Vol. 4 No. 7 DEPARTMENT OF THE ARMY CORPS OF ENGINEERS Marine Biological 4 +:.1: -i- J OFA S79 & 7 hs Re JUL 28 185" WOODS HOLE, MASS. I W H O07 — ; “s ns POC: 2A Ep yom BULLETIN ‘ WAVE CRESTS BOTTOM CONTOURS —- — Th DEPTHS IN FATHOMS Yards 6,000 12,000 _ 18,000 Nautical miles FIGURE 2 3 118°5' VILL A thy, / UMMM AAA AEEE “nf fy Uo; y, Vy, g Af, / SAN PEDRO BAY Yh) Mffy SWELL FROM 190° Y Vy, yy Y ey / yy VY, Yi DEPTH IN FATHOMS WAVE CRESTS BOTTOM CONTOURS ——- —- — 118°20' pon ae || ye 15! REFRACTION FACTOR K BK, y Yyyy UY YYWV) YY LOS ANGELES-LONG BEACH OUTER BREAKWATER 118°5" FIGURE 3 4 submarine valley located south of San Pedro, and leads to a maximum diver- gence between orthogonals c and d. Due to the focusing of wave energy by San Pedro Shelf, the wave crests between orthogonals g and k converge on the sastern portion of the breakwater, the greatest convergence occurr- ing between i and j. On both sides of the breakwater the refraction factors indicate divergence. Figures 4 and 5 show the detailed refraction diagrams for southern hemisphere swell advancing toward San Pedro Bay from 180° and 170° respec- tively. Although the main features of these figures are similar to those of Figure 3, several significant differences exist. These variations are shown best in Figure 6 which gives the refraction factors along the breakwater for all three diagrams. In addition, the refraction factors are plotted for 20 second waves from 160° as computed from the diagram presented by O'Brien (1947). Figure 6 shows that an eastward shift in the direction of wave approach causes the zone of convergence to shift westward along the break- water. The westward shift of the general pattern of wave refraction for 160° beyond that of 170° serves to support this. In the region of greatest divergence along the western portion of the breakwater greater intensity of wave energy is experienced from 160° than from the other three directions because the shadowing effect of the islands is lacking for NGOS. sing bails connection the combined effects of the islands and San Pedro Shelf in shifting the entire refraction pattern may be compared to the action of a fulcrum, about which the wave approach and wave advance are pivoted, The region of convergence indicated for directions of wave approach from 160° to 170° coincides closely with the location of the damaged por- tion of the Long Beach Breakwater in 1930. Applying a refraction factor of 3.50 for this zone of convergence and utilizing the available observa- tions! of wave height, which were made during this critical period at locations seaward of the outer end of the breakwater, a deep water wave height of between 3 and 4 feet is obtained. For southern hemisphere swell of 20 second period the refraction factor would be somewhat modified for slightly different period swell; shorter wave periods would be accompanied by less convergence. Part Ii - Waves from a Tropical Storm. The large waves at San Pedro Bay on September 24 and 25, 1939, were produced by unusually strong winds in the area of the North Pacific to the south of Long Beach. Unlike southern hemisphere swell which originates beyond the present weather reporting area, these waves could be estimated in advance by using available synoptic weather data. In this study the wave characteristics at San Pedro Bay have been computed for September 24 and 25 by use of the forecasting technique given by Francis (1944) and a set of wave forecasting graphs prepared by Arthur (1948) from the revised theory given by Sverdrup and Munk (1947). Investigation of synoptic weather situation. - When the tropical storm appeared on the weather maps it was progressing northward along the 5 1211 footnotes are given at the end of the article. 18°20! Gy LLL Yip ppp ppp) ppt pps) F he i SOG EE Vf Mes Y Vf, y y /, SAN PEDRO BAY YffffifooMyyyy0 Uy SWELL FROM 180° Yyy YY fy Yi PERIOD 20 SECONDS DEPTH IN FATHOMS YH Vif hf if Y Yards Uy, yy, My yy ~ CREST INTERVAL: 4 WAVES 2000 4000 6000 YU“ Y, pio Y Y , ORTHOGONALS —-G——> y / AALS, y YA pfs ff Nautical miles y eu /, VW “4 WAVE CRESTS 7 Nf, BOTTOM CONTOURS —- —- —— REFRACTION FACTOR K &K | 2 3 4 YW); WjfYyyyyy Wy Vf fy Yj YY Y /, = SS FIGURE 4 & 6 SAN PEDRO BAY DEPTH IN FATHOMS Yards 2000 4000 Nautical miles 6000 118°20' f FIGURE 5 7 9 VMMMMLHEY YY), BEACHYYY, 2, et SWELL FROM 170° PERIOD 20 SECONDS CREST INTERVAL : 4 WAVES ORTHOGONALS =O ————>> WAVE CRESTS BOTTOM CONTOURS —- —- —— REFRACTION FACTOR RQAAQas WN N WN 2 3 4 MV bl pli ti th ht fll) CANGF Cj; V2 4 /, > Yi ZY QS (7 Yy Ye UY Ly Y EN S 15! 118° 10" FIGURE 6 Lower California coast, and it subsequently dissipated after it encounter- ed the coast of Southern California. The weather maps in Figure 7 show that the storm decreased in intensity from September 22 to September 25. As it traveled northward toward the coastline the winds in the eastern portion of the storm were always directed toward Long Beach. This con- dition, together with the movement of the storm, produced an effective fetch which exceeded 1,000 miles. The velocity of the storm's center was approximately 15 knots during the interval 1630 P.S.T., September 21 to 1630 P.S.T., September 22, after which it gradually decreased to about 6 knots by 1630 P.S.T., September 24. In order to determine the longest possible effective fetch, within the limits of available weather data, the speed of the wave energy front which remained under the influence of strong winds for the longest time was computed relative to the speed of the storm. This energy front would be expected to emerge from the fetch before the strong winds from the storm reached San Pedro Bay. However, because the wind field quickly elongated and was extended to Long Beach during the period 0430-1630 P.S.T. ' September 24 as shown in Figure 7, the waves comprising the energy front continued to grow under these winds all the way to Long Beach. In addition, the extended wind field represented an earlier local fetch which produced short period wind waves of considerable height. Between 1630 P.S.T., September 24 and 0430 P.S.T., September 25, the storm elongated in an east-west direction. Soon after the 0430 map the winds at San Pedro Bay subsided to calm or light and variable, and the storm center moved toward the coast in the region between San Pedro and San Diego, At about 0700 the winds at San Pedro backed to the northeast, but a small fetch still existed to the south. The existeance of this fetch is verified by the south winds which were recorded at San Pedro for some period after the windshift occurred at San Pedro (Table 1). By 1630 P.S.T., September 25 the storm's center was no longer distinguishable. ‘Computed deep water wave conditions. - The computed deep water characteristics at San Pedro Bay for waves from the tropical storm are tabulated in Table 2 and presented graphically in Figure 8. Swells from westerly directions preceding and following the waves from the tropical storm are also shown on the graph. The time when generation began as shown in Table 2 was the initial time at which the average wind velocity, U, applied. Prior to this time lighter winds which preceded the main fetch had produced low waves of short period. Thsse waves were still present in the fetch area at the time generation began. As a result, the actual fetch, F, shown on the weather maps was effectively increased by the distance required to generate the short low waves at velocity, U. This distance tovether with the fetch shown on the weather maps and the distance. the storm moved with the waves during generation comprise the effective fetch, Fe. The wave height and period at the end of the fetch, Hy and Ty, have been computed using either F or Fy, whichever was greater. The opposing wind which existed in the decay area after about 0700 P.Sol. September 25 was allowed for by increasing the decay distance, D, by a certain amount (Arthur, 1948). The wave height and period at the 9 TRAJECTORY OF STORM Circle indicates position of storm at 0430 PST. Dot indicates position > of storm at 1630 PS.T. 22 SEPT. 1939 1630 PRS.T. 24 SEPT. 1939 25 SEPT. 1939 1630 PST. 0430 PST. FIGURE 7 lO TABLE 1 Hourly Winds for Coastal Stations in Southern California during the Tropical Storm of September 1939 LOS ANGELZS AREA SAN DI#GO LOS ANGELES SAN PHDRO Bate and a fime 1 Dhieecienloya Wedloestione ati Mire Direction Velocity in MPH 24-0900% i) "y ‘ SH 3 1000 _ S 12 Sis 3 LLCO. SE 24 oH 9 1200 S 29 SE 21 1300 $ 29 psi, 30 1400 SE 30 Si 30 1500 ‘Sah 2 SE 40 1600 S5 27 Sa 42 1700 SE 26 SE 36 1800 SE 25 SE 34 1900 Si 24 SH 40 2000 SH 24 SH 37 2100 SE 2b ihe) 39 2200 SE Pole, ESE 39 2300 1 24 ESE 35 25-0000 SE 24 ESS 3% 0100 SE 22 ESE 4C 0200 SE ae, HSE 35 0300 SF 24 HSE Al 0400 SE 29 ESE 43 0500 SE 27 ESE 4l 0600 s 29 ESE 34 0700 Ss} 2h NE 26 0800 5 Be NE 16 0900 iS) 21 NW 12 1000 3 19 NW U5 1100 8 18 V g 1200 3 1S W 24 1300 5 US Vi 22 1400 5 LS 1500 5 13 *% September 24, 1939, 0900 Pacific Standard Time. ++ Wind directions were not recorded at San Fedro. 