pus eek. Cua. Kea OTR TP 76-12 Wind-Generated Waves for Laboratory Studies by D. Lee Harris TECHNICAL PAPER 76-12 AUGUST 1976 U.S. ARMY, CORPS OF ENGINEERS COASTAL ENGINEERING RESEARCH CENTER Kingman Building Fort Belvoir, Va. 22060 Reprint or republication of any of this material shall give appropriate credit to the U.S. Army Coastal Engineering Research Center. Limited free distribution within the United States of single copies of this publication has been made by this Center. Additional copies are available from: National Technical Information Service ATTN: Operations Division 5285 Port Royal Road Springfield, Virginia 22151 The findings in this report are not to be construed as an official Department of the Army position unless so designated by other authorized documents. IUAUAUAUTOUO MBL/WHOI O 0301 00895b4b 2 MM UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) READ INSTRUCTIONS 1. REPORT NUMBER 2. GOVT ACCESSION NO.| 3. RECIPIENT'S CATALOG NUMBER TP 76-12 4. TITLE (and Subtitle) 5S. TYPE OF REPORT & PERIOD COVERED WIND-GENERATED WAVES FOR LABORATORY STUDIES », Technical Paper 6. PERFORMING ORG. REPORT NUMBER - AUTHOR(s) 8. CONTRACT OR GRANT NUMBER(e D. Lee Harris - PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT, PROJECT, TASK AREA & WORK UNIT NUMBERS Department of the Army Coastal Engineering Research Center (CERRE-OC) A31228 Kingman Building, Fort Belvoir, Virginia 22060 - CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE Coastal Engineering Research Center 13, NUMBER OF PAGES Kingman Building, Fort Belvoir, Virginia 22060 14. MONITORING AGENCY NAME & ADDRESS(if different from Controlling Office) 15. SECURITY CLASS. (of thia report) UNCLASSIFIED 15a. DECL ASSIFICATION/ DOWNGRADING SCHEDULE Approved for public release; distribution unlimited 16. DISTRIBUTION STATEMENT (of this Report) 17. DISTRIBUTION STATEMENT (of the abstract entered in Block 20, if different from Report) 18. SUPPLEMENTARY NOTES 19. KEY WORDS (Continue on reverse side if necessary and identify by block number) Air-sea interaction Waves Coastal engineering Wind-generated waves Laboratory wave facilities Wind-wave flumes 20. ABSTRACT (Continue on reverse side if necesaary and identify by block number) Mechanically generated, regular waves are used in laboratory wave basins and channels for testing engineering designs for the coastal zone. Wind- generated waves in the laboratory display irregularity, Suggestive of the irregularity of the open sea. It has been suggested that the validity of laboratory tests would be increased if the labenerery waves were generated by wind. (continued) FORM DD , jan 73 1473 EDITION OF T Nov 65 1S OBSOLETE : UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When, Data Entered) UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered) Examination of a simple approach to wave forecasting, based on dimen- sional analysis, leads to the conclusion that wind-generated waves in the laboratory cannot be expected to have the same form as prototype waves unless they correspond to equivalent scaled fetches. Very low windspeeds must be used to produce waves that are anywhere near fully developed in a laboratory facility of moderate length. The resulting waves are too small to be of much value in testing designs. An examination of the microscale procedures, now believed to be re- sponsible for wave growth and of some-secondary flow characteristics of wind tunnels, indicates that the relative importance of the mechanisms for wave generation in wind channels is very different from that in unconfined air- spaces. Modeling the effects of nearshore wind in modifying waves generated far from shore may be possible if the waveform, as it exists at a modest distance from shore, can be modeled by a mechanical wave generator. If modeling the offshore wave is possible, direct mechanical generation of the desired form may be easier and more economical than adding a wind tunnel above the wave channel. Laboratory wind-wave research facilities can be useful for basic research concerning air-sea interaction even though they are of doubtful value in testing engineering designs. 2 UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered) PREFACE This report presents an investigation of the potential value of a wind-wave research facility for coastal engineering studies. The use of wind to generate waves in the laboratory is frequently suggested by coastal engineers. The report reviews earlier studies of wave generation, the flow of air in wind tun- nels, and early laboratory experiments with wind-wave research facilities to aid engineers in deciding if facilities of this type are useful for solving specific problems. The work was carried out under the wave mechanics program of the U.S. Army Coastal Engineering Research Center (CERC). The report was prepared by Dr. D. Lee Harris, Chief, Oceanography Branch, under the general supervision of R.P. Savage, Chief, Research Division, CERC. Dr. Harris has been interested in the use of wind-wave research facilities for air-sea interaction studies for many years, and expresses his appreciation to the many scientists who have contributed to this investigation. The oppor- tunity of observing many combination wind tunnels-wave channels in action and discussing their merits and shortcomings with scientists responsible for their design and operation has been essential in performing this evaluation. An initial visit to the laboratory at the National Bureau of Standards to observe experiments by Dr. Keulegan was very informative, and was followed by later visits to this lab- oratory after his retirement. Valuable discussions and demonstrations were con- ducted with Professors Per Bruun and Frans Gerritsen, during construction and operation of the combination wind tunnel-wave channel at the University of Florida; and with Professor Omar Shemdin after modification of this facility in the‘late 1960's. Professor E.Y. Hsu, Stanford University, was most instructive in pointing out the necessity of thickening the atmospheric boundary layer at the air-sea interface to obtain the realistic wind profiles needed for activation of the Miles inviscid wave-generating mechanism. Visits to other laboratories with working wind-wave flumes in the United States, Japan, and Western Europe since 1965 have provided additional perspective for the problems. Discussions with Professor James Bole (during the summer he spent at CERC in 1972 and later) were extremely useful in sorting out impressions gained: in earlier laboratory visits and in reviewing reports of scores of experiments involving the interaction of the air and the sea in both laboratory and field. The author acknowledges his indebtedness to all these individuals and to many others with experience in the laboratory study of wave gen- eration who have shared their insights, and takes full responsibility for any mis- understandings which may have resulted from these discussions. Comments on this publication are invited. Approved for publication in accordance with Public Law 166, 79th Congress, approved 31 July 1945, as supplemented by Public Law 172, 88th Congress, approved 7 November 1963. JOHN H. COUSINS Colonel, Corps of Engineers Commander and Director CONTENTS Page SHEGOES, YANTD) DSP STONA ONS Go al by) oh OOo 6 SG 6 66 6 6 So 6 I JGNB UROL NS Go oo 6-010 6 0,615 6 0 0,0 610050 60 50056 7 IT SOME COASTAL ENGINEERING PROBLEMS INVOLVING THE EFFECT OF UND ON WN 5 6 eG alee hind Bllovon oo optic oo 0 o LG Ii.. Wave; Gene Gatlomniss ves wey sie, schearelonkirsuessinigsge ss cgvommecn Le iual merceii cigs nak ae a LO) 2: Wave Modict L. Cats OMe. 3 ot evs Ulchaseuaued icity ILO aeietunst ois inclamteig ORCA ona mL Be WhbnGlophani Syketho S oo ol oo b40 4 00006 600 6 oo MG 4. Surface Currents... . wes ah dbeleoisind Sead tee oe ee 5. Wind-Generated Tunoalencer (Nang Gly tQaheis, Se20eFIR2 Ak SSeS on Wind=Stresis Relationships. te se to cies cite te cy caetctn terse Tes Wind-Stres's on -Flloatinie: ObyleCtS s 1. upea en i en) mene III MOMENTUM AND MECHANICAL ENERGY EXCHANGE BETWEEN AIR AND WATER... . AOR ERS Cit OLEATE. Col ict io y. Jld 1. Generation of Suncaeced Waves! idee so frees hen 23 eee 2. Boundary Layer Theory. . . ee Me bore) x 474 3. Microscale Processes Tanoiveds in the ieeneces! BE Momenitum=Between Air and) Water. ...5 4 «+, «ss cles. ce eueemeece Al SE SUMMA cep ory urna Jowataccnard, cslbaegehcrmmennel’ Gebtal Move ob ies £obh. nein eC mane IV. MODELING THE GROWTH OF WIND-GENERATED WAVES IN A WIND TUNNEL 5... 3.4. eer ora Go 8S 1. Boundary Layer Growehi in ne tebonaton: oagsuike ads. eee ZO 2. The Importance of Limited Fetch. ... 