulting effect of the two opposing actions, therefore, is to cause a small initial de- crease in the height followed by a rapid increase, until the wave becomes unstable and breaks. The initial decrease, first theoretically predicted (O’Brien and others. 1942. Techn. rep. U. S. Beach Erosion Board. No. 2. pp. 35-37) has been confirmed by tank experiments and also by observations at the Scripps and Woods Hole Institutions. represented in an equation 77= 7, n= 108 BREAKERS AND SURF In general, waves that are less than 10 to 15 times as long out in deep water as they are high, are only about as high when they break as they were offshore. But relatively longer waves may increase considerably in height. At South Beach, Marthas Vineyard, for example, the ratio at the 80-foot contour, and at the time of breaking, between the measured heights for waves of different degrees of steep- ness has ranged between 1:1 and 1: 2.2, while ratios of 1:1.1 to 1: 1.9 have been recorded at La Jolla, California, between waves offshore and the breakers caused by them. And the increase in height may be considerably greater yet in the cases of very long swells; in fact, an old swell that is relatively so low out over deep water as to be hardly perceptible, but very long, may mount to such a height during the last few yards of its advance as to cause a dangerous surf, even in calm weather. And it is during calm or moderate weather that the height of surf is chiefly of importance in landing operations. It is much easier to measure the periods of waves than to measure their lengths. The alteration in height on a gently sloping bottom is therefore summarized in table 31 for waves of representative sizes, according to their periods. TABLE 31.—Heights (to the nearest foot) attained by waves, of different initial heights and periods, at various depths on a gently sloping bottom. Blank spaces indicate that the waves would, in all likelihood, have broken in deeper water, or that waves of the stated shapes could not exist. This table is derived from figure 21 and is based upon theoretical studies, substantiated by measurements of waves taken at the Scripps Institution of Oceanography and at the Woods Hole Oceanographic Institution Period of Depth of water (feet) Initial height of wave (feet) wave. [a (seconds)| 39 25 20 15 10 5 It appears, from published observations, that the height of the surf may even be several times the preceding height of the waves in CAUSES OF SURF 109 special situations where the slope of the bottom steepens very abruptly from deeper water, as in the case of cliffs and of breakwaters. Masses of water may then spout high into the air, or up on the shore, as happens frequently against isolated rocky islands or ledges, along the steeper parts of the offshore faces of coral reefs, against light- houses, against breakwaters, over submerged ledges, and also against the nearly vertical walls of the antarctic ice barrier, where the depth of the water may be measured in hundreds of fathoms. In fact, it is not unusual for sheets of water—not just foam—to spout more than a hundred feet into the air under such circumstances (for examples, see page 120). Alteration in steepness—A wave advancing into shoal water not only becomes steeper as a consequence of its decrease in length, com- bined in most cases with an increase in height, but it does so very abruptly just before it finally breaks. Anyone who has occasion to come in through the surf in a small boat has this fact impressed upon him, for his boat, which may merely rise and fall bodily with the longer swell offshore, is pitched up more and more steeply as it rides in on the back of a chosen roller, until her bow may be lifted far above her stern just before the breaker develops. This point is discussed in further detail on page 110. Alteration in the orbital velocities of the water particles—The orbits around which the water particles move are circles in deep water, but become elliptical, with their larger axis horizontal, when a wave runs into water shoaler than one-half its own initial length (p. 00, fig. 3), and the ellipses become more and more flattened as the water shoals, until the water particles in contact with the bottom simply move to and fro in straight lines. The velocity at which the water particles move around their orbits—uniform while these are circular— is no longer so after they are transformed into ellipses, but is greatest near the crest and the trough. This discrepancy between the velocities along different parts of the elliptical orbits increases as the eccentricity of the orbits increases with the advance of the wave into shoaler and shoaler water, for it is proportional to the length of the major (hori- zontal) axis of the ellipse.** And since the transformation of the orbits from circles to ellipses consists in an expansion of their hori- zontal axes, with their vertical axes changing only as much as the height of the wave, the velocity with which the water particles ad- vance in the crests and recede in the troughs grows greater and greater as the wave advances into shoaler and shoaler water. The orbital ve- locities, for example, in the crests and troughs of a wave 15 times as , % According to the equation V’’= ae where V’’ is the orbital velocity along the part of the ellipse where it is at its maximum, a@’ the half-length of the major axis of the ellipse, and T the period of the wave. 110 BREAKERS AND SURF long as high should, theoretically, be almost twice as great when it reached the point where the depth was one-tenth as great as its own initial length (and where it might be expected to break) as they were to begin with. And the longer the wave, relative to its initial height, the greater is the increase that takes place, in this way, in the hori- zontal velocities of its water particles. (This summary has been drawn from Gaillard, 1904, pp. 41, 97, 135-136, pls. 1 and 5.) The water particles at the crest of a wave may thus be moving forward several times as fast, when it is about to break, as they were originally. The question of the orbital velocities at the top of the crest at the instant of breaking has not received as much attention as it deserves from a practical standpoint. But anyone who has had experience in surf knows that any object, such as a plank or a small boat floating on the top of a roller, may be swept forward with astonishing rapidity just as the top of the crest falls forward, if the breakers are of the plunging type (p. 111). And this is one of the reasons why it is so difficult to bring even a surfboat in through high breakers, for it is likely to be carried forward over the crest unless it is well handled, to be pitched down bow foremost into the trough ahead, where it will be in imminent danger of broaching to, as its stern continues to be swept forward in the air, or at the least of filling with the water that pours down upon it from above. Surf running of this sort should never be attempted in small boats, except as a last resort. THE CHARACTERISTICS OF BREAKERS The breaking of waves out in deep water appears to be caused chiefly by the pressure of the wind, which forces the backs of their crests ahead faster than their leeward sides are advancing, until they come to overhang the troughs. Asa rule, it is only the very top of the crest that falls over. Typical breakers on the beach, however, are not caused directly by the wind (although the wind may aid in their formation, if it is blowing strongly onshore), but by the alteration of the wave forms that takes place over shoaling bottom, as described above, by which the waves grow steeper, until they be- come unstable. It is commonly stated that it is the friction with the bottom that causes this alteration in shape by retarding the lower part of the wave, while the upper part continues to advance. But experi- mental studies of waves have failed to show that a frictional effect is of importance. Neither is the developing profile of a breaker what it should be if friction were the sole cause, for its front becomes hol- lowed as the crest steepens, suggesting, rather, that it is a deficiency of water on the front side that causes the crest to overhang the trough in front of it, and consequently to fall forward. BREAKER CHARACTERISTICS Let The breakers that develop over evenly sloping beaches are of two chief types, if the wind is not strong enough to interfere with what may be termed their “normal” development. In the one type, the back of the wave continues well rounded up to the instant of breaking (Figs. 22 and 23), whereas its front may become so deeply hollowed that a swimmer, standing on the beach directly in its path and ready to dive through it, may be able to look up for an instant through a sheet of overhanging water, before his head is submerged. The wave forms are very greatly reduced in the act of breaking when the break- ers are of this type, which may be named “plunging.” And the event occupies only a few seconds—unless, indeed, the wave is coming in at FicureE 22.