92-6 0£00 G2e-6| G2-6| Ge-6 |] G2-6 | Se- GTTe| O€ LT! STST Zee oe Ge-6 |G2e-6! G2-6|S OgTl OO0T | Sig0 QUeISAOM SAGA JO UOTJOOITp O9TSOddo sem PUTM JO UOTAOSATP seqvoTpuT usts SATIeBONy 6| 12-6 | |qe-6 00g) 000¢ 2-6] Ge- aoe ae Of£ TO 42-6 Oc LT | 42-6] 42-61 42-6. 42-6 | 4e-6 O€GT O€ET O€2T O€TT OLOT; SMT Teatize peqndmo) (samoy) 4q ‘vere Leoep | gO pue 09 omy} Toaery, | (spuooes) Ty, ‘vere Let] ent! o€t| gttl 96 GT- Ogr O¢- gt- gT- OL | OF ol G3-6 | Ge-6] Ge-6 O€HT | OS eT] O£60 OT oy es G*_ | 0°6 0°98 — — G2-6 Ge-6 0060 0880 | e 6 0°42 0°92 (seTtm *qneu) %q "98Tp Aeoep OATIOOTIM (sqoux) ,N “sere keep uz £4T90TSA PUTM (S°TF@ °4neU) qd ‘9oueqstp svoeq 2 (ees) \0€L0 0£S0 9° ot €*1T | ee ae 92 6-92\c-Le e 1216°Lele°g2lS-ge JL°TU| HST Leb | HET IO HT\6°S |o°H J9°e (spuoses) dy, “youes _gO pues 4e potted eaem aS grot|rot|s9 (7993) HA ‘yoqer _gO pue 72 94STey SAeM |£Gz aca on | TS” aE icet lose |see €9 ueyy 1078015 (stmoy) BFW ___ uot yeInp WNUTUTW (smoy) Pa ‘pura jo uortyeang 006 |0L6 {099 |00g |0G6 |OOTT OST “| (set Tm ~4neu) | Sq ©YOIOT SATIOOTITZ yoyeg Jo uoz za0d ot | lie +96 496 GQT |O6T |S6T {002 |O02 |002 ooz lost |sct logt a GOT (ee “yneu) 7 “yoqed 9g |9f OE JOE I9€ 9¢ ieoi Ut BUTYSEXS j O£t0 SSAeA TTeUS +2-6 |4d-6 |€2-6 OLOT OE HO |OE ez See Ss es eee €2-6 O£9T €3-6|£2-6|2d-6 |2e-6 | 12-6 OZOT jOS40 |OELT |00L0 |000¢e | keg Olped ueg Joy suotytTpuog eaem teqem deeq Jo suotyeqgndmog - == Ite- 6 te- 2-6 qe- wat qe- 2-6 [OTT |O€TT |OOTT |O =z = ail polsad aapm pajnduwoj—-- .o) N ybiay aaom pasndwog <—WAVE HEIGHT IN FEET 1SaM 3HL isaM 3HL el) GR INS ONION, STON CEN a oe StI end of the decay area, Hp and Tp , which are shown in Table 2, have been computed using the effective decay distance, D,, where applicable. In the computations no diffraction correction (Francis, 1944) has been applied because (1) no decay distance existed until after 0430 P.S.T., September 25 and (2) after this time the fetch no longer resembled the circular fetch characteristic of a tropical storm. The waves from the tropical storm may be divided into four parts as shown in the lower part of Figure 8. The short period wind waves from the earlier local fetch increased rapidly in height at about 1200 P.SoT., September 24 and remained predominant until about 1430 P.S.1T., September 24. At that time waves from the long effective fetch arrived. These had not traveled through decay areas and were still growing under the influence of strong winds when arriving at San Pedro Bay. They were of great height and relatively long period. The rapid build-up in wave height shown in Figure 8 would have been even more accentuated if the earlier local fetch had not developed. Such a quick build-up of wave height is a characteristic common to waves from tropical storms, and it has been reported for certain other tropical storms that strong winds and very high waves arrived simultaneously. Socn after the arrival of waves from the long effective fetch the computed wave height was greater than 28 feet and the corresponding period 14 seconds. For almost 12 hours these waves maintained great height, but their period steadily decreased with time. The waves shown between 0500 and 0700 September 25 represent swell from the small fetch to the south decayed under calm or variable winds. After O700 when the winds at San Pedro backed to northeast the waves represented swell decayed under opposing winds, and the height and period decrease fairly rapidly. Not until about 0500 September 26 did the swell from the west become larger than the swell from the weak residual fetch located to the south. Refraction pattern and distributing of damage. - As indicated by the geographical locations of the tropical storm's wind field shown in Figure 7 the wind waves and swell from this storm approached Long Beach from directions varying between 150° and 190° in deep water. Figure 9 is a portion of the refraction diagram for 175° and 14 seconds period. This corresponds to the period of the highest waves from the long effective fetch reaching San Pedro Bay. The complete diagram from which Figure 9 is taken is shown in the inset and was drawn with a crest interval of 2 waves on a detailed chart of the bottom topography. The refraction factors are presented in the same manner as on the diagrams for southern hemisphere swell. The damaged portions of the Los Angeles-Long Beach Detached Break- water and the intensity of the damage within these areas are also shown in Figure 9. It is evident that the amount of damage was increasingly great from west to east along this breakwater while the Long Beach break- water escaped without damage. From this it appears that the wave forces were considerably greater near the easterly end of the detached break— water. Because of its seaward location, the detached breakwater apparently provided shelter for the undamaged Long Beach Breakwater. 14 175° was about the most easterly direction from which waves could have produced the observed damage pattern, From more easterly directions the waves probably would have resulted in damage to the Long Beach Break- water. Consequently, it appears that the damaging waves approaiche|d San Pedro Bay from directions within the narrow sector from 175° to about 185°. For directions west of 185° the effect of refraction around Cata- lina Island considerably reduced the wave force on the breakwater. Figure 9 shows that the refraction factors increase progressively toward the east end of the detached breakwater from 0.37 between ortho- gonals a and b to 1.65 between orthogonais f and g with corresponding heights varying from 10 to about 45 feet, disregarding interference between wave trains. Unfortunately, actual measurements of wave height and period at San Pe dro Bay during this storm were not made, but the direction of wave approach was observed by means of a transit from Pt. Fermin near the westerly end of San Pedro Breakwater. This observation indicated that waves came from the southwest concurrently with waves from the southeast, and that the southwest waves appeared to be the larger. Although, it is impossible to determine without observations of wave period whether or not one train of waves was southern swell arriving simultaneously with the waves from the tropical storm, the observed directions of wave approach and distribution of damage can be fully ex- plained by the tropical storm waves alone. Since waves from a tropical storm are propagated radially from the storm's center, there is a certain amount of variability in direction from which the waves may come. The higher waves arriving at San Pedro Bay were probably generated near the center of the storm, but at the same time some waves were being generated by the weaker winds nearer the east side of the storm just off the coast, and these smaller waves approached Long Beach from directions which were more to the southeast. Having less height and shorter periods they experienced little re- fraction in crossing San Pedro Sheif and reached the breakwater retain- ing their original direction. On the other hand, the large waves from the long effective fetch approaching from directions between 175° and 185° were refracted most over San Pedro Sea Valley so that the wave crests in the vicinity of the breakwater were oriented in such a way that the waves appeared to come from directions more twoard the southeast. Summary and Conclusions The characteristics of waves destructive to the harbor breakwaters in the Long Beach-San Pedro area have been examined. As a result of re- fraction over the complicated bottom topography in San Pedro Bay this wave energy was concentrated at certain parts of the breakwaters. The refraction effect of the bottom topography upon waves from the tropical storm was similar to that for southern hemisphere swell but less pro- nounced because the tropical storm waves had shorter periods. us OS slsiolsl s| —— YaLVMyV SYNE 2 NVS jL———— WY pebpo|sip 4 K } i S9UOIS C9 =| fe wos000 QaHoviad é Ap dilate _HOW38 ONOT | =S3739NV SOT e k pebpojsip aqvos a39na3y NI SQUOJS OJ AVG OUNGId NVS Aes pebpojsip seuojs Oo} pebowop A\pog 49}DM MO] 9AOGD ado|S pipmpes asijug ZA ese pebowop Ajpoqg 4a}0mM MO| @AOGD ainjonsysuadns a4yug — — SUNOLNOD WOLLO fuel —— SIEM EINIM 0002 000! 