5 65 0. OY 3. The Scales of Motion Involved in Momencumt Exchange Between (Wandyands Waterss circ) cine) tor or or one ancl ODL Leer he Aya Reet ei a Pe ES Buen IMAG 6 0 | OS V SOME LANDMARK EXPERIMENTS ... . Sita toy wn en sab ek wang youre et OM 1. Significant Experimental Results Bi fe u80 Ge a) a Neth eeenas, cee OD 2:2 SSuMMATY: «Wye entree, 6 Mien ole Rom eel Tokace) citron ae (ogee krone cant en RO VI HM MINDE PAD CAC MOMESHKON Sem Bh G6 Bg dG oo oo aldtove 6 5b oo 0 od Wo Summary . Pe ed ee tet rane aCe a A dG 0 Od Di. (GON CdS PONS: eee el eae lig tes Sg tae eat ee ees cet cute a LS LITERATURE + GETED. ice ea) ioaltee GME tee Ach SeCeacl Eodioe oleh ECS TABLES 1 Wave prediction equatiens.;) © 9 3 3s) 202 4 ee eS 2 Stage of wave development. . . . - ee e+ ee ee eee ee ee es 30 CONTENTS FIGURES Comparison of shipboard wave observation and hindcasts. Location of hindcast stations and observation areas . Drag coefficient versus windspeed.... Relationship of wave parameters A plot of the equations defining wave growth. Deepwater wave forecasting curves . . Page 11 12 15 17 19 21 Pa SYMBOLS AND DEFINITIONS drag coefficient of wind over water drag coefficient for wind measured at an elevation of z, z is expressed in meters (unless otherwise stated) phase speed of waves with maximum energy density arbitrary functions acceleration of gravity wave height microviscosity coefficient, due to turbulence wave period duration of wind windspeed mean velocity parallel to the x axis shear velocity free-stream velocity just outside the boundary layer ie friction velocity, u, = (t/p)* perturbation velocities parallel thickness of boundary layer displacement thickness of the boundary layer momentum thickness of boundary layer Von Karman's constant kinematic molecular viscosity coefficient density of air wind stress where WIND-GENERATED WAVES FOR LABORATORY STUDIES by D. Lee Harris I. INTRODUCTION The need for understanding and controlling or moderating the effects of wind-generated waves is one of the most distinctive requirements of coastal engineering. There is also a need to design, build, and maintain structures for the protection of low-lying coastal areas from storm surges. The meteorological, hydraulic, and sedimentary processes involved are variable, complex, and often deductive. Theoretical development and engineering judgment have proven inadequate for most of the needed designs and laboratory studies of many of the processes involved have been required to provide design guidance. Thus, laboratory facilities for studies of coastal processes have become important coastal engineering tools. Long, narrow channels with a mechanical wave generator at one end and a beach or stilling basin for absorbing the wave energy at the other end, are used for testing wave forces on slopes and component members of marine structures. The application of wave channels for testing components of structures is analogous to the aeronautical engineer's use of wind tunnels for testing aircraft components. Wave channels are also useful for testing instabilities of revetments, breakwaters, seawalls, and reser- voirs to wave action. Wide, shallow basins (usually with wave generators, and occasionally with tide generators at one side and absorber beaches around most of the remaining periphery) are used for modeling partial or entire harbor complexes and studying beach processes. Both types of lab- oratory facilities are also used for many other purposes. Although the mechanically generated waves used in most wave channels and basins are generally more regular and symmetric than the waves encoun- tered in nature, experimental results obtained have greatly reduced the uncertainty in predicting the effectiveness of many engineering designs and the consequent cost of building structures which are not adequate for their purpose, or structures which are more massive and expensive than they need to be. Success with relatively simple channels and basins in which measurements of the effects of small water waves or small-scale structures are used to predict the effects of big waves on prototype structures stimulates the coastal engineer to think of small-scale studies involving both wind and waves which might be used to improve the knowledge of wind-generated. waves for engineering studies and perhaps to evaluate the combined effects of wind and waves on marine and coastal structures. Plate and Nath (1969) explicitly suggested this possibility. Shemdin (1972) discussed an experi- ment based on this concept. Bole (1973) discussed many physical processes of engineering importance which might be studied effectively in a combina- tion wave tank-wind tunnel. Bole also listed many difficulties which must be faced for effective laboratory investigation of these processes and suggested means for overcoming the difficulties. Several significant discoveries about wind-wave generation and wind stress on water have been made in laboratory studies, sometimes with very small wind-wave facilities. There is no doubt about the value of labora- tory wind-wave research facilities by well-qualified investigators for basic research dealing with the interaction of air and sea. This study was undertaken to determine design parameters which should be recommended for a wind-wave channel to be used in coastal engineering studies in much the same way that tanks with mechanical wave generators are used. During the study it was found that the process of transferring mechanical energy from the airstream to the water is infinitely more com- plex than the process of transferring mechanical energy from one location to another by means of gravity waves. Further, it was found that a satis- factory technique for modeling wave generation and wind stress on water in a laboratory facility does not yet exist. There are excellent reasons for doubting that a technology satisfactory for all purposes can be developed. Thus, while the study had been expected to culminate in the recommen- dation of design parameters, it does not. Rather, it concludes that although a combination wind tunnel-wave channel could be a great aid to fundamental research in air-sea interaction processes, the state-of-the- art of modeling air-water interaction processes in the laboratory has not advanced to a level which provides any assurance that the validity of laboratory studies of wave effects on beaches or manmade structures is improved for engineering application by using wind to generate or modify laboratory waves. Since these conclusions were unexpected at the initiation of the study, it seems worthwhile to note that several other investigators with con- siderable experience in the laboratory study of momentum exchange between air and water independently arrived at substantially this opinion. A few of the published quotations are given below. "...waves in laboratory tanks seem to grow differently from waves in the ocean)... (Wu 19172 pe elO3))e Miles (1967, p. 166), in discussing the generation of gravity waves in the laboratory by processes believed to be important in nature, stated: "The laboratory generation of the later waves at amplitudes that are adequate for quantitative measurement appears to require a mechanical wave maker. Moreover, it appears difficult to obtain accurate measurements of wind-induced growth rates for such waves over attainable fetches..." Hidy and Plate (1965) presented a plot of normalized spectra which showed that the width of the spectrum peak for wind-generated waves tends to be much broader in the field than in the laboratory. Ramamonjiarisoa (1973) and Coantic and Favre (1973) presented a Similar figure, which does not duplicate any of the data by Hidy and Plate, and showed by numerous laboratory and field wave-generation spectra that the width of the dimensionless spectrum peak is broader for ocean than laboratory waves. Colonell (1972), in describing a new wind-wave research facility at the University of Massachusetts, stated: "...While it is not claimed to be a replica of the ocean environment, it does provide a reasonable simulation of ocean surface characteristics...." Differences between wind-generated waves in the laboratory and field result from two fundamental causes. A wave-generating region 100 to 200 meters (330 to 660 feet) in length is extremely short for natural con- ditions, and extremely long for a laboratory. Consequently, the lab- oratory-generated waves correspond to very short fetches at prototype scale, or they must be generated by very low windspeeds; thus, only very short waves with low wave heights can be obtained. The resulting waves are generally too small to permit accurate measurement of their effects. For such waves, surface-tension effects can distort laboratory results. Both air and water must be confined in the laboratory. This confinement leads to the growth of turbulent boundary layers, not present at pro- totype scale, on the sides and roof of the wind tunnel. Boundary layers also form on the sides and may form on the bottom of the wave flume. These side boundary layers may be either viscous or turbulent depending on conditions, and they have no counterpart at prototype scale. These extraneous boundary layers in both air and water give rise to other phenomena (not present in the prototype scale) which significantly affect the exchange of momentum between air and water, and suppress other phenomena now believed to be important in nature. The importance of the secondary phenomena on wind-wave generation in the laboratory was not clearly recognized until about 1972. Agreement between the spectra of wind waves generated in the laboratory