—A breaker of the plunging type, on the coast of New Jersey, showing different stages of development along different parts of the crest. (Woods Hole Oceanographic Institution photograph. ) an angle with the shore, in which case it begins to break first at its inshore end, and does so progressively outward along its crest as the latter continues to advance, as is illustrated by the aerial photograph reproduced in figure 24. In breakers of the second type, the backs of the crests, as well as the fronts, become concave as they near the breaking point, so that they more nearly resemble the profile of the steepest possible wave (fig. 25), a shape known technically as “cy- cloid.” When the tops of their crests final rise to the angle of instability they do not simply fall forward as do the “plunging” type, but they break continuously (but only along their very tops) as they advance, gradually losing in height by the loss of water from their crests as they near the shore. These may be termed the “spilling” type. We were fortunate to be in a position to watch the development of both these types of breakers on a recent occasion, while looking out 112 BREAKERS AND SURF over a gently sloping beach from a rocky promontory. An old swell was heaving in, the individual members of which were so low that they were not recognizable offshore but which grew to heights of 114 to 3 feet at the breaker line. Those that rose the highest were of the plunging type, but the smaller ones were of the spilling type, and in many cases one part of a single wave crest developed as the one type, FrcuRE 23.—Oblique view of a breaker of the plunging type on the coast of New Jersey. (Woods Hole Oceanographic Institution photograph. ) another part as the other; or a “spilling” breaker might either follow or precede a “plunging” one. Long, gentle swells—initial steepness (H:L) less than 0.005—com- monly produce breakers of the plunging type, especially when the wind is blowing offshore, while waves that are less than 100 times as long, offshore, as they are high, often produce breakers of the spilling type, especially when the wind is blowing onshore. But individual — 113 BREAKER CHARACTERISTICS APTISUBIIO 7V Y MN ? se Iq eu] uo X] oubiyqo iJ oO u (Cyd Il > ’ ad Iq 1soj}oyd AACN ‘SQ I ‘USI Joos € JNoGe ‘od o Iq JO yn a oO ojoyd [e ! Iay— FG o a 1 1 1 1 dI “ J BREAKERS AND SURF 114 Cydvasojoyd paunsy suo.) “Ss 71) ‘pog aduQ Jo Jsvod tejno ay} Uo ‘ad4} SurSunjd oq) Jo oud Sulpoooad ‘odsy Ssurppids a} JO aoyvoaiq We AIA mRt Ye Fy LENA NTE DT PHT bt yon Satna x WAVES OF TRANSLATION 115 breakers may share the characteristics of both the plunging and of the spilling types, for while they resemble the former in their general development, the break does not involve enough of the crest to lower the wave form much (fig. 26). The wave then steepens again in its further advance up the shoaling bottom, breaks partially for a second time, and sometimes for even a third or a fourth time. Breakers of this sort may be termed “intermittent”; they are seen very commonly during onshore storms. WAVES OF TRANSLATION In this connection, it is necessary to mention a very different sort of wave that develops when a wave breaks some distance out, whether on a gently sloping bottom or over the seaward margin of a submarine terrace, for the mass of water that falls forward from it, and that is suddenly added to the comparatively level water surface in advance of it, often sets up a secondary wave of permanent form. Such a wave consists of a crest with precipitous foaming front, and without any trough, so that the water particles all move forward together—hence its name, “wave of translation” (fig. 27). But it seems that the foaming crests of this sort commonly seen almost always represent a combination between these waves of translation and whatever rem- nants of the original wave may still persist, for it is often easy to see that the general advance of the bits of foam is combined with an oscillating movement, forward and back. On a calm day there may be anywhere from 1 to 4 or 5 lines of these combined crests, decreasing in size shoreward, between the innermost heavy breaker and the beach. And they may advance, unaltered, as a secondary, low surf for long distances, perhaps for as much as a mile if the slope is gentle. They are very characteristic in appearance, flat-topped, and with the dis- tances between them many times longer than their own heights. When the form of a wave is largely destroyed in the process of breaking, as it often is with a long swell in moderate weather, the only other breaking waves between it and the beach may be one to several lines of these small crests. But when the undulatory motion of a wave continues after it first breaks, the combination”between it and the waves of translation it produces may cause secondary breakers several feet high, though never so large as the primary breakers farther out. 226794 O - 53 - 11 BREAKERS AND SURF 194NQ ‘ad Ay Sursunytd Cydvas0jzoyd preny ysB0D “§) “POD adey jo 4sBoo ay} jo szayjoue Zurpeooid ‘sadAy Suypids puew sursund oy} UseMzoq 9}BIPOUttopUl ‘qayBolg Y—'9Z AWAD 117 WAVES OF TRANSLATION UO Your ? , oq i vo uldoy s (ydvasojoyd uolynyysuy orgdrasouvasg aeV_-SpooM) “poo adr Ayj}ues & dn TayV d1q & SUIpsdeid u0T}B [suv 1} JO VACA pedoye Aap Il9 @) M ®B JO 4sa 1d SuUIUIB JO JsvOd 19]N0 ayy OF 8IqU L— LG aan DI w G Vila ove 1 if Beh) p 4 . sy ; Tt . - , a) , 0 a i | : : ® | Chapter 7 THE CHARACTER OF SURF UNDER DIFFERENT CONDITIONS The character of the breakers that will develop at any particular place on the coast, at any particular time, for waves of given heights and lengths—or even whether there will be any breakers at all—de- pends on local factors. Among these the general contour of the bottom, the presence or absence of obstructions offshore, the nature of the coast, the stage of the tide, the strengths and directions of currents, and the direction and strength of the wind all play their parts. or 4 —— % —_— = bid rm ae 7 eae of pg eat emi Ss LoS —a _ em ae = ee ae FIGURE 28.—The heavy surf of November 22, 1944, at Winthrop, Massachusetts, beating against the water front boulevard to which it has done great damage. (Photograph, courtesy of Edward R. Snow.) THE HEIGHT OF SURF Rough estimates of the heights of breakers are apt to be too high, so impressive a spectacle is a heavy surf. It is also important to distinguish between the heights of the actual wave forms at the in- stant of breaking and the height in the air to which sheets of water may be cast when surf beats against steep ledges, sea walls, cliffs, or breakwaters, for the breakers may spout to almost unbelievable heights in severe storms in situations of these sorts (fig. 28). And 119 120 CHARACTER OF SURF it is these that have been stressed the most often in published accounts, because of their importance from an engineering standpoint. In severe easterly gales, for example, masses of water sometimes entirely envelop Minot’s Lighthouse, a 97-foot tower standing on an ott-lying ledge in the southern side of Massachusetts Bay (fig. 29) ; we have seen it do so, ourselves. The bell has been broken loose by the surf at a height of about 100 feet above sea level at the Bishop’s Rock Figure 29.