3 : (pabowop jou) <—-—— D— S1VNO90H1YO | S| : YSLVMyVSYE HOVSE ONOT SGUMVA = = My oy 2 SSAVM 8 ny), 5 :WAYALNI 1S3Y9 SGNOOSS vl GOlYsd AVG ONGad NVS iE > SLI WONS S3AVM ~ 01,811 SWOHIVS NI! Hid 92°04S 16 The predominant characteristics common to all the preceding re- fraction diagrams can be attributed to specific features of the bottom topography. In each case a zone of divergence is produced by the sea valleys located on either side of the San Pedro Shelf. And, these valleys aid in producing greater convergence over the extended shelf lying between them, Slight changes in wave direction result in size- able displacement of the zones of convergence and divergence, while the effect of wave direction upon the magnitude of the refraction factor is somewhat less marked. Because of interference between wave trains, the largest waves at certain parts of the breakwater may contain greater intensity of energy than the amount indicated by the refraction factors, The computed wave height and direction of approach of the tropical storm waves agree with observed conditions. Without additional ob- servations of both wave height and period, it is impossible to test the accuracy of the existing technique for estimating waves from a tropical storm. The computations indicate that waves at Long Beach from such a tropical storm contain far greater energy than wind waves or swell from other northern hemisphere storms which pass to the south of Long Beach. However, because of the rarity of occurrence of tropical storms which can produce damaging waves in the Long Beach region it may be more economical and practical to plan to repair the existing breakwaters after each of these storms than to build the breakwaters heavy enough to withstand such wave attack. Acknowledgements The U. S. Weather Bureau, Department of Commerce, and the Calif- ornia Institute of Technology have furnished the meteorological data needed for this study. Mr. R. O. Eaton, Corps of Engineers, has pro- vided information pertaining to wave observations and damage to harbor structures in the Long Beach-San Pedro area. LADS MD SESL SLM NL SM SOL SDL KISS SISSIES Footnotes it Measurements of wave height were made by Mr. R. O. Haton, Corps of Engineers and communicated by letter to Dr. Walter H. Munk of Scripps Institution of Oceanography. Wave heights of 15 and 18 feet were recorded in depths. of 37 and 27 feet, respectively. 2 Lieut. Ho. F. Nowak, U.S.N., has recently given a verbal descrip-— tion of the height of the wave crests as he observed it from aboard the aircraft carrier Lexington on September 24, 1939. The Lexington was at anchor in water between 50 and 60 feet deep east- northeast of the eastern end of the detached breakwater. Lieut. Nowak estimated the tops of the wave crests to be about 24 feet above mean water level. If it is assumed that the trough of the waves is one-fourth of the wave height below the mean water level the total wave height is 32 feet. The computed wave height in this area, allowing for refraction and depth, is between 32 and 39 feet, depending upon the exact petaten for which the refraction factor is computed. 17 REFERENCES Arthur, Ro S., 1948. Kevised Wave Forecasting Graphs and Procedure; Wave Project Number 73, Scripps Institution of Oceanography of the University of California, 14 pp. Francis, W. Jo. Jr., 1944. Waves and Swell from a Tropical Storm, Wave Project Report No. 29, Scripps Institution of Oceanography of the University of California, 29 pp. Munk, W. Ho. and MoH. Traylor, 1947. Refraction of Ocean Waves: A Process Linking Underwater Topography to Beach Erosion, Journal of Geology, Vol. LV, No. 1, pp. 1-26. O'Brien, M. Po, 1947. Wave Refraction at Long Beach and Santa Barbara, California, Technical Report HE-116-246, Fluid Mechanics Laboratory Berkeley, California, 14 pp. Sverdrup, H. U., and W. H. Munk, 1947. Wind, Sea and Swell; Theory of Relations for Forecasting, U. S. Hydrographic Office, Technical Report No. 1, H. 0. Publication No. 601, 44 pp. 18 THE WIND ELEMENT IN BEACH EROSION Martin A. Mason Chief, Engineering and Research Branch Beach Erosion Board (Presented at Symposium on Hydrometeorological Problems, American Geophysical Union, 2 May 1950) The art of beach protection against loss of sand has been develop- ing for decases through the thought and experiment of engineers, geo- logists, and others whose interest derived chiefly from circumstance and only rarely for othsr reasons. Harly students of shore control problems had little to guide their thinking and experiment other than their ob- servational acumen. Thus, waves were recognized as a factor causing transport and possible loss of sand, but local wind, usually most evident when waves were observed, was considered to be of prime importance. Possibly much of the regard in which local wind has been held as an important factor in beach erosion stems from the early reports of the Beach Hrosion Board. These reports accorded a prominent place to dis- cussion of the local wind and its probable effects. Today, when it is believed that the mechanism of loss of beach is better understood than previously, there is a notable tendency to assign to local wind a much less important place as a factor in sand loss. Wind is believed presently to be the ultimate source of the energy which, when expended on a beach, either directly as wind or indirectly through the medium of surface water waves, causes transportation of sand along the shore and the bottom, and ravages the land boundaries of the water mass. In the process of expending energy on the shore local winds are recognized now as playing usually a relatively minor role. Investigators long have recognized the beach as the primary source of supply for shore dunes and correctly identified local wind as the eroding and transporting agent responsible for the dune formations. The conditions requisite to erosion, or deflation of beaches by local winds can be stated as; 1. An expanse of dry beach sand, of sufficient extent in the direction of wind movement and so located with respect to the surrounding topography as to permit sand transport by a local wind system. 2. The existence of wind in intimate proximity to the sand surface. This second condition appears at first glance to be trivial, however, those familiar with beaches located adjacent to appreciable topographic irregularities often have expsrienced absence of wind immediately con- tiguous to the sand surface when local wind was present elsewhere. 19 So far as is known presently the mechanism of erosion and transport of sand by wind, is analogous in all respects to that by water; the Reynolds numbers of the process in the two media is similar, and observations of the actual movement of sand grains shows the motion to be analogous in air and. ~ water. An additional factor not yet investigated to the author's knowledge is that of the role played by water content of the beach in causing a time delay in the erosion-transportation sequence. The differences in character of a given sand or beach mixture when dry or wet have been noted often; generally, moist sand has a higher load bearinc capacity than dry, while wet sand often shows a much lower capacity than cr,;. Moist sand appears to ex- hibit more cohesion than the dry, while wet sand appears to be more fluid even than the dry material. Yet the author has observed apparently dry sand blown in considerable quently from beach areas still wet from a receding tide. O’Brien and Rindlaub report that "on one occasion, sand was un-— pleasantly evident at 8 feet above the beach curing a heavy rainstorm ac-— companied by wind with an intensity of 48 miles per hour." They report also an observation that wind of 15 miles per hour velocity moved sand in the moist area below the last high water mark. Tle evaporative effects of the wind seem to be important to the problem, probably entering chiefly by changing the erodibility characteristics of the material. Bagnold(2) has shown that sand movement in air occurs as a sand cloud (sand in suspension) and as surface creep (bedload), in analogy to sand movement by water. Similarly to sana movement in water the motion of the sand grains occurs as rolling, saltation, and suspension. His experiments show that the threshold velocity required to sustain sand movement can be expressed ass lo sok C9 ad where O and P are the densities of the sand grain anc air respectively; d is the grain diameter; and k' is the height above the surface at which the threshold velocity occurs, related to the surface roughness (parameter K in the Prandtl turbulent flow law). Vy, = 0047(TE* See Through application of Prandtl's rough-surface law for turbulent flow and consideration of surface drag relations Bagnold suggests the following expression for relating total sand flow to wind velocity p= cid £ (Vze-Vr)? G 5.75 5.75 1Og=/K' where d is the mean diameter of any sand; D the mean diameter of a so-called standard sand (0.024cm); Vz the wind velocity measured at a height Z above the sand surface; k' has the value 0.3 cm. for uniform sands; and C is a coefficient varying from 1.5 for uniform grading of sand to 2.8 for sand with a wide range of grain size. (1) The Transportation of Sand by Wind - M. P. O'Brien and B. D. Rindlaub, Civil Engineering, Vol. 6, No. 5, May 1936. (2) The Transport of Sand by Wind, R. A. Bagnold, The Geographical Journal Vol. LXXXIX, No. 5, May 1937. 