and wind waves observed in nature should be improved by using a programable wave generator to produce an initial wave field which is acted on by the wind. This procedure is now being used by several coastal engineering laboratories. It appears that programable wave generators, with or with- out wind, lead to improvement in modeling natural waves. It has not been established that any quantitative improvement in modeling wave conditions of engineering importance can be achieved by adding a wind tunnel on top of a wave tank equipped with a programable wave generator. The capabilities of programable wave generators have not been fully exploited. The further development of more versatile wave generators and, if possible, develop- ment of a technology for establishing surface currents in the wave channels appear to offer more potential benefits for engineering application to coastal engineers for the costs involved than the construction of a wind- wave research facility. Possible uses of a combination wave channel and wind tunnel in coastal engineering research and difficulties which must be overcome to obtain Satisfactory results, are discussed later in this report. Several practical problems in coastal engineering which involve the action of wind on water and which generate the need for considering the construction of a wind tunnel for coastal engineering research are discussed in Section II. Hydrodynamic phenomena of geophysical scale responsible for these practical problems are discussed in Section III. The use of laboratory facilities in studying the interaction of wind and waves, brings important new problems not present under prototype conditions. These are reviewed in Section IV. Some earlier laboratory Studies are reviewed in Section V; a summary and conclusions are pre- sented in Section VI. II. SOME COASTAL ENGINEERING PROBLEMS INVOLVING THE EFFECT OF WIND ON WATER Several practical problems and solutions which might be facilitated by the use of a wind-water research facility are discussed in this section. The applicability of existing wind tunnel-wave channel technology is discussed only to the extent necessary to clarify the problem, and is designed to provide motivation for technical discussions later. 1. Wave Generation. The waves of the real sea are generated by wind. Nearly every wave differs from its immediate predecessors in height, period, and shape. Mechanically generated laboratory waves are usually nearly uniform in height, period, and shape. Wind-generated laboratory waves share some of the irregularities of natural waves. Thus, there is a reason to believe that a better simulation of natural waves would be achieved if the lab- oratory waves were generated by wind. The coastal engineer is often faced with the need for wave infor- mation from locations where no wave records exist. The standard method for dealing with this problem is to simulate wave records in the form of significant wave heights and periods from the available meteorological records by using wave hindcasting procedures. Verification of available hindcasting procedures suitable for use in engineering offices shows that they are not fully capable of satisfying coastal engineering needs for wave data and that different procedures lead to conflicting results. Estimates of the wave climate obtained by two hindcasting procedures are compared with each other and with an estimate based on visual observations in Figure 1 (U.S. Army, Corps of Engineers, Coastal Engineering Research Center, 1975, p. 3-43). Locations for prediction points and verification areas are shown in Figure 2. A wave-wind research facility could be use- ful in evaluating some of the proposed theories for wave generation and some of the assumptions employed in developing hindcast procedures. This should help in developing more satisfactory hindcasting procedures. 2. Wave Modification. The profile of mechanically generated waves in the laboratory is gen- erally symmetric with respect to the wave crest. Wind-generated waves in the laboratory and waves in the sea, with high winds, are generally steeper 10 (Ww) jybiaH aA0Mm (SZ6T *(uotjeuetdxs sin3stz 105 ) ZejUEeD YDLeeSey SuTL99UTSUYg [Te seo) ‘sra0uTSUq Fo sd10D ‘AuIy *S*p 02 IeZeL) 6p-Ly6I steeXk oy OF sornpsdord (SGS61) CNd PU OS6I-SP6I SteOA YI LOZ soinpesoid (1961) AWS Aq sisedputy uo pue gg-SOGT SIeO9X OY} IOFZ SUOTIeAIESGO pzeoqdtys uo poseg oO (2) NOODOrFWO MN TM NN — Ow MOorWOMNT MN — S a8ws—s— J ¥ONolsS 01 8Ws Q u0lj0IS *sZSeOpuTY PUB SUOTJEALASGO aAeM Paeogdtys FO uostxeduod y ‘*T ean38Ty 00! payooipul ‘uous Jay61py SaA0M 30 abojUadJag Ol @ |-01 (45) sy61aH aAoM (W) jybIaH aA0M (o) ©) OOMDOrFONTMN 20! 0 —~-OMD@OMWFONM TM N— 01 oO! ,-01 2-01 SWS WV UO1j0IS 101 00 1-01 2-0l aws @ ¥0!j0}S (43) su619H BAM STATION B 41°50° 69° 30° Figure 2. Location of wave hindcasting stations and Summary of Synoptic Meteorological Observations (SSMO) areas (from U.S. Army, Corps of Engineers, Coastal Engineering Research Center, 1975). 12 on the front face of the wave than on the trailing face. This asymmetry of the waves demonstrates that the acceleration on the front face of wind waves is greater than predicted by elementary wave theory and suggests that the peak force exerted by the waves on a structure may also be greater than the peak force predicted by elementary wave theory, or meas- ured in ordinary wave tanks. 3. Wind-Driven Spray. Seawater, carried over a seawall, can add significantly to the problems of controlling coastal flooding in severe storms. Seawater can be carried over the seawall in the form of wind-driven spray, or in the form of wave runup and overtopping. It is believed that the height to which waves can carry water up a beach or over a levy is increased by strong onshore winds. Fuhrboter (1974) suggested that the wind-driven spray can significantly increase the windloading on structures in the surf zone. Quantitative studies with a natural distribution of wave heights and periods are lacking. 4. Surface Currents. Wind blowing over a water surface always generates a surface current in the direction of the wind or, in the northern hemisphere, to the right of the wind. When the wind is directed toward the shore, or parallel to the shore to the right of the wind, this surface current has a shoreward component. Continuity of mass requires a subsurface current away from the shore which may contribute to beach erosion. Subsurface currents, result- ing from a seaward flow at the surface, may lead to sediment transport toward the beach and contribute to natural beach restoration. Suitable laboratory experiments involving both waves and surface currents should contribute significantly toward an understanding of this process. Lab- oratory experiments may be essential. 5. Wind-Generated Turbulence. Wind shear at the water surface adds vorticity to the water, increasing the turbulence and the effective viscosity of the water and the effective mixing coefficients for heat, salt, or any polluting substance. Little quantitative data relative to this effect are available, and suitable laboratory experiments in a wind-water facility could be extremely useful. 6. Wind-Stress Relationships. Storm surge is the most important coastal engineering problem where wave action is not the most important natural phenomenon. High winds, pro- duced by severe storms, pile water against the coast and cause severe flooding in low-lying coastal and estuarine areas. The principal cause of the water motion which produces these floods is the shear stress between wind and water. This stress is generally estimated in engineering practice by expressions of the type: G2 On GA US 5 (1) 13 where t is the wind stress, Pg the density of air, U the windspeed, and C, is a coefficient which must be evaluated from some combination of theory and empirical data. The coefficient, Cy, depends on the ele- vation at which the windspeed, U, is defined, the surface roughness, the vertical temperature gradient in the air, the windspeed, and perhaps other variables. Several proposed laws of Cg as a function of U are shown in Figure 3. The variability of Cg is discussed in greater detail in the next section. Well-designed laboratory experiments involving both wind and water might be useful in obtaining a better definition of Cy. 7. Wind Stress on Floating Objects. Trajectories of floating objects, floats or drogues, are often used to Measure mean currents in a wave field. Since a part of the float must be exposed to the wind, the resulting motion is determined partly by the wind and partly by the water motion. Laboratory studies of floats and drogue motion in a water-wind facility should lead to improvement in the interpretation of current measurements obtained in this way. Wind plays a role in many other oceanographic phenomena of interest to coastal engineers. The most important of the phenomena and a representa- tive sample of those of secondary importance have been discussed in this section to provide background for evaluating the technical discussion of hydrodynamic phenomena in the following sections. III. MOMENTUM AND MECHANICAL ENERGY EXCHANGE