—Aerial photograph showing the surf almost wholly enveloping Minot’s Light, Massachusetts, during the gale of January 12, 1941. (Photograph, courtesy of Edward R. Snow.) Light, England; the light tower has been broken in at an elevation of 195 feet on the Island of Uist in the Shetlands; the glass in the lamp has been struck at an elevation of 158 feet at Tillamook Rock Light- house on the coast of Oregon, where on February 11, 1902, water from the surf fell back in solid masses upon the roof of the dwelling at a height of 200 feet above the sea. (See Johnson, 1919, for a long list of happenings of this sort.) And we, ourselves, from the United States Fisheries steamer Albatross, December 14, 1904, saw the surf from a low swell, topped by a moderate sea, breaking right over the lower parts of the islet Sala y Gomez, in the southeastern Pacific, with sheets of spray flying even over its highest parts, some 80 feet above sea level. Spray spouting upward over steep submerged ledges is also HEIGHT 121 a common spectacle off many coasts, but spouting takes place off beaches only when breakers come together. Surf of this sort is not of immediate concern as regards landing operations in any case, be- cause no one in his senses would attempt to come in through the break- ers under the conditions of wind and weather and of coast, under which it develops. In general, the height of the breakers depends on the height and steepness of the waves offshore, as shown in table 32. The steeper the waves in deep water, the less will be their proportionate increase in height before breaking. The average relationship is shown in table 33, but it must be noted that observations may vary by 25 percent. Moreover, very steep waves may break while the height is still less than the original height. TABLE 32.—The approximate heights at breaking (boldface) and the ranges of depths at which breaking occurs (italic) for waves of different dimensions. It is assumed that the waves break where the depth is from 1.3 to 2 times the wave height at that instant. The heights at breaking are based on studies made at the Scripps Institu- tion of Oceanography and the Woods Hole Oceanographic Institution rd Initial wave height (feet) . engt eas Cy Le ee es eS Period of wave (seconds) Raehore (feet) 4 6 8 10 12 16 20 MenEMEEUERE Bt SS 82 4 6 8 10 | eae (eee aoe E 5-8 8-12 10-16 13-20 16-24 =e apitee (i 5- Se ee ee eee oe 184 8 10 12 18 20 6-10 8-12 10-16 13-20 16-24 21-32 26-40 (hoo a 328 5 11 13 17 20 6-10 9-14 12-18 14-22 27-26 22-34 26-40 i =--4 eS re 512 10 12 14 18 21 8-12 10-16 13-20 16-24 18-28 23-36 27-42 Ee eee eee bt ee SS 738 11 13 15 19 22 8-12 12-18 14-22 17-26 19-30 25-38 29-44 Ch Uw See ee eee ee | 1, 003 10 12 14 16 19 24 9-14 13-20 16-24 18-28 21-3 | 25-38 31-48 Ubige, = <2 Ae SS ee ee ee 1, 310 10 13 15 17 20 25 10-16 13-20 17-26 19-30 £2-34 26-40 32-50 TABLE 33.— Ratio of breaker height to offshore height for waves of different degrees of steepness in deep water Ratio between breaker height Ratio between length and height of wave in deep water and height of wave in deep water 2 VEU: 2 sole ee ee Se a ee eae at te oe oe et eek ee 1.0:1 LIU oile 2 2 SSSR oe ee SE Ss Oe ee ee ee ee ee ee ee See Bea | UU 22a oa eee Re 2s eS ee ee ee ee ee eee ee 1.4:1 15 Te eto oteces bee oe pe ne Se eS as ee ee ee ee a ae 1.6:1 Waves that are 6 to 8 feet high out at sea—a common height in moderate weather—are only of about this same height when they break on the shore, if their ratio of length to height offshore is small. Storm waves, say 15 to 20 feet high offshore, are likely to cause a surf at least 18 to 22 feet high, if their crests are parallel to the coast, though }22 CHARACTER OF SURF somewhat lower if they are coming in at an angle, because of their refraction (as explained on p. 157). And high breakers are also often caused by old swells, for while these are often much lower than the storm waves that engendered them, they are so much longer that they begin to pile up in much deeper water than would a storm wave of equal height. Thus, a swell that was 1,500 feet long (period of about 17 seconds) and 5 feet high would produce a 10-foot surf; and it is not unusual for old swells to produce breakers more than twice as high as their own deep water heights, for this reason. The breakers that form in moderate weather are ordinarily highest at the instant that the overfall takes place, with the precise heights governed chiefly by how high the parent waves are over deeper water offshore, as compared with their lengths there, i. e., on their initial steepness. And since waves vary almost infinitely in their lengths and heights offshore, surf exhibits a corresponding range, from only an inch or two high up to the heights of the largest storm waves. Breakers have, for example, been measured from 2 inches up to 7 feet in height at St. Augustine, Florida (Gaillard, 1904, p. 33) ; from a few inches up to about 13 feet at South Beach, Martha’s Vineyard; and from 114 feet up to 20 feet or so on the coast of Morocco (p. 69), after the establishment of a swell that was fairly consistent in period for a num- ber of hours. Some records of high surf, culled from available data, are the fol- lowing: a. Rollers 12 to 20 feet high have been observed at the Island of Ascension, at the 10-fathom line, during a period of violent surf that was probably somewhat higher than this, because produced by a swell.** b. The heavy swells that run in from storms at sea are described as breaking. about 20 feet high against the coral reefs of the Hawaiian Islands.” c. Near Peterhead, Scotland, measured waves that were 26 feet high and 500 feet long in 7 to 8 fathoms crested and broke along the 514- fathom line, by which time they may be assumed to have attained a height well over 26 feet. d. At Algoa Bay, South Africa, unbroken waves, measured from a staging, were 21 feet high close in to the breaking line, where the depth of water was 23 feet, indicating a deepwater height of perhaps 17 or 18 feet. e. Breakers which damaged the breakwater at Wick Bay, Scotland, were estimated by the resident engineer to have a maximum height of 42 feet. 38 Buchanan, J. Y. 1888. The exploration of the Gulf of Guinea. Scott. geogr. mag., vol. 4, p. 235. 37 Blake, Tom. 1935. Hawaiian surf board, Honolulu, Paradise of the Pacific Press, p. 63. HEIGHT 123 This last instance is the greatest breaker height that we have found recorded in print. But we have no doubt that breakers are sometimes as high as this on the Pacific coast of the United States from northern California to the Straits of Juan de Fuca, where the surf is as heavy as it is anywhere in the world, to judge from the very considerable depths over which it develops there during the stormy season. Thus sea captains of long experience, and local residents, as well as mem- bers of the United States Army Corps of Engineers, of the United States Coast and Geodetic Survey, of the United States Lighthouse Service, and of the United States Revenue Marine Service (the two latter services have since been incorporated in the United States Coast Guard) have reported breakers in depths as great as 42 to 54 feet, and perhaps even to 60 feet on the San Francisco Bar; at 56 to 57 feet at Cape Mendocino, California; commonly at 42 to 45 feet, sometimes at 60 feet on the Columbia River Bar during severe onshore gales; and at 42 to 60 feet at various points along the coasts of Oregon and Washington (for further references to these instances, and to their source, see p. 126). Assuming that the heights of the breakers aver- aged about one-half to two-thirds as great as the depth of water where the surf developed, a ratio usual when the wind is blowing strongly onshore (p. 130), the foregoing instances suggest a surf com- monly 21 to 35 feet high in stormy weather, occasionally 30 to 40 feet high, and perhaps even as high as 45 feet during the most severe gales. And surf no doubt as high, because breaking at depths equally great, has also been reported in the North Sea off the coast of Holland, off the Guianas, and along Yucatan in the Caribbean, as well as in other parts of the world (p. 127). In localities where the state of the sea depends chiefly on the wind distribution nearby, and where long swells traveling from afar are unusual, the surf is usually highest when the wind is strong onshore, as might be expected, and very low or nonexistent otherwise. And the height of the breakers in stormy weather is governed by the effec- tive fetch at the time. The surf, for example, is seldom more than 12 to 15 feet high anywhere along the beaches of the northeastern United States, because it is very unusual for a strong easterly wind to blow (and to persist) over any fixed area of large extent in middle or high latitudes of the western North Atlantic. But a heavy surf may develop, during periods of calm, from old swells on coasts re- mote from stormy regions, or even during periods of offshore wind. if these are not too strong. Thus Wallace * wrote, that at the harbor of Ampanan, on Lombok, in the East Indies “Where we lay anchored, about a quarter of a mile from the shore, not the slightest swell was perceptible, but on approaching nearer undulations began, which 88 Wallace, A.R. 1869. Malay Archipelago, vol. 1, p. 228. 