20 Shore dunes are the visual evidence of a sedimentation process and occur as a result of a local climatic condition by which the sand trans-— porting wind loses its competence. This may occur by reduction in wind velocity; by change in wind direction; or by sheltering, either natural or induced artificially. So long as sand is available on the beach and local wind conditions favorable to sand veneers exist the process of deflation continues. Q'Brien and HRindlaub\~/report rates of movement as high as 2,200 pounds of sand per foot of beach per day measured on Clatrop Spit at the mouth of the Columbia River. In many areas the loss of sand from beaches by wind de- flation is doubly troublesome, as at Hollywood Beach near Port hueneme where dune formations induced by shore cottages threatens to engulf the buildings, the structures acting as effective sand fences in promoting dune formation and growth. In this area the loss of sand by-local wind action probably approximates 50,000 cubic yards annually, which is more than sufficient to maintain excellent beaches almost anywhere in the Great Lakes area where annual littoral drift is smaller than on most ocean shores. The indirect effects of wind on the shore face are mich more important than the direct effects briefly discussed above. The case may be stated in this fashion. If wind is assumed to blow over an initially rough water surface energy will be transferred from the wind to the water by normal - pressure and frictional drag, thus generating wave motion. The area in which this transfer occurs, i.e., the generating area, corresponds roughly to the area of the wind system. Considering the wide extent of the re- latively unobstructed water surface, and the possibility! in large bodies of water that several wind systems may contribute to the energy of waves, it. can be presumed that the energy carried to the shore by waves greatly exceeds that which it is possible to obtain by the action of local winds. The energy budget of wind generated waves has been studied by Sverdrup and Vunk (3), who have stated that "It seems probable that the energy used for wave formation represents only a small fraction of the wind energy which is dissipated below a height of 8 to 10 mters.---— A very small fraction, about 1 per cent, of this amount is transferred to the sea for maintaining the pure wind current and another fraction goes into formation and maintenance of waves. -—--- Analysis indicates that 10 per cent or less of the wind energy dissipated in the lowest layer (of wind) goes toward increasing or maintaining the energy of the waves." Among other factors to be considered are: that, 1. The waves existing at any moment are the result of wind action in one or more generating areas; 2. Interference occurs between waves; 3. The generating wind is variable in velocity, direction, and duration; 4. A wind of given velocity probably generates a spectrum of waves of various periods and amplitudes. 21 (3) Wind Waves and Swell-A Basic Theory for Forecasting, H. U. Sverdrup & W. He Munk, Scripps Inst. of Oceanography, Wave Rpt. No. 1, Sep 1943. Sverdrup and Munk succeeded in establishing a fundamental equation relating wind action to wave action, and showing that the energy content of the waves gensrated depends primarily upon the wind velocity, the wind fetch, and the wind duration. Waves forecast by the Sverdrup-Munk relationship have been shown by comparative observation to approximate reasonably well natural conditions, thus confirming their theoretical concepts. It can be concluded that the waves reaching a shore are, in most instances, due to the net effect of one or more wind systems transferring energy to the water, with the wave motion serving as a collecting and transporting medium conveying the net energy con- tained in the waves to the shore. At the shore interface wave motion can no longer exist and the wave energy built up over long intervals of time and space must be dissipated abruptly. A large part of the energy is believed to be lost in the turbu- lence of the breaking wave, in the pick-up and throwing into suspension of bottom or beach material, in impact, and other losses, the remainder being lost in the rush of the broken wave, carrying its load of suspended sand, up the beach slope. This is an ideal situation for the erosion and trans- port of large quantities of sand or beach material. Waves commonly approach the shoreface at an angle and there is a resulting component of motion of sand and water along the shore, giving rise to the well-known littoral transport of sand. The annual rate of loss of sand by littoral transport due to wind- generated waves varies widely in different situations, the maximum known - to the author occurring south of Port Hueneme, California, and approximat- ing 1,000,000 cubic yards. This rate is some twenty time the estimated loss due to local wind action in the same general area. In other areas, such as the south Florida coast losses due to local wind are not discernible while littoral transport approximates 250,000 to 270,000 cubic yards annually. The effects of wind action on water in causing wind-generated currents and wind set-up or depression are considered to be negligible in the usual shore problem in comparison with the effects discussed above. It should not be presumed that the effect of wind on beaches is wholly destructive. In fact the destructive effects of local winds in denuding beach areas beyond the range of normal wave and tide action can be turned to good purpose by management of the wind-transported sand. The use of planting and sand fences to build dunes on or immediately adjacent to the landward portions of a beach is an effective means of conserving and stock-— piling sand against the day of unusually destructive storm wave or tide action. This conservation practice has been notably successful in rebuild- ing and maintaining the protective dune ridge of the south shore of Long Island. In the September 1938 hurricane that devastated much of the New York and New England area it was the dune ridge built naturally by local wind action and acting as a dike that prevented engulfment of the Great Barrier beach of Long Island by the sea. Further, the sand of the dunes, once lost from the beach, was returned to the beaches by the waves to preserve the famous strand characteristic of this area. Careful management 22 of the local wind transported sand since that time has rebuilt the dunes and reestablished the natural stockpile of sand against the next hurricane. The wind element in beach erosion mst be considered as the one most important factor of the entire problem. Its net influence appears to be degenerative, and not susceptible of effective control. It is most apparent in its indirect effect of wave generation, however, in many instances its direct effects appear to be subject to management in a conservative fashion. & of “. % aS os 23 THE LAG AND REDUCTION OF RANGE IN TIDE GAGE WELLS The following paper first: appeared in limited issue as Technical Memorandum No. 14,.U. 5. Tidal Laboratory, Berkeley, California, by Morrough P. O'Brien, Consulting Engineer. The paper is reproduced here to bring the findings to the attention of a larger group of research workers and others having an interest in tidal phenomena. Abstract The problem of the lag of high and low water and the reduction of range has been treated by Chapman (Philosophical Magazine, Vol. 46, 1923), for the case of a simple orifice connecting a primary tidal basin with a secondary basin on the assumption that the instantaneous rate of flow corresponds to the instantaneous head. In the analysis which follows, the treatment is generalized to include the effect of both laminar and turbu- lent friction and the effect of acceleration. Theory General Equations. - The equation of continuity relating the average velocity in the connecting line and the velocity of rise of the water surface in the well is (for symbol meanings see Appendix I) av = A dH! (1) dt At any instant, the elevation of the primary tidal surface is H and that in the gage well is H'. The working head at that instant is h =H - #! Hi = (H - h) (2) Flow occurs into the well when H>H', or h>O, and out of the well when H>H!., The primary tidal surface exhibits periodic variations and for the _ purpose of this analysis, these variations will be assumed to be sinusoidal, 1.e. H = H, sine bt; & = 2 9 — ii (3) The curve of H' will also be a sine curve of lesser amplitude lagging the curve of H but having the same period. Therefore, the equation for the working head may be written as h Ho sin & t - Ho! sine a(t +€) h =h, sin a(t + € ) (4) 24 Here, € is the time interval by which corresponding tidal events in the tide gage well lag those in the outside basin. The equation of continuity may also be written: aV = A d (H-h) dt (la) Laminar Flow. - For the usual tide gage installation in a tidal model, the flow in the connecting pipe line is probably laminar. The criterion for the occurrence of laminar flow is that VD < 2300 (approx. ) (5) V Since the velocity increases periodically from zero to a maximum, Vm, the Reynolds number (Vd) increases from zero to a maximum value, Fm, and for the purpose of limiting the present treatment, it will be assumed that for laminar flow Fal =) ime se 22300 (5a) v Periodic reversal of flow introduces some disturbance and the critical value of the Reynolds number may be slightly lower than 2300 but there are no data available on the magnitude of the reduction. Poiseuille's equation for laminar flow in a long tube is V = wh Su L (6) The tube is assumed to be long in order that the velocity head loss at discharge will be negligible as compared with the overall working head, h. The head necessary to accelerate the water in the connecting pipe is neglected. Substituting equation (6) in equation (la), td (Hh) = awR@h