BETWEEN AIR AND WATER 1. Generation of Surface Waves. Modern studies of surface wave generation follow two basic lines of development. The first, and simplest, is a heuristic development along dimensional lines, with little consideration of microscale physical pro- cesses. The second, more complex line of development, begins with a consideration of the processes by which a single water wave may gain energy and momentum from the wind and seeks to explain the development of a wave field by integrating, over all waves, the governing equations for a single wave. The two approaches are not mutually exclusive and both require empirical support from observations. a. Dimensional Analysis Applied to the Generation of Surface Waves. It is readily verified from field observations that when an offshore wind begins to blow, the wave height and period increase with distance from shore and with the duration of the wind. Thus, the simplest realistic model, which can be applied to wave generation near a well-determined boundary after a substantial increase in windspeed, must depend on the windspeed, the duration of the wind, and the fetch. The fetch is defined as the overwater trajectory of the wind. Dimensional analysis shows that the appropriate relations for wave height and period may be expressed in the forms: Sheppard (1958) Ruggles (1970) Ye lA x wean Cardone (1969) ‘ = ‘ Weiler and Burling (1967) Davidson and Portman (1971) (smooth flow) Smith (1967) 2 4 6 8 10 Uig m/s"! Figure 3. Various suggested forms of the drag coefficient (Cz) versus windspeed (Uz) at 10 meters (from McConathy, 1972). and sll ot, (, &) - (3) where g is the acceleration of gravity, T the wave period, U the reference velocity of the wind, F the fetch length, t the duration of the wind, and H the height. The functions f,; and f) cannot be determined from dimensional analysis, but may be estimated from observa- tions or theoretical considerations. Many secondary variables may be included in equations (2) and (3). Wiegel (1964) reviewed much of the empirical data in support of this formulation and discussed the quality of the data from various sources. Figure 4 is a compilation of data from many individual studies (Wilson, 1955). The reference velocity used by Wilson is an "anemometer wind."’ The importance of providing a precise definition of the reference wind velocity was not fully recognized when most of the data used by Wilson were gathered. Much of the later data have been better documented, and at least three distinctly different definitions of the reference velocity have been widely used. Similar figures have been presented in other reports. The data in Figure 4 can be approx- imated by a smooth curve, and for most of the figure, variability about the smooth curve is no more than a factor of 2 or 3, although the dimen- sionless wave height and period vary by factors of more than 100. A relation which is reliable within a factor of 2 or 3 as the primary variable changes by factors in excess of 100 represents a great deal of predictive skill. However, it also leaves something to be desired for accurate engineering calculations. Analytic equations for curves which summarize data of the type shown in Figure 4 (derived by many authors) are given in Table 1. Graphs of these equations for comparison with Figure 4 are shown in Figure 5. Some of the spread in data and in the curves is due to differences in the defini- tion of the reference velocity. In some earlier studies, U was defined as the anemometer wind without specifying the height of the anemometer or other information relating the reference windspeed to the actual overwater wind. An attempt was made to adjust many of the observations to a stand- ard anemometer height of 10 meters, but the procedure employed in the adjustment is not always clear. The curves diverge more for values of gF/U > 10+ than for shorter fetches. The equations derived by Bretschneider (personal communication, 1970-71) have been used in the construction of a nomograph for estimating wave height and period from estimated values of windspeed, fetch, and duration. This nomograph and the defining equation are in the "Shore Protection Manual" (SPM) (U.S. Army, Corps of Engineers, Coastal Engineering *(SS6T ees SONVMs weneny BBN WOLNVAS S2ABy Limdd Guddmoa. 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G°0*2 (9961) uosttM | [{_ 1 (zM/43)800°0 + 1} - T)zE°t | [z-{z 1 (2N/s3)r00'0 + 1} - Tos*o (v961) 1982tM 99h‘ 0 (zN/d8)20S0°0 99h +0 (zN/d3)S0¢00°0 (SS61) UOSTTM [e +9 (zN/a3) 9¢70°0)] yuer OPT [5 +9 (gN/43) 10°0] yuer 92°0 n0T > 2/s3 ,0T > 2f/as (£S6T) Tepteuyssjeig pue prey * ¢*9(zN/43)0020°0 * §*9(zN/s3)Pz00°0 "(n/13) potsed pue ,(2N/H3) IYystey QuedTZTUsIS ssaTuoTsuaUTp oz suoTJENba uoTIDTpetd oAeEM ‘T STqRL 18 8 (25173 }-5] aF 0.25] u2 [0.077 gF u2 -{1+0.0 n/9 = “au h[o.01 ade ) 0.466 oF a2 ( {140.004 (96)!'/2}-2] OF )0.47 2 oF 0.5 ue yorez)] gF nh [o.o12s (5 —+— 0.0016 —--— 0.2831 ° SS r) a ‘sis 2) © o a So = oO 0.0024 (2505 ) 0.2 ( A plot of the equations defining wave growth from Table 1. Figure 5. Research Center, 1975). The part of the nomograph which applies to fetches of 1,000 miles or less is reproduced as Figure 6. b. Microscale Processes Involved in Wave Generation. It is well known that the generation of waves on the water surface must be dom- inated by pressure forces (e.g., for wave growth the pressure must be higher on the backface of the wave than on the front face), since any differences between the behavior of real waves and the predictions of potential flow theory are generally too small for detection by standard measurements. If pressure forces were not the dominant factor, potential flow then would not give reliable answers. Some departures of real waves from "linear" potential theory can be adequately explained when the nonlinear terms in the governing equations are considered. If viscous shear forces played a prominent role in wave generation, the waves would be rotational and differences between real waves and the predictions of potential flow theory would be easy to detect. The first substantial success in explaining the generation of surface water waves by pressure forces was achieved in 1957. Phillips (1957) showed that waves could be initiated on the surface of otherwise calm water by the random pressure pulses due to turbulence in the airstream. Miles (1957) independently showed that if waves existed on the upper surface of the water, similar waves must also exist on the lower surface of the atmosphere and that under quite general conditions, the atmospheric waves would extract energy from the airstream and pass it on to the water waves in the form of pressure pulses. The rate at which energy and momen- tum are extracted from the airstream and passed on the wave field is a function of the vertical profile of the horizontal wind velocity. Jeffreys (1925) proposed a similar theory in which the pressure differ- ential arose from the separation of the windstream in the lee of the wave crest. This theory depended on a sheltering coefficient which had to be determined empirically. The sheltering theory, however, could not become effective until the waves were of near maximum steepness. All three of the above processes are inviscid. Miles (1962) pro- posed a viscous instability theory which could be effective at very short fetches and high windspeed where the inviscid theories of Jeffreys (1925) and Miles (1957) could not apply. The generating mechanisms, as initially presented, were partially idealized in the effort to simplify the presentation of complex concepts. None was quantitatively correct, but together they presented an essential foundation for later study of wave generation. These theories have been merged and extended in many later reports by various authors. Coherent developments of the theory, based on many individual contributions, are presented in monographs by Phillips (1966) and Kraus (1972), and are devel- oped here only to the extent necessary to consider the modeling of wave generation in the laboratory. Later studies have shown that the mechanisms proposed by Jeffreys (1925), Phillips (1957), and Miles (1957) can account for the generation of waves 20 Fetch Length (mi) (u/iu) peadspuim Seu ere reac asl scisisiveat geastiat : st UAL ATA TEAR TS Ete ESOT ATTA THE FACIE PLU TIP sl: AED PSI TE LE YAM hd PEI ete yd VT EL is SER A At peace) DALY ti fs : ue 4 / £ Wot? Re eof] 200 250 300 400 $00 600 700 8009001000 8 (l-u/u.) dz . (12) z=0 26 The momentum thickness is defined by: co On -[ (u/u,,) (1-u/u,) dz z=0 The loss of momentum of the fluid in the boundary layer is given by: fe) us Sm Calculations by the Blasius (1910) theory show that for viscous flow: L 8g lew 20 SmGox/us)ie and L ONG64 Ux tea ae Sm Schlichting (1968) presented experimental data which indicated that the Blasius solution is satisfied within the limits of measurement. The Blasius theory showed that the Cg of equation (1) must decrease with increasing fetch because an increase in thickness of the boundary layer leads to a decrease in the velocity shear near the boundary. Analytic solution of the steady-state