124 CHARACTER OF SURF rapidly increased, so as to form rollers which toppled over on the beach at regular intervals with a noise like thunder. Sometimes this surf increases suddenly during perfect calms, to as great a force and fury as when a gale of wind is blowing.” A moderately heavy surf also develops, similarly, from time to time on the coast of Peru in calm weather, as described many years ago by Humboldt, who ob- served breakers 10 to 14 feet high at Callao, on such occasions. And we can assure the reader that it is no less spectacular a sight now than it was then, as one looks out over the sea, to watch the swells, so small as to be imperceptible offshore, being reborn, as it were, over the shoal- ing bottom in glassy calm weather, and then increasing in height, without apparent cause, until they break. Two examples in the development of breakers of moderate size from a swell so low offshore that the photographs give no hint of its ex- istence to seaward of the breaker line are pictured in figure 30. Nor is it unusual for the breakers that form in this way to be of the same general order of magnitude as the seas are that break out over deep water in windy weather, i. e., as high as 6 to 20 feet, and some- times even higher. The surf that so constantly pounds the exposed faces of coral reefs and islands in the western tropical Pacific and Indian oceans, even in calm weather, are cases in point. The individual breakers that compose a surf always vary consid- erably in height as they succeed one another. Thus it has been esti- mated that the heights of the breakers on the Californian beaches usually vary between two-thirds and four-thirds of their mean heights, which probably applies to breakers from swells in general. And our own observations suggest that the variation is often wider still for breakers caused by storm seas. These variations are due in part to the fact that the individual members of any train of waves always differ more or less both in height and in initial steepness, one from the next, partly because it is a common event in a storm for a train of waves to come considerably larger than the common run (p. 00), and also because two or more waves, or series of waves, ofen unite be- fore they reach the surf zone, whether advancing in the same direction or coming from different directions, so that a breaker or series of breakers much larger than the others may come at intervals. One of 15 feet, observed at Long Branch, New Jersey, February 8, 1944, when the average height during a 10-minute interval was only 4 feet, may have had this origin. And while there is no foundation for the old notion that every seventh or every ninth breaker is invariably the largest, experienced surfmen are well acquainted with the fact that an unpredictable single huge breaker, or a series of such, may develop on days when the general run are low, or of only moderate heights, * Tlumboldt, A. von. 1858. Kosmos, Stuttgart. vol. 4, p. 229. HEIGHT 125 Ficure 30.—Breakers rising 5 to 6 feet high over a bar along the south shore of Long Island, New York, above), and running along a stone pier on the coast of New Jersey (below). In both cases, the breakers are caused by swells so low that they are hardly visible offshore. (U. S. Coast Guard photograph.) 126 CHARACTER OF SURF and take advantage of the series of smaller breakers that succeed a series of larger ones, when coming in to land. A cross sea also renders the surf much worse than it would be otherwise, partly because it disturbs the regularity of the wave pattern, but especially because steep peaks may shoot upward along the breaker zone, when waves coming from different directions chance to join just before breaking, as happens offshore under similar conditions (p. 124). The resulting surf may be so high and so confused that any attempt to land through it would be much more dangerous than an observer offshore would expect, if he did not detect the presence of the opposing trains of waves. DEPTH OF WATER IN WHICH SURF DEVELOPS Waves of moderate steepness, generated in deep water, but then advancing over a shoaling bottom in calm weather, have been found from tank experiments and from field observations on the coast of California to break when they reach the point where the depth is no longer more than about 1.3 times as great as their own heights there, which is close to the theoretical expectation. But common experience in various localities is that the ratio between height of breaker and depth of water where it breaks varies considerably, under different conditions of wind, sea, and current (if there is any). Thus, the surf at St. Augustine, Fla.. has been seen breaking where the depth was only about 0.72 as great as the height of the breakers in some cases, but where the depth was twice as great as the heights of the breakers in others (Gaillard, 1904, p. 120). Measured waves have also been seen to break in depths ranging from 1.3 to 1.7 times as great as their own heights at South Beach, Martha’s Vineyard; in depths 1 to 2.7 times their heights on Lake Superior (Gaillard, 1904, pp. 121- 122) ; and in depths of from 0.9 to 2.0 as great as their own heights at La Jolla, California. Measured waves that were 26 feet high at the 7 or 8-fathom line have been seen breaking at the 514-fathom line (i. e., in 33 feet of water) at Peterhead, Scotland; swells 5.5 to 8 feet high have been seen breaking where the depth was 2.2 to 2.3 times as great as that at Scarboro, England; and ground swells 10 to 12 feet high break commonly where the general low tide depth is about 10 fathoms (60 feet) on Riy Bank off South Africa, sometimes for days at a time. Other striking cases of breakers in water considerably deeper than the probable heights of the waves at the time are the surf often reported at depths of 7 to 9 fathoms (42 to 54 feet), and some- times to 10 fathoms (60 feet) on San Francisco Bar, and on the Co- lumbia River Bar; at 90 feet at Cape Foulweather, Oregon; at 48 feet off Port Orford, Oregon; at 42 to 48 feet between Trinidad and Pilot WATER DEPTH Coe Rock, Oregon; and at 48 to 60 feet near Yaquina and Coos Bays, Oregon. Surf has also been reported over depths as great as 72 feet along the Washington coast, and even at 90 feet there in the most severe weather,*® as it also has in the southern part of the North Sea, where the seas break heavily over Borkum Ridge in depths of 10 to 15 fathoms (60 to 90 feet) during onshore gales. Surf has been recorded at depths of 50 to 56 feet off the coasts of the Guianas; at 56 to 66 feet off Yucatan; at 66 to 100 feet around Madeira; at 66 to 77 feet off Al- geria; also at 80 feet off northern Spain, although a conflict between waves and currents may perhaps have been responsible for some of these extreme cases (p. 51). The instances cited are enough to show that the statement, often made, that a wave may be expected to break where the depth is equal to its own height is not an adequate one; nor does this even apply to the common run of surf. The range of variation which may be ex- pected with waves of different sizes is shown in table 32. The chief reason for the very considerable variation that has actually been ob- served in the ratio between height of surf and depth of water is that waves tend to break in somewhat deeper water with a strong onshore wind than they do in moderate weather, because the direct pressure of the wind against the windward sides of their crests increases the steepness of the latter, thus hastening their overfall. Thus waves, advancing over a bottom slope of 1 in 100, off St. Augustine, Fla., have been described as breaking where the depth was 1.25 times as great as their own heights with a strong onshore wind, though they did not do so in calm weather until they reached the point where the depth was equal to their own heights at the moment. It also appears, from various observations, that waves of equal lengths and heights break in considerably deeper water where the slope of the bottom changes abruptly than when they run in over a uniform slope. Thus, waves may perhaps break where the depth averages about 1.7 to 1.8 as great as the breaker height, where a steep bottom slope is followed by a more gentle one, if the weather is calm and if there is no current. This probably is the explanation for the broken water that is often to be seen along the offshore edges of shoals and of réefs, over depths greater than those at which surf would other- wise be expected with waves of the sizes running at the time. The interference that often develops between trains of waves coming from different directions, also may increase their heights and the steepness of the individual crests, not only causing these to break in considerably deeper water than would happen otherwise, but rendering the breakers so much more complex in pattern, as greatly to increase 40 The information as to the depth of which surf breaks along the northwest coast of the United States is abstracted from a summary by Gaillard, 1904, pp. 115-117. 