dt Su L (7) Substituting for H and h from equations (3) and (4) gives oe sin & t-h sin o& (t +€)|= awR@h dt ° ae Su L Substituting equation (4) in this expression, and differentiating, Ae [Ho cos xt - h, cos & (t+€ )|= awR< . hh sinx(t +€ ) SUL Inserting the constant Cs8u Qa _ AL awk C [ Ho cos xt - hh (cos xt cos KRE- sin xt sin ow €)] = hh (sin-a& t cosa € + cos o& t + Sinn E) (8) 25 When cos&% t =0, Cho sin@€ = hy cos € and tan w€ = 1 C (9) When cos Xt =1, CyHo =) 0) boyicos CCC ="hewsanlicgic and substitution for C from equation (9) gives hh = cos aE Ho (10) Equations (9) and (10) determine the constants necessary for computa- tion of the working head at any instant, t. The actual elevation H' in the tide gage well is a Se el dat eh) calla) ee (( te = S)) Expanding this equation and inserting equations (9) and (10) gives 2 Ha! RO dey) 2] lag =s1-costx€ = sine a & ae a 0 Ho tan&@ = - cob aE . (aigh)) Here, XE = conta (1). The lag in seconds of events on the H'-curve C after the corresponding events on the H-curve is the quantity 6. Both the lag and the reduction in range are seen to be functions of the dimensionless quantity C which may therefore be regarded as the model criterion for the fluctuations in tide gage wells connected to the outside basin by lines which are long in proportion to the maximum velocity head. Turbulent Flow. - In completely developed turbulent flow in pipes, the head loss is proportional to the square of the velocity. If this quadratic relationship is taken as the definition of "turbulent" flow, then very short pips lines connecting two reservoirs may be regarded as being in "turbulent flow", even though the flow may actually be laminar, because the working head is utilized almost entirely in creating velocity - head which is proportional to vy in both turbulent and laminar flow. In other words laminar flow through an orifice or avery short tube should obey the same type of equation (not the same equation) as turbulent flow in a long pipe. The exact length of tube which divides turbulent and laminar flow as defined here cannot be specified exactly but it will de- pend upon the relationship between the friction head and the velocity head. 26 The resistance to steady flow through a pipe line connecting two res— ervoirs is Here, K represents the entrance, elbow and other losses due to fittings, f is the friction factor corresponding to the velocity V and VY, is the final velocity at exit. The values of K and f depend upon the Keynolds number. The ratio V_/V equals the coefficient of contraction in the case of an orifice. For 4 simple pipe connection, V, = V. Inserting the coef- ficient of contraction and solving for V, V (12) Here & is the velocity head coefficient and C, is the coefficient of con- traction at discharge. The continuity equation is s h) = ate (1b) Assuming that h is sinusoidal as before, 1 = 3 [Ho sin a t - h, sin a(t + €)]=+ * fa: Sin &(t €)/ (13) a The solution given by Chapman expresses [sin a(t + & )]? as a Fourier series which preserves the absolute value of the right hand member. sin? X = a] Sin x + a3 Sin 3x + as sin 5x + ..... + a, Sin nx. the valuesof the constants are: yy cea HE Gabats) =aly/7) ten = 5/77 ay The series becomes sin us +€))? = 1.113 [sin oc (t +€) + 1/7 sin 3a(t +€) + 5/77 sin 5a(t+&) + eee 27 Substituting in equation (13) Ac [Hp sin at - hy sin c/( (t+) =)1-113 a es 2eho ys [sin a(t +€) + 1/7 sin 3x (t +€) + 5/77 a 5 x(t +€) & Gscoo] (14) Substituting t! for X(t +€) and differentiating equation (14), a Hp cos (t' -x€) - hh cos t' =a . 1.113 (78Po ye [ series] A of M a L letting (2N)2 = 2 a bolls (2) A OK M 2 Hy cos t' cos & E+ H sin tiax€ = h, cos t! = (2Nh,)? [series | (15) When cos t! =1, H, cos &E = hy | (16) and when cos t' = 0, al Hy sinx€= (2h)? [1-1/7 + 5/77 - + eel (17) The series converges to unity. Squaring and adding equations (16) and (17) 2 Hy” cos" KE = ho® + Ho~ sina - 2Nh, = 0 ne z BL o As = Ala. 20 2 ho = (N° + H,~)z - N (18) Also 2 aL cos@ME=(1+N )2 -W Ho° Ho (19) The equations for the range in the tide gage well are: 2 a Hy'? = Ho? = ho? = Ho? - [ (N? + Ho2) - an (Ne + #2)" + We | i [ (Ne + H2)2 = N = 2Nho : (20) tan & =- cot n€& (21) The dimensionless equations are: 28 Ho Ho (22) fy Ho 2N Sima et) (COSROCG (23) Ho Ho tan X&@ = -cot XE (2) The phenomenon is seen to be a function of the Jimensionless ratio N/E for the condition assumed. Acceleration. - In the preceding analysis of the problem, it was assumed that the instantaneous rate of flow in accelerated motion is the same as in steady motion under the same head. This assumption neglects the head necessary to accelerate the flow. The magnitude of the error will now be analyzed for the case of laminar flow. The equations of motion are, h-h! =L a g dt (24) h' = 8uU LV w Re 2 V = A dH! qv = A da H! a dt dt a q¢- 2 h- 8 LA dH' = L A da°H! wa Re dt ga date. (242) From the first approximation, hh = Hp cos HE h = ho sinw (t +€) Ho" = Ho sin oc € H' =H)! sina (t - 6) If these relationships are substituted in equation 24a, the equation becomes an inequality since the first approximation was obtained on the assumption that dv = 0. Making the substitution dt Hp cos XEsin a (t +E )-ax& SUTA HH, sin & cos & (t - 9) > waR oo te Re sanvecé) sin 0G “(hb —="6) =°0 (25) ae a 0g jt 29 ert Since tan & 0 =- cot aE ,x~ 9+KE= 4 and sin « (t +€) = cos c (t- @). Substituting this relationship in equation (25) and dividing through by cos w€ cos & (t - 9) gives ie rn 1 - BXULA tanoe&y oc LA tanaé tan ax (t - 0) =0 waR? ga The first two members do not vary with time and are equal. The third member then expresses the error resulting from the assumption that the flow at each instant equals the rate of steady flow under the same head. Since tan (t - 0) c0oas ao (t- 0)» W/o , the error is certainly not negligible over some portion of the cycle. Taking the ratio of the acceleration and viscosity terms given by the first approximation, of * TA tanc € tan « (t - 0) oR tan cc (t-0) aes 2) ena : Sax wu LA [ea Oe wak' An approximate method of determining a limit for & such that the acceleration term will not appreciably affect the results is to hold this ratio below a value n over a certain percentage of the cycle, p. Thus oR BV For example, to hold the ratio of inertia forces to viscous forces below QO.l over 75 per cent of the cycle, tanec (t = O)en; of (t - 0) Zp WH (26) 2 = 67.5° 3 tan p =) 2/207, tw UW 2 A= Ol1xsx V_ 2414 pe With ¥ = 1.0 x 107° ft.“/sec. and R = 0.0112 ft. (1/8" pipe), o = 0.033 radians per second. As these figures for & , R, and Y are approximately those obtaired in the experiments reported here, the conditions were such that the inertia forces probably account for some of the discrepancy between the theoretical and experimental results. The preceding analysis indicates that in long lines the effect of inertia will have a very great effect on the results before the flow becomes turbulent in the usual sense. Referring back to the Reynolds number (Equation 5a) q Ra = ume = Sey te eee Hy sina€[eos & (t - )|Vmax v Fy le aa =) eho) sanicceati ate (27) ay 30 The criterion for the maximum value of co is cea Sia eget (P a 2 (26a) If R, exceeds = 2300 and & from equation (26a) is within reasonable limits for a particular case, then the analysis of the maximum value of C¢ must be modified to fit the case of turbulent flow, starting from ee (24) but uSing the previous analysis of turbulent flow as the first approximation. Cn the other hand, if R, 2 2300 and & siven by equation (26a) is ae iyelan the value of o for the experimental installation, the connection to the tide gage well should be modified or its lag and reduction of range should be determined experimentally. ~ Coefficients. - Practically, the case of turbulent flow is important only in very short lines in which the connection is equivalent to an orifice or Short tube. Hence the friction coefficient f in turbulent flow probably enters the equation for M in very few cases. Since the Reynolds number is generally small, the flow through the orifice is laminar and the coefficient C, is mec: unity. The coefficient K is smaller than in truly turbulent flow but not mich is known about the correct value. Whether a particular problem should be solved by the equations for laminar or turbulent flow depends on the ratio of that portion of the resistance which is proportional to v and that proportional to V. Taking the simple case of laminar flow in a short connection, 6 in equation (12) equals 2, Cera olke The two components of the head h are then » Me em SLY 2g we Taking the ratio Soe) We 75 AG wR i 2g 2vRe Inserting the value of V given by the laminar solution V=A GHt = &AHO sing€ cose (t - Q) a ‘ at A Ve Nicene We 8a PV Rika | G2 ineoenees If this ratio is large as compared with unity, the head necessary} OV viscous resistance is large as compared with the velocity ae ad and the solution applies. If it turns out to be small as compared with 31 turbulent solution probably applies but further analysis of the problem mst be made. Experimental Procedure. - A water level recorder (Steven's Type M) was operated in a gage well placed in the model basin and connected to the water in the basin by pipes and openings of various lengths and diameters. Another identical water level recorder was operated in a second gaze well which was completely open at the bottom. The two recorders were synchronized by de- pressing the pens simultaneously. Experimental Results. — The problem has been analyzed earlier in this paper on the basis of two types of flow, viz: Laminar; head loss @V_ 3; long lines Turbulent; head loss « v* ; short lines Under usual conditions the flow probably seldom is turbulent in the strict technical sense but even in laminar flow through a short tube or orifice the effective head is proportional to the square of the velocity and it is in this sense that the term "turbulent™ is used here. On the assumption that the instantaneous rate of flow is the same as during steady flow under the same operating head (inertia neglected) analysis of the problem yields the following results: (a) Laminar flow. dy eS Bo) dan ch B 2 D200 ap fee si OS BT ee Ne ‘al = awk? tana @ =-cot ME 9+E = MT or 90 (b) Turbulent flow. 32 GOS Clie a (il & oe Ves Ni 12% H.