boundary layer equations for unstratified air have also been obtained for turbulent flow near a smooth plate. u, is the airspeed just outside the boundary layer. These solu- tions are reviewed by Schlichting (1968, ch. 21). The momentum thickness, Sm» for turbulent flow is given by: 1/5 Ore= 00 56x (uy) (13) Turbulence actually occurs in bursts and the instantaneous thickness of the turbulent flow is variable. Thus, the boundary layer thickness described here, is a meaningful concept only when the average over some finite time is considered. Analytic solutions are not available for rough surfaces, but numerical techniques are possible. Wade and Debrule (1973) used the method developed by Truckenbrodt and presented by Schlichting (1968, ch. 22) to integrate the equations governing the turbulent flow near both smooth and rough boundaries. The numerical solutions agree with equation (12) in indicating that the turbulent boundary layer thickness increases nearly linearly (0.8 power) with x and decreases very slowly aS Us. is increased. Presumably equation (12), established analytically for laboratory flows and flows past objects of finite size, breaks down in the atmosphere when 6 ~ reaches the value at which the pressure gradient and Coriolis acceleration must be considered, e.g., at a value OU of & near 100 meters. If the rate of boundary layer growth over water shown by Wade and Debrule persists, the boundary layer thickness would grow to 100 meters in a fetch of about 3 kilometers. If the air is stably Stratified, as it generally is, boundary layer growth will be somewhat slower. Turbulent boundary layers are developed along the sides and ceiling of the laboratory wind tunnel as specified by equation (12) as well as above the air-water interface. The air-water interface is generally rough; the roughness may increase with distance from the intake because of wave growth. Therefore, the resulting boundary layer is thicker, by an unknown amount, than indicated by equation (12). The transport of air through the wind tunnel must be independent of distance from the entrance. If the cross section available for airflow is also constant for the length of the tank, the boundary layer growth will result in a continually decreasing cross section for the flow outside the boundary layer. The process is fairly well understood for laminar boundary (Schlichting, 1968, pp. 176-178). The convergence of the flow results in acceleration of the core flow with distance from the entrance. In agreement with Bernoulli's equation, the accelerating flow is associated with a decreasing pressure. This pressure gradient adds another con- tribution to the pressure differential between the backface and front face of each wave, and contributes to the growth of waves in the lab- oratory. Bole (1973) discussed the importance of this pressure gradient on wave growth. Harris (1975) and Bole (1976) continued the discussion. Neglecting the stream-wise pressure gradient which results from boundary layer growth may introduce errors in all quantitative measurements of wave growth mechanisms in laboratory facilities. Turbulent flow with a pressure gradient is not as well understood as laminar flow, and the effects of pressure increases in the direction of flow have been studied more thoroughly than the effects of pressure drops (Schlichting, 1968, ch. 22). Nevertheless, a few important prin- ciples have been established. The boundary layers for accelerating flow are thinner than those for a zero-pressure gradient. It appears that this thinner boundary layer would lead to an increase in the boundary shear for a given mean speed of the airstream and a departure from the logarithmic velocity profile described by equation (9), but the available evidence is not clear. This possible departure of the velocity profile from equation (9) is important in wind-wave laboratory studies, because equation (9) is usually employed to evaluate the boundary shear and to relate laboratory and field velocity measurements. The boundary layer growth can be accommodated with acceleration of the core flow by expanding the cross section of the flow just enough to per- mit constant mass flux with a constant current speed in the nonturbulent region near the center of the wind tunnel. Expanding cross sections through adjustable ceiling heights are used in the micrometeorological wind tunnels at Colorado State University (Plate and Cermak, 1963) to 28 eliminate pressure gradients. Wade and Debrule (1973) calculated the amount of expansion in cross section required to eliminate pressure gra- dients for several conditions. Boundary layer growth near the ceiling can be reduced by sucking air from the boundary layer and reinjecting the air with increased momentum (Schlichting, 1968, ch. 14; Coantic and Favre, 1970). Wind-generated waves and currents are results of processes taking place in the boundary layer above the air-water interface. Therefore, it may be desirable to accelerate the generation of this boundary layer near the entrance of the airstream. Shemdin and Hsu (1966), Shemdin (1969a, 1969b, 1970), and Shemdin and Lai (1973) used artificial rough- ness elements on the floor of the air intake to expedite the development of the boundary layer near the air-water interface. Similar procedures have been used by many other investigators. 2: The Importance of Limited Fetch. If there is any chance of modeling the wind-wave generation process in the laboratory, it is necessary to have identical values for the scaled fetch for both laboratory and prototype conditions. Any of the equations in Table 1 will permit an estimate of the approach of the developing wave to the fully developed state. The uncertainty about the wave height and period in the fully developed state may exceed a factor of two (Fig 5). Representative values might be expected for waves that have attained between 90 and 99 percent of the maximum wave height. This is unlikely to be true when the waves have obtained less than 10 percent of maximum height, i.e., less than 1 percent of maximum energy. Table 2 gives the wave height, wave period, and the percentage of the final value achieved within fetches of 100 and 200 meters. A fetch of 100 meters will permit 90 percent of full-wave development for a speed of 10 centimeters per second. The resulting wave height is only 0.3 millimeter and the corresponding period is 0.07 second. There appears to be no evidence that the equations in Table 1 are valid for such low windspeeds. Tables 1 and 2 indicate that waves large enough for convenient use in engineer- ing studies could be generated by wind alone only for the initial stages of growth. There is no assurance that the resulting waveforms will be typical of the waveforms encountered in the field. The effect of longer fetches might be simulated by using a programable wave generator which can reproduce a sequence of waves with variable height and period to simulate the wave conditions expected for some finite fetch. D'Angremond and Van Oorschot (1969) compared wind-generated waves in the laboratory and in the field and reported that wind-generated laboratory waves characteristically have steeper wave fronts than wind- generated waves recorded in the field. They attributed this feature to the short fetches available in the laboratory. Some improvement is achieved by adding mechanically generated monochromatic waves; greater improvement is obtained by adding a programable wave generator to the 29 Table 2. Stage of wave development!. Fetch = 100 meters Percent T Percent H T ) developed (s) Eris ie developed 0.039 95.3 0.107 0. 86.6 0.347 0. 62.4 1.0 0. 40.6 2.0 0. 30.0 3.0 0. 24.4 4.0 0. 21.2 5.0 0. 19.0 7.0 0. 16.1 10.0 1. 13.5 15.0 ie 11.1 20.0 1. 9.6 25.0 1. 8.6 30.0 Ly 7.8 Fetch = 200 meters 0.07539 | O. 0 95.3 0.15156 | 0. 0. 86.6 0.4901 0. 0. 62.4 1.0 0. 0. 47.18 - 2.0 0. 0. 34.7 3.0 0. l. 0. 28.7 4.0 0. e)e 0. 25.1 5.0 0. 7. 0. BOOS 7.0 0. So 1. 19.13 10.0 0. 4. Ik 16.06 15.0 0. So lie 13.15 20.0 0. ORs 1. 11.406 25.0 0. Pie i 10.211 30.0 CG. 1. 2. SG GYS7/ 1A11 calculations are based on the equations identified by U.S. Army, Corps of Engineers, Coastal Engineering Research Center (1975) in Table 1. 30 wind-wave facility. The growth of the mechanically generated waves under the influence of wind in the wind tumnel may then be studied, but the pressure gradients resulting from growing boundary layers would still need to be considered. Considerable progress has been made in recent years in modeling wave spectra with programable wave generators to obtain laboratory wave trains with statistical characteristics similar to those observed in nature. The major contribution to an improved simulation of natural waves in lab- oratory facilities equipped with both programable wave generators and the ability to blow wind over the water appears to be due to the programable wave generators. 