128 CHARACTER OF SURF the danger of landing if they are more than a few feet high. A very striking example of the geometric nature of the patterns that are produced on shelving beaches in this way, when small breakers come together from different directions is pictured in figure 31. A current (tidal or other) flowing against the wind will also tend to cause waves to break in water deeper than would otherwise be the case, as illus- trated by the aerial photograph reproduced in figure 32, for when a wave meets an opposing current it is not only steepened, but its height is increased as described on p. 53. A strong current may, in fact, be as effective as a shoal or bar in causing large breakers to develop well RO T, 7 5 . al ¥! 4 ? ‘it y : t | Wied 8 Se a i he ; by. 02 . oe ae 7 a y e Na ‘ A A, 9 iy ‘ 4 es mi ie ‘ “ t ‘oe {= he P ‘ F ‘ id. * , ~ ‘ “1; ‘ a : ae) $4 | 4 _ - \ pa ws ; ’ ‘ b jul 5 aot *) 4 . - ' rae if am ae] , a a | , Pr :. a r Ji 4 bg Chapter 8 DIRECTION AND HEIGHT OF BREAKERS IN RELATION TO THE SHAPE OF THE COAST It is much the easiest, and the safest, to bring a boat in end on, if the breakers are large enough to be troublesome, lest she be swamped. Hence, it may be important to know the angle at which the breakers are striking the shore. THE REFRACTION OF WAVES The angle at which breakers strike the shore is governed by the general direction of advance of the waves offshore in relation to the contour of the bottom and to the shape of the coast. Observers not accustomed to surf are often astonished to find that the breakers may be striking the beach at only a small angle, even at times when the line of advance of the waves of swells out at sea is parallel to the general trend of the coast. This is because the inshore ends of the waves are delayed in their advance by the shoaling bottom, as explained on pages 56 and 103, while their crests farther out are moving more rapidly; consequently their inshore ends are bent around or “re- fracted,” as the alteration is commonly termed. It is often easy to observe this refraction, if one looks out over the water of some cove, pond, or river, when a smart breeze is blowing parallel to the shore, and it is shown clearly on photographs taken from airplanes (fig. 45). The amount that a wave approaching the coast is refracted can be calculated, provided that the angle is known that it makes with the coast while it is still in deep water, that either its length, its period, or its velocity is known there, and that the shape of the bottom is also known. The relationship for straight beaches with parallel bottom contours is summarized in table 35. In general, short waves are refracted less than long ones, unless they advance into very shallow water indeed, because they are slowed less, as described on page 104. Old swells are thus bent around much more than younger storm waves are. Table 35 also illustrates another in- teresting point namely, that the surf often breaks on the beach much more obliquely than one might gather from a cursory reading of the literature on waves. A high wave, too, of a given length, suffers less j a 46 The basic formula is: ame =< ; where % is the angle offshore, * is the angle o at any given point inshore, and Co and O are the corresponding velocities. 155 BREAKER DIRECTION AND HEIGHT 156 (‘ydeasojoyd AatN ‘§ “9 TRO) pue jo[sI pue pur [pvey vB puno IB So. AB M Jo ‘BIUAOJITRD ‘puRIS]T sJUeMeIH UBg JB Aeq B OJUT uoTjov IJod ayy B5} ul Moys yde 130}0y4d [Vllay—cF ano REFRACTION 157 refraction before it breaks than a lower one of the same length, because it breaks in deeper water ; hence, it may break at a considerably greater angle with the coast. TaBLE 35.—The angles which breakers make with a straight shore line, when all bottom contours are parallel with the beach, for waves of different degrees of steepness in deep water approaching the shore line at different initial angles. It is assumed that the waves will break where the depth of water is 1.3 times the breaker height Steepness Angle between wave in deep water and shore line of wave in ane water ength: ° ° ° ° ° C) height) 10 20 30 40 50 60 The alteration in the angle between a wave and the coast that results from refraction is both gradual and cumulative, so that the crest be- comes more and more strongly curved in toward the beach. Calcula- tion of the precise shapes of such curves is complex, for it involves the determination of the velocity of the wave at different points along its crest at successive intervals of time, from which the successive posi- tions of these points can be plotted. But the degree to which a wave is refracted over straight and parallel bottom contours can be pic- tured roughly by laying its crest down asa series of short chords cross- ing one contour of the bottom after another, at the angles indicated in table 36, as has been done in figure 46, for a wave, the offshore ends of which are at an angle of 70° with the coast line. TABLE 36.—The angles which waves (approaching at different initial angles) make with a straight shore line in diminishing depths of water (relative to the length of the wave in deep water) Depth of Initial angle of wave in deep water with shore line water in ee terms of Wee net 10° 20° 30° 40° 50° 60° 70° 80° S28ess eosssssso i) 8s ea ta 33 10° 10 9 8 8 7 5 4 4 3 THE LOSS OF WAVE HEIGHT BY REFRACTION Refraction also affects the heights of waves, for when their inshore ends are delayed, while their offshore parts continue to advance un- checked, they are expanded sidewise—are stretched out as it were. 158 BREAKER DIRECTION AND HEIGHT And the inshore ends tend to lost height in consequence, because the energy that the waves carry with them is spread through a longer distance by this alteration. Theoretically, this decrease in height is inversely proportional to the amount of sidewise expansion. And since the amofint by which a wave crest is expanded sidewise in this way depends on how much it has been refracted, it follows that the greater the angle is between the wave in deep water, and the coast, the more the wave tends to lose height as it is refracted around. Table 37 FIcurE 46.—Diagram to illustrate the refraction of waves along a straight shore line, when the wave crests in deep water form an angle of 70° with the coast. The depths of the bottom contours are given in terms of the offshore wave length. The wave crest at the left has been plotted by the simplified procedure described on page 157. The arrows indicate the lines of advance of the waves at successive points along their crests, shows the theoretical loss in height by refraction for waves of different degrees of steepness, coming in at different angles. Multiplication of the heights offshore by the ratio given in the ap- propriate column of table 33 (p. 121) will give the approximate height, at breaking, for waves of varying degrees of initial steepness, coming in parallel with the shore. And a further correction of the heights calculated in this way, using the percentages given in table 37 will #8 According to the equation: H=H,,/{,i where Hy is the height of the wave over deep water; H, its height when it strikes the beach; dlo, the sidewise extent of a given segment of its crest over deep water; and dl, the sidewise extent of this same segment of its crest at any given point during its advance shoreward. But the few pertinent observa- tions indicate that waves which have been refracted through large angles are somewhat higher than indicated by this equation, suggesting a flow of energy sidewise along their erests. There is reason to believe that the effect of refraction is slightly different for waves of different steepness, but the matter has not been studied in detail. SURF AROUND BAYS 159 give the approximate height of breaker, for waves that come in ob- liquely, provided always that the bottom is smooth, with a similar slope off all parts of the beach. Calculations of this sort are not as simple as they sound if precision is sought, because they involve an exact knowledge of the initial ratio between the heights of waves offshore and their lengths—or between their heights and their periods, which last can be translated into length. But it is not difficult to make rough estimates of heights and periods of waves, if the weather is moderate; and estimates of the height of the surf are not likely to be helpful, except in moderate weather. TABLE 37.