* ac ae) aha oe Ho 2N cos KX E€ Eo tan o& 9 =- cot K § The two types of flow are seen to be functions of the dimensionless quantities C and N/Ho for laminar and turbulent flow respectively. Figures 1 and 2 are constructed on the basis of these dimensionless variables. The tide gage measurements were made using straight lengths of standard wrought-iron pipe connected to a 4-inch gage well. The reference measure- ments were made in a gage well open at the bottom located immediately adjac to the inlet to the connecting pipe line 1. Laminar Flow Connecting Veasured Pipe Diamete 1 DELO nea | ee OUI | ely ans peta N : e ft ft. | Ho wo e ° OWN Or OND i 2 2 ie) 6 18. 29 al i 6 H Wwrvno ° 33 Be Turbulent Flow Connecting Hole Diameter A Tidal | Nom. | Actual Period] in. in. Veasured 70.8 1/8 Boe || th 627 138.0 | 1/16 20384 140.5 Experimental Accuracy The elevations on the tide graphs can be measured to + 0.001 foot. The time intervals can be read to at least + 2 seconds and perhaps even more accurately. The maximum range of H, was about 0.025 feet and H,' went as low as 0.003 so that the error in elevation measurements was roughly + 4% and + 35% with the smaller error occurring with the larger ranges. As the lag increased, the percentage error in the measured values decreased but was always greater than + 5%. The remarks on accuracy are made as an explanation of the scattering of the experimental points, shown on Figures 1 and 2. Sample Calculation (a) A tide gage is to be located in a 4-inch well and connected to the main tidal basin by 40 feet of 4 inch standard wrought iron pipe. Hy = 0.025 ft. A = 123 = 5 Ty = 4Orft. fh = DUG UNG ssn Cee, R = 0.0152 ft. T = 138.0 sec. w = 62.4 lbs./cu. ft. a = 0.0447 rad./sec. C= 8HXTA = 8 x 2.35 x .0447 x 107° x 40 x 123 = 2.87 wea 62.4 x (.0152)* HS tate) 203 Gea oo 5 Ao” @=- 70.7 x 14005 = 27.5 sec (measured 31 + 2 sec.) 360 Ho! = Hp cos «@ = 0.025 x 0.331 = 0.008 ft. Ve asured Ho! = 0.003 + 0.001 fatare 34 (b) Same conditions as in (a) except that connecting line is made up of 10 ft. of 1/2 inch wrought-iron pipe. Bly 2 Os023) see (= 2.3 x 10> lb.sec. /ft.sq. 1) a 10 ft. T = WA0.5 SCC R = 0.0111 ft. A = 223 ; a iW = C2ok, Mesiaiotige ian : aan Oh = O17 radians/sec. LAO 45 G = Stloo ay = 8 x 2.35 x Or? x O.0407 x 223 x 10 = 2.3% waRe C2) (Or Olle) GCe) =) =67°) = Zor Q = 67.7 x 140.5 = 26.4 sec. (measured 30 + 2 sec.) 360 Ho! = 0.023 x 0.380 = 0.0088 ft. Measured Ho! = 0.006 + 0.001 ft. A tide gage is’ to be placed in a gase well 4 inches in diameter. The connection is a 1/8" cylindrical hole drilled through the tube wall. (a) Ho = 0.025 A/a = 223 i @) (aiojeiatep'e, ») m=2=27T = 0.0888 rad./sec. : 70.8 2 = OGOD7/ Selo) shac T. = 70.8 sac. Wi = az Niei2 (ae pleiia\> -eorsr= (iy Ml gue \e G4ee = On0ge A x M 23 x 0.0888 ee ho = 0.089 - 0.088 = 0.001 ft. The measured value of ho was of the order of 0.001 ft., the precision of the gage being + 0.001 ft. and no reduction in range being observable. —) (Eee snOsO24) fue & = 0.0447 sec. p10 Cpe A i) =70 a St ALSO) i - kK = One T = 140.5 sec. M=1.2 IN Gea inl ealalsy uy Shah =| (Goto 4150 x 0.0447 2 ho = 0.023 ft. Ho! =\f2Nho = 0.0068 ft. (measured = 0.003 + .00l ft) COs) C¢E =) oll) =) 06023) =)10.915)7) se Eater SO! tano @=- cota@E CG 9 = —- 73° = 10! or -1.28 radians Q@=-1.28 140.5 = 29 seconds 27 Measured © = 34 + sec. Referring back to the same calculation on page 34, (Laminar flow, Example (a) ga Vv 8 x 1.05 x 107 = 16 CO AHR? sinxé 0.0447 x 123 x .0125 x (0.0152)° x 331 The viscous head is large as compared with the velocity head. Conclusions Qn the basis of the comparisons made it is believed that the theoretical curves may be relied upon more than experimental results because the error in the experimental results is relatively great. This statement is made on the assumption that the various criteria developed in the theory are satisfied. 36 H! Ho! tl ul APPENDIX I SYMBOLS elevation of primary tide above mean level at time t half the amplitude of the primary tide curve elevation of tide in gage well at any time t half the amplitude of tide curve in mana effective head at any, time t half the amplitude of effective head =! time od (t +€ ) lead of effective head in seconds lag of tide curve in gage well in seconds tidal period ‘ratio of inertia to viscous head percentage of cycle during which ratio of inertia to viscous heads is less than n 2 Oy 7A area of connecting line area of tide-gage well radius of connecting pipe diameter of connecting line length of connecting line characteristic of gage well and connecting line for laminar flow characteristic of gage well and connecting line for "turbulent" flow. coefficient of contraction at discharge from connecting line : coefficient of loss at bends, contractions, inlet, etc. \ friction factor for connecting line overall resistance coefficient for turbulent flow. (iq. 12) 37 velocity in connecting line average mean velocity at discharge from connecting line velocity head coefficient absolute viscosity kinematic viscosity weight of fluid per cubic foot Reynold's number for flow in line at maximum velocity Reynolds number at any velocity V 38 (3009 Wal) 734/2S esl * GETZ = (QD) \2poW \OPL' SN yo wands -S{UI0g) OH /,°H SRULOG [D{UAWIIadxe SajprIipul o "BAAN QD UO SJULOd [DJUaWIedxd SayDIIPUL agnasai MO14d YVNINV 1 JO SOILSIYSLOVYVHD S 114M 49V9 JdiL NISV 1 AWUV S°AN SUBANIONA JO SdHOD “LNANLYVWd3AG YWM 39 AAG Been) a) MO14 INF INGUNL JO SOILSIYILIVYVHD SE AOVO AGIL NI OV 1 40 BEACH EROSION STUDIES The principal types of beach erosion reports of studies at specific localities are the following: a. Cooperative studies (authorization by the Chief of Engineers in accordance with Section 2, River and Harbor Act approved on 3 July 1930). b. Preliminary examinations and surveys (Congressional authorization by reference to locality by name). c. Reports on shore line changes which may result from improvements of the entrances at’ the mouths of rivers and inlets (Section 5, Public Law No. 409, 74th Congress). d. Reports on shore protection of Federal property (authorization by the Chief of Engineers). Of these types of studies, cooperative beach erosion studies are the type most frequently made when a community desires investigation of its particular problem. As these studies have, consequently greater general interest, information concerning studies of specific localities con- tained in these quarterly bulletins will be confined to cooperative ‘studies. Information about other types of studies can be obtained upon inguiry to this office. Cooperative studies of beach erosion are studies made by the Corps of Engineers in cooperation with appropriate agencies of the various States by authority of Section 2, of the River and Harbor Act approved 3 July 1930. By executive ruling the cost of these studies is divided equally between the United States and the cooperating agency. Information con- cerning ths initiation of a cooperative study may be obtained from any District Engineers. After a report on a cooperative study has been trans— mitted to Congress, a summary thereof is included in the next issue of this bulletin. A list of completed cooperative studies and of those now in progress follows. SUMMARY OF REPORT TRANSMITTED TO CONGRESS STATE OF OHIO - LAKE COUNTY The area studied is located in Lake County on the south shore of Lake Erie from 20 to 30 miles east of Cleveland, Ohio. It lies between ths mouths of the Chagrin and Grand Rivers, a distance of about 10 mles. Fair- port Harbor, which has been improved by the United States for navigation, is located at the mouth of the Grand River, the east limit of the study area. 4l Lake County had a population of about 50,000 in 1940. The principal center of population is the city of Painesville, which had a population of about 12,000. The property along the shore line of the study area has been developed mainly for private residential and recreational purposes. The principal summer colony is at Mentor Headlands. The population of the area as a whole is