3. The Scales of Motion Involved in Momentum Exchange Between Wind and Water. In the atmosphere, the boundary layer equations can be used only in the lowest 100 meters. Boundary layer thickness is expected to approach this value within a fetch of about 3 kilometers in neutrally stable air. Wave growth may continue for fetches of more than 1,000 kilometers, 300 times the fetch of boundary layer growth. In the laboratory, boundary layer growth generally continues for the full length of the facility. Hence, a quasi-stable boundary layer condition independent of fetch (similar to prototype condition) is not developed in the laboratory for usable windspeed. In laminar airflow over calm water, only one of the wave-generating mechanisms (discussed in Section III)—the viscous shear theory of Miles— can be effective. This condition cannot hold over any large fetch in nature unless the windspeed is extremely small and the atmospheric strat- ification is extremely stable because the wind, with any significant speed, is always turbulent. Laminar flow may prevail for the first few meters in laboratory facilities unless turbulent flow conditions are generated before the air contacts the water. The part of the flow which is laminar, where wave generation is controlled by viscosity, cannot be regarded as modeling prototype wave generation. For turbulent flow over calm water, the Phillips (1957) mechanism for wave generation will be effective in both laboratory and field. Wave growth by this mechanism is controlled by the local structure of turbu- lence. The size of the turbulent eddies which can be effective in this process is limited, to a large extent, by the thickness of the turbulent boundary layer. The thickness of the turbulent boundary layer in the atmosphere varies with the density stratification of the air, the windspeed, and the surface roughness but is generally about 100 meters. Thus, the Phillips mechanism can contribute to wave growth at all wavelengths from a few centimeters to 100 meters or longer, if the windspeed is sufficiently high. In the laboratory the thickness of the turbulent boundary is always limited by the thickness of the airspace, which is often less than 1 meter. Generally the thickness of the turbulent boundary in the wind tunnel is much less than the thickness of the airspace. Thus, the Phillips mechanism 3| in the laboratory would be restricted to wavelengths of a few meters at most. The Phillips mechanism, therefore, can be effective over a wide range of frequencies in all stages of wave growth in nature, but only in a small range of high frequencies in the laboratory. The range of possible effectiveness is determined by the geometry of the laboratory flow. If the airstream is laminar as it enters the working section of the wind tunnel, only the smallest of the possible eddies will exist near the entrance. If the airflow is turbulent as it enters the wind tunnel, the nature of the turbulence will not be determined by the surface boundary layer alone, and no basis exists for assuming similar- ity of the structure of turbulence at laboratory and prototype scale or the validity of equation (9) for estimating boundary shear; i.e., if the Phillips wave-generation mechanism is modeled in the laboratory it is necessary to model the structure of turbulence. No method for fully accomplishing this modeling in wind-wave facilities has been established although the importance of duplicating atmospheric turbulence has received attention at some laboratories. The Miles (1957) invicid mechanism can be effective in laboratory and field as soon as waves of sufficient height and length have been devel- oped to let the phase velocity of the waves equal the component of the wind velocity in the direction of wave propagation at some level above the viscous sublayer. The onset of this mechanism must begin under the same conditions in both laboratory and field. The magnitude of the energy exchange by the Miles mechanism depends on the first and second derivatives of the wind profile near the level at which windspeed and wave speed are equal. This implies the necessity of modeling not only the turbulent structure of the flow, but also the wind profile. The wind profile changes along the flume in response to boundary layer growth, pressure gradients, and the changes in surface roughness due to wave generation. However, pressure gradients do not play a significant roll in determining the wind profile in the turbulent boundary layer above an open water surface in the prototype. Boundary layer growth is believed to be unimportant for fetches longer than a few kilometers. Controlling the wind profile to approximate real prototype conditions for the length of the flume will be a difficult or impossible task. The Jeffreys (1925) sheltering mechanism becomes effective in both laboratory and field when the waves exposed to the mean wind are near maximum steepness. For short fetches with no high waves in both lab- oratory and field, separation may take place from ripples short enough to be governed by surface tension, and the Jeffreys mechanism will involve surface tension. At longer fetches and higher waves, unrealizable in the laboratory, these ripples and some waves long enough to be outside the capillary range will be modulated by the longer waves and maybe sheltered from the mean wind by the larger waves for a part of each wave cycle. The Jeffreys mechanism will not be able to operate on these waves for a part of the long-wave cycle. Thus, the Jeffreys mechanism in the lab- oratory cannot be a geometrically similar model to the Jeffreys mechanism in the open sea. 32 Wave-wave interaction feeds wave energy from the part of the wave spectrum where it is received to both longer and shorter waves. Several wave-wave interaction processes have been identified; all require the preexistence af a range of wavelengths, and some depend on the three- dimensional characteristics of the natural wave field. These mechanisms become significant only at scaled fetch lengths unobtainable with wind- generated laboratory waves when waves large enough for engineering studies are required. Laboratory studies of wave-wave interaction, where a pro- gramable wave generator is used to develop the desired range of wavelengths, may be useful in further development of this concept. Wind-stress coefficients above a rigid boundary in the laboratory decrease with fetch because the increase in boundary layer thickness leads to a decrease in the intensity of the shear near the surface. This mech- anism is effective only for short fetches, probably no more than a few kilometers in the field. Wind-stress coefficients in the field also appear to decrease with increasing fetch, but here the cause is varia- tion in the stage of wave growth. This effect could be measured in a well-designed laboratory experiment, but the decrease will not follow the scaling laws expected to govern wave growth or wave forces. 4. Summary. The growth of boundary layers on the sidewalls and ceiling, and above the air-water interface, leads to a constriction of the airflow and a pressure gradient in the direction of the airflow in wind tunnels of con- stant cross section. This pressure gradient provides a contribution to wave growth not present in nature. The importance of the pressure gradient was not recognized before 1970, and has been neglected in the analyses of most laboratory data dealing with the growth of waves and wind stress on water. Boundary layer growth also leads to a reduction in the wind-stress coefficient with fetch in laboratory experiments dealing with rigid bound- aries. Laboratory studies of wind stress over water have generally con- sidered only the mean stress between two designated positions in the wind tunnel. Studies of wind-stress variability over natural water surfaces also indicate a decrease in the wind-stress coefficient with increasing fetch, but for different reasons than those applicable to laboratory flows. Wave growth with fetch is rather slow in nature, and can be modeled in the laboratory only for very low windspeeds or very short-scaled fetches. Wave height obtained for very low windspeeds is too small for use in engi- neering experiments. Large waves with natural characteristics can be obtained only with the aid of programable mechanical wave generators. The microscale processes responsible for wave growth vary with fetch, the wave spectrum, and the stage of wave growth. It seems unlikely that all important processes can be modeled to scale in a single experiment. 33 Surface waves play an active role in transferring momentum from air to water. Thus, the generation of currents by wind cannot be modeled quantitatively without first modeling the generation of waves. Since the two most important processes for momentum exchange between atmosphere and sea cannot be modeled in a quantitative sense, it seems unnecessary to discuss the difficulties of quantitative modeling of such secondary processes as the generation of spray. V. SOME LANDMARK EXPERIMENTS Although it appears impossible to model the full process of wave gen- eration for waves of significant size in a single experiment, many lab- oratory studies have contributed significantly to an understanding of the processes involved in wind-wave generation and the transfer of momentum from air to water. The analytical skill of the investigator has generally been more important than the size or sophistication of the laboratory facilities in determining the significance of the experimental results. A few significant results are briefly reviewed in this section. Significant results were obtained in some of the early experiments in spite of the lack of understanding of some of the phenomena discussed in Section IV. Quantitative agreement between laboratory and field data, however, has rarely been achieved. 