—Percentage decrease in height between deep water and the breaker zone, for waves of different initial degrees of steepness approaching a straight shore line (with straight and parallel bottom contours) at different angles. It is assumed that the waves break where the depth of water is 1.3 times the breaker heights Steepness of Angle between wave in deep water and shore line AVE NAEY LLL (ors) OX Ee RT SS cee ee ey See ee ee ee water (length: height) 20° 30° 40° 50° 60° 70° Percent | Percent | Percent | Percent | Percent | Percent 0 4 30 10:1 18 20:1 5 10 16 26 38 40:1 1 6 11 17 27 39 100:1 2 6 12 19 28 40 As a general rule, the decrease in the height of surf due to refrac- tion is negligible for waves that come in at angles smaller than, say, 30°, no matter what their steepness may be offshore. But when the waves are coming in at an angle greater than, say, 60°, the decrease in their heights may make landing possible at a place where this wouid not be so otherwise. Waves advancing in a uniform direction are refracted to the same degree all along a coast that is straight, if the bottom contours are parallel with the shore line (fig. 46); hence the decrease in their heights (if any) from this cause will be as great at one point along the shore as it is at another. But if the coast is strongly curved, the waves are refracted much more at one place than at another, so that the breakers may differ considerably, in their heights, from place to place. The local differences in the character of the surf that results are most conveniently discussed (a) around the shores of bays and beaches, and () around headlands and in the shelter of these. SURF AROUND THE SHORES OF BAYS Bays can be classified, roughly, as short and broad, or as long and narrow. Wave crests that are parallel to the general trend of the shore line are not refracted at all along the central sector of a short, broad beach, 160 BREAKER DIRECTION AND HEIGHT and the only change in their heights there, as they near the breaker line, is such as may be directly due to their advance over the shoaling bottom. But it is evident that the waves offshore might be at a con- siderable angle with the coast around the flanks of a beach of this shape; hence they would be refracted there to a degree depending on the precise shape of the coast, on the contour of the bottom, and on the initial shapes and dimensions of the waves, as explained above (p. 155). Calculation of the precise amounts by which refraction affects the heights of waves at successive places around a curving coastline in- volves tedious computations. But the approximate amount of reduc- tion, from refraction, to be expected from place to place, for waves of different degrees of steepness, may be taken directly from table 37, if one first marks on the chart the general trend of the wave crests offshore, and then measures the angle at different places between the latter and the depth line where surf is to be expected with waves of the heights that are running at the time. In the case, for example, that is represented above in figure 47, where the wave crests offshore are parallel with the central sector of the bay, but make an angle of about 40° with its flanks, refraction would tend to reduce their heights by about 10 to 12 percent at the points marked B and C by the time they broke, if they were 20 to 100 times as long as high while still out in deep water, and if they broke where the depth was equal to 1.3 times their own heights at that moment, but by only 6 percent if they were only 10 times as long as high to begin with. Reduction of the waye heights by refraction would naturally be greater along the more sheltered of the 2 flanks of the beach, if the waves were coming in at a considerable angle with its central sector. This is illustrated by the lower diagram (fig. 47), where the height of the breakers to be expected would only be about half as great at the point B—other things being equal—as at the point C. And the more abrupt the curvature of a beach is, the more likely it is that the angle at which the waves are coming in will be so great, off one or other of its flanks, that the reduction of breaker height by refraction will be considerable there. It is necessary, however, to remember that this tendency for a wave to decrease in height, as it is refracted around toward the coast, may be more than offset by the opposite tendency, i.e., for it to increase in height, as it advances shoreward over the shoaling bottom. These two opposing tendencies must therefore be balanced one against the other before one can judge whether landing on an open curving beach will be aided much by refraction at any given time. Under the circumstances that are illustrated, for example by the upper dia- gram in figure 47, any reduction by refraction would be more than counterbalanced in that way, unless the waves were steeper than about SURF AROUND BAYS 161 25:1 to begin with, so that the waves 6 feet high in deep water and 250 feet long would produce breakers at least 6.5 to 7 feet high at A, and 6 to 6.5 feet high at B and at C. But waves of that same PARALLEL TO SHORE I'rgurRE 47.—Diagram of a short, rounded beach with waves advancing parallel with its central sector (above), and at an angle of 40° with its central sector but parallel with one of its flanks (below) height offshore, but 100 times as long as high (as swells often are), might be expected to rise to heights of nearly 8 feet at B and at C, as contrasted with a little more than 9 feet at A. These examples illustrate the general rule—well recognized by persons who have to do with surf—that when the wave crests offshore 162 BREAKER DIRECTION AND HEIGHT are approximately parallel with the coast of the central sector of a short, wide, and evenly rounded beach (and sandy beaches usually do face the prevailing direction from which the largest waves come), the breakers are not likely to differ enough in height around its shore- line for landing to be easy anywhere along it, if the surf is dangerous along its central part. When the waves are advancing on a beach of this shape at a wide angle—or advancing directly on a more deeply concave beach—the reduction in the heights of the breakers by refrac- tion may be great enough to make landing possible on the more shel- tered flank in the one case, or on both flanks in the other case, if the waves offshore are steep and not more than 6 feet or so high. But this is not to be expected if they are much higher than that, or if they are the product of a swell, the initial steepness of which is small. The situation is different for long, narrow bays, where there may be no surf at all at the head, even when the waves driving in are so large that they cause heavy breakers at the mouth on both sides. We believe the reason to be that the ends of the wave crests break more or less along one or both shores in their advance up the bay while their central sectors are still far away from the head of the bay. And since the waves expand sidewise to compensate for being “worn off” in this way at the two ends, they decrease correspondingly in height. If a bay of this character is long enough, compared to its breadth, the waves may be drained of so much of their energy in this way that they cause only a weak swash on the shore by the time they arrive at the head, i. e., Just where the surf is usually heaviest in a crescent-shaped bay. In this connection, we think of St. Mary Bay, Nova Scotia (fig. 48), which is about 8 miles broad at its entrance by about 30 miles long, but which offers safe anchorage and easy landing for small boats at its head at most times, although it is wide open to storm seas, or to swells coming from offshore. And many other long, narrow harbors in vari- ous parts of the world owe their safety to their shapes, in this same way. This generalization might seem (at first reading) to contradict the statement, commonly made, that waves, running up a narrow, funnel- shaped, and steep-walled indentation of the coast, are condensed side- wise as the sides of the cove draw together, so that their heights are increased. Indeed the waves should (theoretically) double in height by the time they reached the point where such a bay was only one- fourth as wide as at its entrance, provided that its bottom were deep and perfectly level from side to side so that the shapes of the waves were affected by the shape of coast, alone. The breakers that sometimes spout in the air at the head of a narrowing chasm, in a rocky coast, afford a spectacular illustration of this principle. And the difficulty of landing may increase, for this reason, toward the head of a very nar- row and steep-walled cove, into which a sea is heaving directly. But SURF AROUND HEADLANDS 163 this effect is not often of practical importance otherwise, because the bottom usually does shoal toward either side of a bay, whether the latter be broad or narrow, so the waves, being refracted around, break all along the shore and lose in height more than they gain in their run up the bay. NOVA SCOTIA Fiaure 48.