not increased greatly by summer visitors. Inland areas are devoted mainly to agricultural uses. The shore is publicly owned at the Painesville Water Works and at Mentor Township Park. The latter is used for recreational purposes. The State of Ohio intends to acquire lakefront and upland property between the Painesville Water Works and Fairport Harbor for public beach and park development. There are wide beaches on existing and proposed public ownership frontage. The shore area immediately east of the mouth of Chagrin River is subject to pollution by sewage discharged untreated into that stream. Plans are being made for proper treatment of this sewage. No apparent hazards from sewage contamination exist in the eastern portion of the study area. The shore line of the study area consists principally of eroding bluffs of clay, silt and sand fronted by narrow beaches of sand and gravel. Analysis of samples of bluff material indicated that in general approximately 27 per cent of the material is suitable for beach building. Rapid erosion of the bluffs makes available a considerable volume of beach material. A wide beach has formed naturally on both sides of Chagrin River. West of Mentor and Fairport Harbors wide beaches have formed by accretion caused by the harbor structures. Miscellaneous groins, walls, and bulkheads have been constructed in an attempt to prevent erosion of the shore. Shore groins have generally caused minor accretion on their west sides and have reduced recession of the bluffs to some extent. The pronounced accretion west of the harbor structures and the accretion west of short groins indicate a marked eastward predominance of littoral drift. The purpose of the study was to determine the best methods of preventing further erosion and of restoring and creating new beaches, with emphasis on determining effective and economical methods of shore protection and on the possibilities of development and improvement of publicly owned park and beach areas. The district engineer considered the desires of the cooperating agency, studied the sources and movement of beach material, the changes in the shore line and offshore bottom, the effects of winds, waves, ice, and storms, the effects of existing structures, and developed four general plans for pro- tecting and improving the shores of the study areas. He concluded that the most economical and practical general plan of protection consists in grading and draining of the bluffs, revetment of the toe of the slope, and mainten-— ance of relatively narrow beaches by means of short groins. He concluded further that the beaches at the proposed State Park west of Fairport Harbor and other publicly owned shore frontage require no improvement at this time. He recommended that owners of private property adopt one of the four proposed plans of improvement best suited to the desired utilization of their shore front property. Since no improvements or protection of publicly owned pro- perty in the area were considered necessary at the time, he recommended no 42 Federal participation in the cost of any proposed improvements. The division engineer concurred in the conclusions and recommendations of the district engineer. The Board carefully considered the reports of the reporting officers. It concurred generally in their views and recommendations, subject to the following comments. The Beach Erosion Board concluded that protection and improvement of the shore by means of long groins would involve too long a period of time before adequate filling of the groin system by natural processes would be effected. The plan could be supplemented by provision of artificial fill, but no need exists for beaches of the width that would be provided in this manner and such a supplemented plan probably lacks economic justification. Grading of the bluffs and armoring of the toe by a rock sea wall or cellular steel pile bulkhzad would provide positive protection for the bluff, but would inhibit the use of the beach for recreational purposes. The Board con- curred in the opinion of the reporting officers that an economical and pra- ecticable general plan of protection comprises grading and draining of the bluff, revetting the toe of the slope and maintaining a narrow beach by means of relatively short groins. This plan provides protection for the bluff as well as an improved beach for recreational purposes. Filling of the groin system depends on supply of material from erosion of the bluffs within the study area and also those along the shore west of Chagrin River. If the entire shore within the area is protected under this plan, filling will be dependent on the supply of material from west of the area and will therefore be slow. More rapid filling could be effected if bluffs within the area where protection is not essential are permitted to erode and supply material. The Board considered the possibility that this plan may be beyond the means of some private owners of shore frontage. Where this condition exists and no structures are located so close to the top of the bluff as to necessitate positive protection against recession of the bluff, a less costly modifica- tion of this plan may be used. This modification consists of short groins a minimum of about 100 feet in length from the toe of the bluff on a spacing of about 100 feet. Under this modified plan the slope armoring would be omitted so the erosion of the bluff would supply material to fill the groin system. The groin would operate to retard erosion of the beach and the beach might be expected to build up to protect the toe of the bluff. In order to retain the beach at the toe of the bluff, the inner ends of the eroins should be above the height reached by the highest waves. It appears that a height of 10 feet above low water datum would meet this requirement. The top of the groin should parallel the natural slope of the bottom and adequate provision should be made against flanking of the groins. The Board called attention to the desirability of coordinated action by owners to protect a stretch of frontage under this plan. Although an individual owner of a short frontage could protect his property by a groin near his east property line, the protection would not be permanent. Erosion would eventually flank his property and necessitate further protective measures. The Beach Hrosion Board recommended that private owners adopt one of the four plans of protection and improvement proposed by the district engineer or that described in the previous paragraph, selecting that most 43 suitable to the desired use of their shore frontage. As existing Federal law includes no policy for Federal assistance in the cost of protecting privately owned shores, and as no protection or improvement of publicly owned property is considered necessary under present conditions, no Federal participation in the cost of any of the proposed work was recommended by the Beach Erosion Board at this time. % oe & & # COMPLETED COOPERATIVE BEACH EROSION STUDIES Published in Location Completed House Doc. Congress MAINE Qld Orchard Beach 20 Sep 35 NEW HAMPSHIRE Hampton Beach 15 Jul 32 MASSACHUSETTS South Shore of Cape Cod (Pt. Gammon to Chatham) 26 Aug 41 Salisbury Beach 26 Aug 41 Winthrop Beach 12 Sep 47 764 80 Lynn-Nahant Beach 20 Jan 50 Revere Beach 12 Jan 50 Nantasket Beach 12 Jan 50 Quincy Shore 2 May 50 RHODE ISLAND South Shore (Towns of Narragansett, South Kingstown, Charlestown & Westerly ) 4 Dec 48 490 81 CONNECTICUT Compo Beach, Westport 18 Apr 35 239 ra Hawk's Nest Beach, Old Lyme 21 Jun 39 Ash Creek to Saugatuck River 29 Apr 49 L5/, 81 Hammonasset River to Hast River 29 Apr 49 NEW YORK Jacob. Riis Park, Long Island 16 Dec 35 SoH) 74 Orchard Beach, Pelham Bay, Bronx 30 Aug 37 450 QS: Niagara County 27 Jun 42 271 78 South Shore of Long Island 6 Bug 46 NEW JuRSBY Manasquan Inlet & Adjacent Beaches 15 May 36 al AS Atlantic City 11 Jul 49 538 81 ‘ VIRGINIA Willoughby Spit, Norfolk 20 Nov 37 482 WS Colonial Beach, Fotomac River 24 Jan 49 333 81 NORTH CAROLINA Fort Fisher 10 Nov 31 204 ie Wrightsville Beach 2 Jan 34 218 3} Kitty Hawk, Nags Head & Oregon Inlet 1 Mar 35 155 74 State of North Carolina 22 May 47 763 80 SOUTH CAROLINA Folly Beach 31 Jan 35 156 7h GEORGIA St. Simon Island 18 Mar 40 820 76 FLORIDA Blind Pass (Boca Ciega) 1 Feb 37 187 US Miami Beach 1 Feb 37 169 75 Hollywood Beach 28 Apr 37 253 75 Daytona Beach 15 Mar 38 571 75 Bakers Haulover Inlet 21 May 45 527 79 Anna Maria & Longboat Keys 12 Feb 47 760 80 Jupiter Island 13 Feb 47 765 80 Palm Beach (1) 13 Feb 47 ine 80 MISSISSIPPI Hancock County 3 Apr 42 Harrison County - Initial 15 Mar 44 Harrison County - Supplement 16 Feb 48 682 80 LOUISIANA Grand Isle 28 Jul 36 92 75 TEXAS Galveston 10 May 34 400 3 Galveston Bay, Harris County 31 Jul 34 74 7h 45 (1) A cooperative study of experimental steel pile groins was also made, under which mthods of improvement were recommended in an interim report dated 19 Sep 1940. Final report on experimental groins was published in 1948 as Technical Memo. No. 10 of the Beach Erosion Board. CALIFORNIA Santa Barbara - Initial 15 Jan 38 552 715 Supplement 18 Feb 42 Final 22 May 47 761 80 Ballona Creek & San Gabriel River (Partial) 11 May 38 Orange County 10 Jan 40 637 76 Long Beach 3 Apr 42 636 il Mission Beach 4 Nov 42 Coronado Beach 4 Apr 41 PENNSYLV ANITA Presque Isle Peninsula, Erie (Interim) 3 Apr 42 (Final ) 23 Aug 49 OHIO Erie County — Vicinity of Huron 26 Aug 41 220 79 Lake Erie Shore - Michigan Line to Marblehead 30 Act 44 177 79 Cities of Cleveland & Lakewood 22 Mar 48 502 81 Lake County 22 Nov 49 ILLINOIS State of Illinois 8 Jun 50 WISCONSIN Milwaukee County 21 May 45 526 79 PUERTO RICO Punta Las Marias, San Juan 5 Aug 47 769 80 CGOPERATIVE BEACH EROSION STUDIES IN PROGRESS NEW HAMPSHIRE HAMPTON BEACH. Cooperative Agency; New Hampshire Shore and Beach Preservation and Development Commission. Problem: To determine the best method of preventing further erosion and of stabilizing and restoring the beaches, also to determine the extent of Federal aid in any proposed plans of protection and improvement. 