1. Significant Experimental Results. a. Keulegan's Experiments. Keulegan (1951), using a wind-wave flume 28.5 centimeters (11.2 inches) deep, 11.3 centimeters (4.5 inches) wide, and about 20 meters (65 feet) long, made several discoveries of fundamental importance to all future wind-wave laboratory studies. Although these discoveries have been confirmed many times, all have not yet been adequately explained, and they are sometimes overlooked. It was discovered by accident that adding soap to water inhibited the formation of waves by wind, but did not seem to interfere with the dynamics of mechanically generated waves. Later investigators confirmed this dis- covery and found that the same result can be obtained with synthetic deter- gents in the field and in the laboratory. Keulegan used soap to suppress wind-wave generation, and measured the stress of wind on water with and without waves, while holding other exper- imental conditions nearly constant. He found that the presence of waves greatly increased the stress for all winds above a critical velocity which depended on the viscosity of the water. This result has been confirmed for field and laboratory measurements by Van Dorn (1953) and other investigators. By using soap to suppress wave formation and clean water to permit wave formation, Keulegan also measured the velocity of the water surface with and without waves. He found that for the conditions of his experiments, water depths of 4 to 14.5 centimeters (1.5 to 5.7 inches) and reference 34 windspeeds of 3.5 to 9 meters per second (7.3 to 20 miles per hour), the ratio of the water surface speed to the reference windspeed tended to 0.033 and was not affected by waves. No effect of fetch could be estab- lished. The speed was inversely proportional to the Reynolds number UH/v, where U is the reference windspeed, H the water depth, and y the kinematic viscosity of the water, when the Reynolds number was less than 30,000. Keulegan used the average velocity in the wind tunnel as his reference velocity. Hidy and Plate (1965), Wu (1968), and other investigators also reported that the ratio between surface speed of the water and reference windspeed is near 0.03 in laboratory experiments. Van Dorn (1953) and others reported similar ratios from observations in natural flows. The close agreement in the ratio between surface water speed and reference windspeed in laboratory and field, without regard to the precise definition of the reference windspeed has not been satisfac- torily explained. Keulegan reported that the reference windspeed increased with fetch in his wind tunnel; the relative increase was greater in the presence of waves and seemed to increase with wave height. This result has also been confirmed by later investigators. Keulegan and some later investi- gators attributed this increase in windspeed to a reduction in the cross section of the free airflow with increasing fetch, brought about by the growth of waves and the setup, i.e., the increase in water level at the leeward end of the flume resulting from wind stress. It has long been recognized (discussed in Section IV), that an increase in windspeed with fetch results from the decrease in the cross section of the free airflow. Schlichting (1934) was probably the first to explain that this effect results from boundary layer growth and to demonstrate empirically that it is real. These results were later summarized by Schlichting (1968, pp. 176-178). In explaining the increasing windspeed in wave-wind flumes, Hidy and Plate (1965) recognized that boundary layer growth is a more important factor than any effect of waves or wind setup. b. Liang's Experiments. Liang (1972) demonstrated the effect of pressure gradients on wave growth and boundary stress in a laboratory facility. He used a wind tunnel 61 centimeters (24 inches) wide, 50 centimeters (19.7 inches) deep, and 11 meters (36 feet) long. A mean water level of 19.37 centimeters (7.6 inches) was used in all experi- ments. The top of the channel consisted of nine movable louvers which could be opened. By allowing some air to leave the tunnel through openings in the roof, it was possible to maintain a nearly constant free- stream velocity and to nearly eliminate the pressure gradient in the direction of airflow. As expected, the rate of wave growth and the boundary stress were reduced by a reduction of the pressure gradient. The bottom boundary layer thickness was less in the presence of a pressure gradient. These results were expected on the basis of the theoretical concepts discussed in Section IV. Liang was not able to maintain perfect control over boundary layer development in this small facility, and the quantitative accuracy of the results may be doubtful. 35 The primary purpose of the study, however, was to show qualitatively that the pressure gradient developed in laboratory wave-wind flume of constant cross section contributes significantly to wave growth. This result was achieved. c. Experiments by Shemdin and Hsu. Shemdin and Hsu (1966) made a Significant contribution to the art of laboratory study of wind-wave generation by introducing a rough transition plate to speed the develop- ment of a turbulent boundary layer above the water surface and thereby achieve a more natural velocity profile. This is essential for modeling the Miles invicid wave-generation process. Shemdin and Hsu used a combination wind tunnel-wave channel with a working section 28 meters (85 feet) long, 1.89 meters (74.5 inches) high, 90.2 centimeters (35.5 inches) wide, with a nominal water depth of 91 centimeters (3 feet). They neglected the constriction of the free stream and the consequent pressure gradient in the downward direction. Shemdin (1969a) extended this verification study of the Miles mechanism and reported that the actual wave growth was generally greater than that predicted by the Miles theory. This result is consistent with Liang's finding that the pressure gradient developed in a laboratory wave-wind flume contributes an addi- tional factor to wave growth not observed in nature. Shemdin used a com- bination wind tunnel-wave channel with a working section 36.6 meters (120 feet) long, 1.93 meters (76 inches) high, including a nominal water depth of 91 centimeters (36 inches). The facility was 86.4 centimeters (34 inches) wide. Although pressure gradients were neglected in this study, Hsu (1965) présented figures showing an acceleration of the core flow in the facility at Stanford University used by Shemdin and Hsu. Shemdin (1969b) reported similar figures for the University of Florida facility used in later studies. The neglect of the pressure gradient in the direct- ion of wave growth casts some doubt about the quantitative validity of many of Shemdin's results. Latif (1974) reported another phenomenon at the University of Florida wind tunnel-wave flume (and presumably in most other research facilities) in which a wind was blown over mechanically generated waves. The wind was led to the water by a ramp which terminated in front of the wave gen- erator slightly above the wave crest. Each mechanically generated wave pushed a slug of air into the wind tunnel forming an acoustic wave in phase with the water wave at the inlet. This pressure wave has the same fre- quency as the mechanically generated wave; however, since the pressure wave traveled at the speed of sound its phase was nearly constant throughout the facility. This pressure wave does not have a counterpart in nature. According to Latif, the amplitude of this acoustic wave was large enough to question the quantitative results of most earlier studies of the relation between atmospheric pressure pulses and wave generation in the laboratory. Since Latif was a student of Shemdin at the time, it may be assumed that Shemdin accepts these findings. However, the qualitative evidence of wave- induced pressure pulses, Reynolds stresses near the water surface, and the effects of surface water waves on atmospheric turbulence is undisputed. The desire to obtain experimental proof of the reality of these predicted effects was among the principle motivations of Shemdin's studies. 36 d. Ramamonjiarisoa's Experiments. Ramamonjiarisoa (1973) presented a comparison of wave spectra from field and laboratory studies which showed that the spectra generated in laboratory wind-wave flumes are more narrow than those obtained in the field and that, in nature, unlimited fetches lead to broader spectra than limited fetches. This increasing spectrum width with increasing fetch length is believed to result from the greater variance of wind conditions over long fetches, and a greater variance in the specific mechanisms responsible for wave generation when long fetches are involved. 