—Chart of St. Mary Bay, Nova Scotia. Soundings in fathoms. SURF AROUND HEADLANDS It has been stated that when the waves are advancing directly toward a promontory in the direction of its main axis, they are focused more or less on its tip, so that the surf is more severe there (figs. 49, 50) than it would be on a straight coast line, with waves of the same size, and coming in parallel with the coast. But this is true only where the water off the headland in question is so shallow, and the waves running at the time are so long, that they are refracted enough to make them advance upon it from the two sides, as well as against its tip. Sand spits illustrate this, as do higher headlands that are fronted by sloping beaches or by boulder zones, as many are. And it is seldom, 226794 O - 53 - 14 164 BREAKER DIRECTION AND HEIGHT Ficurr. 49—Surf around a low-lying projection of the Hawaiian coast and on the neighboring beach. (Photograph, courtesy of Mrs. William E. Schevill.) Fieure 50.—Surf dashing against the eastern headland at the entrance to Havana Harbor, Cuba, on a windy day, as viewed from across the narrow entrance. (Photograph, courtesy of American Photo Store, Havana.) SURF AROUND HEADLANDS 165 if ever, possible to land small craft under these circumstances, if the waves are more than 3 or 4 feet high or so. But there are many rocky headlands, close in to which the water is several feet or fathoms deep, even at low tide. And in such cases waves, advancing directly, may be refracted so little that the breakers are not apt to be as heavy on the tip of the headland as along its flanks. In extreme cases of this sort, the inshore ends of waves that are low and short may not be visibly refracted at all, as they run in by the flanks of the headland, either breaking along the latter, if the shoreline is a broken one, or simply rising and falling along it, if the rocks are both smooth and steep. In such circumstances, there may be no regular breakers at all on either flank of a rocky promontory, though a low sea may be producing a surf of moderate size on a beach nearby. But a heavy surf may be expected, not only on the beach, but on both its headlands as well, in stormy weather, because the waves are then so much higher and so much longer that they break in much deeper water. It chances that we are personally familiar with a location of this sort, where we have long watched the varying state of the sea and of the surf with much interest. We should point out, however, that mere absence of surf along a rocky shore does not necessarily mean easy landing there, for it may need only the rise and fall of the water level of only a few feet, with the passage of successive crests and troughs, to render it difficult to embark or to disembark from a small boat—especially since these conditions are apt to exist only when the rocks are both so steep and so smooth that it is not easy to find foothold. Ifthe rocks are more broken, the waves are sure to be breaking there, more or less violently, according to their sizes and according to their direction of advance. The degree to which the one side of a promontory will be protected, when the waves are coming in against its other side, depends chiefly on how abrupt the alteration is, in the direction of the coast, from the more exposed side to the more sheltered. The inshore ends of the waves may be refracted right around a short headland with broadly rounded tip, no matter from what direction they come, if it fronts on a sloping bottom, and may thus be directed up a bay or harbor, where better shelter might be expected, if one were to judge from the direction of the wind alone. Marblehead Harbor, Mass.. affords an illustration of this for it sometimes suffers from swells from the east through southeast to south in this way, although it actually faces about northeast. And Gloucester Harbor, facing a little west of south, was plagued similarly during storms from northeast, east, and southeast, until a breakwater was built for its protection. Rollers may even follow around the shore line until the breakers resulting from them may run directly against the wind, if the coast gradually falls back far enough to bring the wind offshore, a phenomenon de- 166 BREAKER DIRECTION AND HEIGHT scribed more than a century ago. And situations of the sort are not uncommon. In situations, however, where the direction of the coast alters abruptly, and when the waves are advancing at an angle of more than, say, 90° with the sheltered side of a promontory, the re- fraction of their inshore ends may expand their crests sidewise so suddenly and so widely, (as illustrated in fig. 51), that the resultant breakers decrease abruptly in height as they pass inward along the lee shore. And the actual loss of energy from the inshore ends of the Ficure 51.—Diagram to illustrate the refraction of waves around an abrupt cor- ner of the coast, when the wave crests in deep water form angles of about 35° with the more exposed shore and of about 155° with the more sheltered shore. The depths of the bottom contours are given in terms of the offshore wave length. The arrows indicate the lines of advance of the waves at successive points along their crests. waves, as they break, tends to reduce their heights still further, as they continue their advance, just as happens along the shores of a long, funnel-shaped bay (p. 162). Short waves may, indeed, suffer so little refraction, as they pass an abrupt alteration in the trend of a coast where the water is moderately deep close in to the tide line, that they do not follow around to the more sheltered shore at all, but continue right on past the corner, and so out into deeper water again, leaving what may be termed a “shadow zone” of quiet water, which may be of considerable extent, along the SURF AROUND HEADLANDS 167 more sheltered shore behind them. Shadow zones of this sort are commonly to be seen in the lee of steep headlands in moderate weather, as we have observed; they are also found in the lee of steep-walled islets, and of ledges that rise from a comparatively level bottom where the water is deeper than, say, twice the height of the waves at the time. But they are largely or entirely obliterated in heavier weath- er, because the waves are then so much longer that refraction alters their lines of advance out in much deeper water. The precise interplay of factors that determines just how much protection from surf may be expected behind a projecting corner of the coast is thus as varied as are the shapes of coast lines, the angle with the coast at which the waves may be advancing, and their sizes and shapes. But the general picture that results from theory and observation combined, is clear enough to allow the following generali- zations: a. The more abrupt the alteration in the trend of the coast and the greater, and the wider the angle between the oncoming waves and the more protected stretch of shore, the more shelter one may expect there from the surf, under a given condition of wind and weather. b. If the angle between the oncoming waves and the more sheltered stretch of coast is much more than, say 100°, one can expect a very abrupt decrease in the height of the breakers, within a very short distance inward from the corner. c. The farther in one goes from the corner along the more protected shore, the lower may one expect to find the breakers. The shelter afforded