2. Summary. A small sample of laboratory studies of the interaction between wind and water is sufficient to show that these studies have provided con- siderable new insight for the hydrodynamic processes involved. The phe- nomena of concern are extremely complex. Some essential aspects of the phenomena have been neglected in every experiment described in the lit- erature. It appears that the technology necessary for quantitative modeling of the processes by which momentum is passed from air to sea has not yet been developed. It appears unlikely that a technology for modeling the complete process can be developed in the foreseeable future. VI. SUMMARY AND CONCLUSIONS 1. Summary. The mechanically generated monochromatic waves, generally used in laboratory studies of coastal engineering problems, are more regular in height and period than the wind-generated waves observed in coastal regions. The possibility of laboratory generation of waves which bear a closer resemblance to prototype waves by combining a wind tunnel with a wave flume, has a natural appeal to many research engineers. Moreover, the existence of a combination wind tunnel-wave channel in engineering laboratories would inspire much useful research related to the air-water interaction processes of greatest concern to coastal engineers. A review of the extensive literature related to laboratory studies of wind-wave generation shows that much qualitative understanding about wind- wave generation has been obtained from laboratory studies, that much more remains to be learned, and that every past experiment could be improved in the light of knowledge available today. Thus, a combination wind tunnel-wave channel could be a great aid to fundamental research in air-sea interaction processes. The review of the literature dealing with the physical aspects of wave generation shows that many complex microscale processes are involved. Modeling these processes in the laboratory involves a great deal more than blowing a known quantity of air across the water surface. Comparisons of wave growth with increasing fetch and comparisons of the spectra of wind- generated waves obtained under both laboratory and field conditions gives little support to the notion that waves generated by wind in the laboratory will be more suitable for engineering studies than mechanically generated waves. 37 A literature review of the frictional drag of wind on solid surfaces or water indicates that the process.is not adequately understood and that the usual engineering practice of expressing the wind stress on water as the product of a coefficient, which is constant or a function of wind- speed only, and the square of the windspeed as in equation (1), is inade- quate for agreement between calculations and natural phenomena. The momentum exchange between air and water, to form wind-driven currents in the water, is a complex process involving both the growth and decay of waves. Thus, quantitative agreement between model and pro- totype experiments is not to be expected unless the wave generation and decay processes are correctly simulated. A laboratory facility for air-water interaction studies might be use- ful in obtaining a better understanding of some of the processes discussed in Section II without achieving quantitative results or a quantitatively correct modeling of the wave-wind current-generating mechanisms. 2. Conclusions. 1. Wind-wave research facilities, designed with specific research objectives in mind and a clear understanding of the many difficulties in modeling air-sea interaction processes in the laboratory, can be inval- uable for fundamental research. 2. The state-of-the-art in modeling of air-water interaction processes in the laboratory has not advanced to a level which provides any assurance that the validity of laboratory studies of wave effects on beaches or manmade structures is improved for engineering applications by using wind to generate or modify the laboratory waves. 3. Mechanical wave-generation systems which can reproduce the spectra and waveforms of natural wind-generated waves more accurately than the mechanical wave generators now in common uSe are essential for the full utilization of a wave tank-wind tunnel. . Thus, further development of mech- anical wave-generating systems is an essential part of any plan for the effective utilization of a wave tank-wind tunnel for coastal engineering research. It may be possible to obtain nearly as much improvement in coastal engineering studies through more effective use of wave-generating systems, as through the combination of a wind tunnel with a wave tank. 4. 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WU, J., "Physical and Dynamical Scales for Generation of Wind Waves," Journal of the Waterways, Harbors and Coastal Engineering Diviston, ASCE, Vol. 98, No. WW2, May 1972. pp. 163-175. 44 d3igcn* £09 Gi=9 15 Ou. d3rgcn* £0¢OL *Z1-92 ‘ou aeded TeoTuysey “Teque) YyrPresoy ZutiseuT3suq yeqseop ‘sf : setses “II “eTIFL “I “SyUe eAeM-puTM “4 *uoT e19ues aaeM ‘¢ ‘BupTIeeuTZue TeISeOD *Z ‘UOTIJOeISRUT eTeydsowj;e-UPZDO *| *SOTIIT TORS VACM-pUTM YITM SqJuowTIedxe A10}e10qeT A[Taee pue ‘sTouun} ut MOTJ ite ‘uoT}Je19Ues sAeM Jo SeTpN}S LeTT1es smeTAei 310dey ‘pequeseid st setpnjs BuTiseuTsue Te}sSeod 105 AQTT TIS yoaeasel aAeM-puTM e Jo asn [eTIUejod ay} Jo uoTIeBTISeAUT Uy "hy -6€ °“d :Ayderz0TT QTE (ZL-9L “OU £ raqUeD yoieesey SutiseuT3uqg TeIseoD *s°n — aeded TeoTuYyIeL) “TTT : sd oy "9/6, ‘19}UaD YOAeesey BuTIeeuTsuq TeqseoD : “eA ‘ATOATEG 3109 — ‘stziey ae] ‘a fq / sezpnys fz0}e10GeT OJ SeAeM paze1eUes-puTM eet °a Sstiz1ey daigcn* £09 Glictys, "OL d3igcn* €0cOL "ZL -92 ‘ou aeded Teotuype]l ‘*‘ieqUeD YyoiPessy SutiveutTsuq Teqseop *Ss*N : SeTeS “II “eTITL “1 “sue saeM-putM °y *uoTJe198Ue3 aaem *¢€ “SuTseuTZUe TeISeOD °Z “UOTIIeIEIUT eToYydsowje-ursIO *| *soTJITTOey SAPM-puTM ITM SqUeMTIedxe A10}e10qeT A[Tiee pue ‘sTauunj uz MOTJ ite ‘uoTIe19Ues BAEM JO SaTpnjs iteT[1ve smaTAei j10dey ‘*pajqueseid sft seTpnjs ZuTiseuTsue Te}seOd OJ AVIT TORS yoreesel aAeM-puyM e jo asn TeTIUe}od By} Jo uOTIeSTISEAUT UY *yy-6€ *d :hydersotTqta (ZL-9L “Ou $ taequeD yoreesey Sutrseutsuq Teqseog *s*n — azeded TeotuyoeL) “TTT : sd hy °9/6| ‘203UeD YOIeeSeYy BuTiseuTZug Te}seoD : *eA SATOATEG 3104 — *sTazey ee7 ‘a Aq / setpnqs Kz0jze1OgeT oF seAeM poje1sUss-puTM eey °d ‘stisey dargcn* £29 ZL-9L “Ou daigsn° €07OL "71-92 ‘ou aeded TeoTuyoe, ‘itejueD yorresoy SuTrseuTsug Teqseop *S'N : SeTteg “II “eTIFL “1 = “Syuey sAeM-puTM “H *uoTJe19Ue3 aaem *¢ ‘SuTAseuTSue TeISeOD *Z “UOTIOPIeQUT sAeYydsowje-UR|DO *| *SoTITTTOeJ IACA-PUTM YITM sjUuewTiedxa A10}JeIOgGeT ATiee pue ‘sTouun3 ut MoTF Ate ‘uoTeLT9Uad aAeM JO SaTpNjSs 1eT{T1ve smatTAei qiodey ‘*pajqueseid st setpnjs BuTirseuT3ue Teqyseod 1035 AQTT PIRI yo1easei aAeM-puTM e& Jo asn TeTIUS}Od ay} Jo uoTIeSTISeAUT Uy *h-6¢ °d :AydeasotTqta (ZL-9L “Ou £ JequeD yoieesoy SutTraeutT3uq Te 3seoD “Ss°n — geded ~Teotuyoey) “TIT : °d 4H “Q/6| ‘193UeD YIIeeSey BuTIseuTSuq Te SeOD : *eA *zTOATeaq 3104 — *sTzieH ve] ‘Gd Aq / setpnys AzojeIOGeT 103 saaen peje i9ued -putM ae7 ‘a ‘stizeH d3igcn° £79 TL=9L “Ou d3igcn* £0Z0L *ZL-92 ‘ou deded Teotuyse, *taqueD yo1eEeseYy suTiseuT sug qeyseop °S°*N : SeTsJes “II “eTIFL “I *Syuez aaem-purtmM *y ‘uot ereues aAeM *¢ ‘“BuTreeuTBue TeIseOD *Z “UOTIOPTeRUT ateydsowje-ursIO “| *SOTITTPORJ SAPM-PUTM YITM SJUewTIedxe A10}eI0GeT Ajiea pue ‘stTeuun3 uyt MoT Ate ‘uoTIe1eUes aAeM JO SaTpny}Ss 1eTT[1ee smatAei yiodeay ‘paqueseid st satpnjs Buyteeuft3ue Te seod 10jJ AQTT eS yoreased aAeM-purM e Jo asn TeTIUajod ay, jo uoTIeBTISeAUT UY “hy-6¢ °d :Ayderzzorrqta (ZL-9L “Ou $ 4taqUaD yoreesey ButzseuTsugq Te seo) *S*n — Joded TeoTuyoeL) “TTT : *d ph "9/6, ‘2eqUeDQ YyOTeeSsey BuTissuT3ug Te IseoD : “eA SaToATeg 31049 — *staaey veT *q Aq / setpnqs Arojze1OGeT 10fF saaeM pe eraue3-putM aeTt a ‘stiieH a DAN ‘= d3igcn° 129 ZL-9L *OU daigcn° €O7OL "ZL -92 ‘ou aaded [eoTuyoey *1ejqUeD YAeesey BuTIseUTsUy qeqseop *S'n : Setzes ‘II ‘eTITL ‘I ‘syue eaeN-puTM *y ‘UOTIeIOUES aaeM *€ “BSuTIVeUTSUS TeISeOD *Z ‘UOTJOeIEJUT s19ydsowje-urZD0 “| *SOTITTTOeJ SAPM-pUTM YITM SjUeWTIedxe A10}ZeIOGeT ATiee pue ‘sTouunj UT MOTZ ATe ‘SuOoTJeIEUeZs sAeM JO SeTpN}S AeTTA1ee smaTAei jiodey ‘*pajueseid st setpnqys B3uTrteauT3ue Te seod AOJZ AATT TIF yoreesedl dAeM-puTmM e Jo asSn TeTJUajod ay} Jo uoTIeBTISeAUT UY *yy-6¢ °d :AydersorTqta (ZL-9L "OU $ reqUeaD yoieesey ZuTiseuT3uq Te3seoD *Ss*n — Jeded Teotuyse]) “TTT : sd bh *Q/6| ‘1eqUeD YOIeesey BuTAseuTZUq Te seo) : “eA *ATOATEG 310g — *‘staiey ee7 *q Aq / setpnqs Ato}eAOGeT 10J3 seaen pe .er9ues-putmM eet °d *stzzey daigcn* L£e9 GL=9L ~ou daigcn* £€02OL "71-9 ‘ou aeded TeoTuype] ‘*1aqUeQ yoieesey BuTAseUTsUq yeqseoD “stn : SeTzeS “II “STITL ‘1 ‘“syue eaem-putm *y ‘uoTWJeI19Ue3 aAeM *€ ‘BUTA@eUTBUe TeISeOD *Z ‘UOTIIe1aIUT etToYydsowje-ureDO *| *“SOTITT IOP SAPM-PUTM YITM SjUeUTIedxa A10}P10QGeT ATiee pue ‘sTouun} ut MOT Ate ‘uoT}Je198ued eAeM Jo SaTpNjS iaTT1ee smetaei yioday “*pejueseid st setpnys B3uTrseuTsue Teyseod Joy ATT Te; 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