by a projection of the coast line is greater still if its more protected side is broken by lesser headlands and by coves, because these tend, further, to break down any rollers that may follow in along the shore. If the alteration in the trend of the coast is not only abrupt, but is through so wide an angle that the two sides of the promontory are nearly parallel, one with the other, as is true of a narrow spit, or of a breakwater, the inner side may be so fully protected that landing is easy there, and out nearly to the extreme tip, even when a heavy sea is running directly against the exposed side. And the inner ends of the waves may not be refracted around sharply enough to touch the inner shore at all, if the alteration in direction of the coast is sufficiently abrupt and if the submarine slope is steep enough, as al- ready remarked (p. 166). Enclosed harbors and lagoons that connect with the open sea through narrow channels, as between pairs of spits, or between break- waters—also the lagoons of coral atolls—are fully protected from surf, no matter from what direction the waves may be coming, nor how high they may be, for once the crests have passed through the 168 BREAKER DIRECTION AND HEIGHT cut, the only limit to their sidewise expansion, as they advance across the basin, is such as is imposed by the sides of the latter. The rela- tionship between the breadth of a basin, and the degree to which en- tering waves are reduced in height as they spread sidewise within it may be illustrated by the Duluth Harbor opening on Lake Superior (fig. 52), where measured waves that were 9.9 feet high at the nar- SCALE OF FEET Figure 52.—Sketch map of Duluth Harbor. Soundings in feet. (After Gaillard.) row entrance were only 1.17 feet high at the station marked A on figure 52, and 1.0 foot high at station B; while waves that were 11 feet high at the entrances were only 0.45 foot high at station C, the distances in from the entrance to these stations being 1,200 feet, 2,600 feet, and 4,195 feet, respectively. But waves that were 9.9 feet high at the entrance were still 2.5 feet high at the station marked D on the narrow side of the harbor (a reduction of only 3.6 to 1 in a distance of 3,857 feet) because there is so little room for the wave crests to expand sidewise in that direction (Gaillard, 1904, p. 89). The rate of reduction in wave height that is to be expected in locali- ties of this sort is calculable, according to Gaillard, by a formula that takes account of the breadth of the entrance (for this limits the breadth of the wave crests that pass through it), the heights of the waves as they emerge from the entrance, the sidewise breadth of the harbor at the place of observation, and the distance of the latter inward from the entrance. SURF AROUND ISLANDS The factors that determine the differences in heights of the breakers from place to place along coasts in general, act in the same way around SURF AROUND ISLANDS 169 the shores of islands, whether large or small. Thus, the waves are likely to be focused, as it were, on the exposed side of an island that is rounded in outline if it rises from water shoal enough to alter the di- rection of advance of the waves to any considerable degree (fig. 53). Consequently, just as at the tip of a headland (p. 163), a worse surf FIcuRE 53.—Diagram to illustrate the refraction of waves around a circular is- land that is surrounded by an evenly and gently sloping bottom. The depths of the bottom contours are given in terms of the offshore wave length. may be expected there with a given wind than would develop on a straight coast. But while the waves are often refracted right around a small island of this shape, the heights of the breakers they produce will decrease following around the shore, as their inshore ends are delayed more and more by the effect of the bottom. Theoretically, the inshore ends of waves, that were initially 20 to 100 times as long as 170 BREAKER DIRECTION AND HEIGHT high, should break at angles of about 16° to 35° with the part of the shore that was at right angles with their crests offshore, assuming that they did so where the depth was equal to 1.3 times their own heights at breaking, while their heights would be reduced by a little more than one-half there accordingly, as compared with the most exposed part of the island. Observations suggest that the reduction in height might actually be of about this general order of magnitude. Theoreti- cally, too, the inshore ends of the waves should lose still more in height by the time they reach the more sheltered side of the island. However, landing is not apt to be as much easier there as this might suggest, especially if the island is small, for the following reasons: a. Since the inshore ends of the waves are still at a considerable angle with the coastline when they break, and since the coasts of round islands are usually rocky, bouldery, or strewn with coral heads, landing is much more difficult for practical reasons, than it would be if waves of equal height were breaking parallel with the shore, and if the latter were sandy or pebbly. b. Although the reduction, by refraction, in the heights of the waves around a small circular island is greatest on the most protected side, the surf may be made very confused there because of the inter- ference that often develops between the two trains of waves that meet, as they are refracted around from the two sides. We ourselves have vivid memories of attempts to land on rocky islets that were unsuccess- ful for this very reason. In short, the chance is not very good of landing anywhere around the shore lines of a small rocky island that is circular in form, if the sea is too heavy to allow this on one or other of its two lateral quad- rants, and if the submarine contour is such that the waves are re- fracted right around it. But there may be a shadow zone of quiet water in the lee of an islet, if its shores rise abruptly from water so deep that the waves then running are refracted but little, as they approach it. just as there may be in the lee of a promontory of similar. character, and for the same reason (p. 166). But anyone who takes advantage of this to land wil} be well advised to keep a sharp eye on the state of the sea, and be prepared to put off again at once if the latter rises, for a troublesome surf may develop with astonishing suddenness, as we have often seen. The more irregular the coast of an island is, and the more abruptly it alters from place to place, the more likely it is that one can find a place in some cove, or in the lee of some headland that will be sheltered from the surf, under conditions of sea that would prevent landing on the more exposed parts of the shore. One or the other of two shallow bights, for example, marked A and B on figure 54, that flank a short promontory on the northern side of No Man’s Land, off SURF AROUND ISLANDS 171 70°48’ NO. MANS LAND 70° 48” Figure 54.—Chart of No Man’s Land, Mass. Soundings in fathoms. Martha’s Vineyard, is usually sheltered enough from southerly swells for landing, except in really heavy weather, although the island is only about 114 miles, east and west, by about 1 mile, north and south, with a very even shoreline, and without any offlying shoals or reefs to break the seas. Similarly, when coaling from one steamer to another was impossible in Cook Bay on the southeast side of Easter Island off the coast of Chile in the third week of December 1904, because of a heavy swell from the southwest, we found La Perouse Bay on the northeast side so protected by Cape Roggewein on the one hand and by North Cape on the other side, that the two steamers could lie side by side in the open roadstead. A cove on the leeward side of even a small island may, indeed, be perfectly sheltered if the shore line is broken up by a succession of headlands, especially if there are offlying ledges or islets to interfere with the wave pattern. The harbor on the east side of St. Pierre Island off the south coast of Newfoundland (fig. 55) is an excellent example, 172 BREAKER DIRECTION AND HEIGHT being well protected in this way from swells from the southward, - southwestward, and southeastward, although it is wide open to the northeast, and although the distance from its entrance to the most easterly promontory of the island is only about 114 miles. What was said above (p. 163) about the height of surf around prom- ontories applies equally to islands that are much longer than they s 2 sh a Great Colombier