46 CONNECTICUL STATE OF CONNECTICUT: Cooperating Agency; State of Comecticut (Acting through the Flood Control and Water Policy Commission). Problem: To determine the most suitable methods of stabilizing and improving the shore line. Sections of the coast will be studied in order of priority as requested by the cooperating agency until the entire coast is included. NEW YORK JONES BEACH. Cooperating Agency: Long Island State Parks Commission Problem: To determine behavior of the shore during a 12-months cycle, including study of littoral drift, wave refraction and movement of antificial sand supply between Fire Island and Jones Inlets. NEW JERSEY OCEAN CITY. Cooperating Agency: City of Ocean City. Problem; To determine the causes of erosion or accretion and the effect of previously constructed groins and structures, and to recommend remedial measures to prevent further erosion and to restore the beaches. VIRGINIA VIRGINIA BEACH. Cooperating Agency: Town of Virginia Beach. Problem: To determine the mthods for the improvement and pro- tection of ths beach and existing concrete sea wall. SOUTH CAROLINA STATE OF SOUTH CAROLINA. Cooperating Agency: State Highway Department. Froblem: To determine the best method of preventing srosion, stabilizing and improving the beaches. FLORIDA PINELLAS COUNTY. Cooperating Agency: Board of County Commissioners. Problem: To determine the best methods of preventing further recession of the gulf shore line, stabilizing the sul? shores of certain passes, and widening certain beaches within the study area. LOUISIANA LAKE PONTCHARTRAIN. Cooperating Agency: Board of Levee Commissioners, Orleans Levee District. Problem; To determine the best method of effecting necessary re- pairs to the existing sea wall and the desirability of building an artificial beach to provide protection to the wall and also to provide additional recreational beach area. TEXAS GALVESTON COUNTY. Cooperating Agency: County Commissioners Court of Galveston County. Problem; To determine the best method of providing a permanent beach and the necessity for further protection or ex- tending the sea wall within the area bounded by the Galveston South Jetty and Hight Mile Road. To determine the most practicable and economical method of preventing or retarding bank recession on the shore of Galveston Bay between April Fool Point and Kemah. CALIFORNIA STATE OF CALIFORNIA. Cooperating Agency: Division of Beaches and Parks, State of California. Problem; To conduct a study of the problems of beach erosion and shore protection along the entire coast of California. The initial studies are to be made in the Ventura-—Port Huneme area and the Santa Monica area. WISCONSIN RACINE COUNTY. Cooperating Agency: Racine County. Problem: To prevent erosion by waves and currents, and to determine the most suitable methods for protection, restoration and development of beaches. KENOSHA. Cooperating Agency: City of Kenosha. Problem: To determine the best method of shore protection and beach erosion control. 48 OHIO STATE OF OHIO. Cooperating Agency: State of Ohio (Acting through the Superintendent of Public Works). Problem: To determine the best method of preventing further erosion of and stabilizing existing beaches, of re- storing and creating new beaches, and appropriate locations for the development of recreational facilities by the State along the Lake Erie shore line. TERRITORY CF HAWAII WAIKIKI BEACH. Cooperating Agency: Board of Harbor Commissioners, Territory of Hawaii. WAIMBA, HANAPEFE, KAUAI. Problem: To determine the most suitable method of preventing erosion, and of increasing the usable recreational beach area, and to determine the extent of Federal aid in effecting the desired improvement. 49 BEACH EROSION LITERATURE There are listed below some recent acquisitions to the Board's library which are considered to be of general interest. Copies of these publications can be obtained on 30-day loan by interested official agencies. "Measurement of Ocean Waves," R. G Folsome, Trans. American Geophysical Union, Vol. 30, No. 5, October 1949 Laboratory and field investigations demonstrate that theoretical pressure ratios for pressure wave recorders are correct to within ten to 20 per cent. The theoretically corrected measured wave heights in shallow water are low. The University of California Mark III and Mark VY wave recorders are described and typical records from the latter are reproduced. The limitations of the available information on spar buoy damping disc systems for deep water wave measurements are summarized. "Hydrodynamic Forces on a Rough Wall," Hans Albert Hinstein, Review of Modern Physics, Vol. 21, No. 3, July 1949. The dynamic forces which a turbulent flow exerts on the individual protrusions of a rough wall have been measured. It was found that even in the case of an extremely high relative roughness, the drag force on the protrusions may be determined from the logarithmic friction laws. A very significant lift force which tends to pull the the protrusions away from the wall and into the flow was measured. This lift force was divided into two parts; A constant average value and a random fluctuation superimposed over the average. A careful statistical analysis showed that the frequency of different pressures or lift forces at the wall follows very accurately the normal error law. This fact seems to indicate that in the description of turbulence near a rough wall, the pressures must be regarded as the primary influence, not the velocities. "Scale Effects in Hydraulic Models Involving Wave Motion," J. W. Johnson, Trans., American Geophysical Union, Vol. 30, No. 4, August 1949. A summary of the various instances where wave theories have been verified experimentally is presented briefly. A more detailed dis- cussion is given for those problems where models built to several scales have permitted an evaluation of the effect of scale in the application of data from hydraulic models. tAn Analysis of Data From Wave Recorders on the Pacific Coast of the United States," R. Lo. Wiegel, Trans. American Geophysical Union, Vol. 30, No. 5, October 1949. The wave heights and period from wave recorders installed off Point Sur, California, and Hecta Head, Qregon, have been compared for the period from April 1947 to June 1948. These data, together with some obtained at Point Arguello, California, showed that the ratio of the 50 maximum wave recorded each day to the average of the highest ten per cent for that day was 1.46 and the ratio of the average of the highest ten per cent to ths average of the highest one-third of the waves each day was 1.29 for any place along this section of the Pacific Coast. It was also found that the average period of the swells (that is, excluding the local storm "chop") was 12 seconds. "A Theory of the Hydraulic Injector," Duilio Citrini (Saggio Di Teoria Dell'Iniettore Idraulico), Memorie e Studi dell'Istituto di Idraulica del Politecnico di Milano, No. 72, 1948 The analysis of the motion in the mixing-room of a hydraulic injector (jet pump) is developed, for incompressible fluids, without using the hypotheses, usually but incorrectly admitted, of constant pressure head and negligeable losses of head. The increase of the pressure head along the device is evaluated, For the losses of head an approximate analytical expression is given. The efficiencies of the device for different situations are ex- amined and examples of practical calculation are given. The theory is developed for the injector with cylindrical mixing- room, but successively the case of a convergent mixing-room is too examinated, according to a type proposed by Rateau; the comparison shows that the cylindrical type furnishes in general a higher efficiency. "Critical Comparison of Measurements of the Vertical Distribution of Wind On the Sea," Hans-Ulrich Roll, (Vergleichende Betrachtung und Kritik von Windprofilmessungen auf See) Annales of Meteorology, March-April 1949. A comparison of the measurements of the vertical distribution of wind in the lowest atmospheric layer above the sea-surface leads to the following results: The profiles measured by Montgomery, Shoulejkin, and Roll agree satisfactorily, disturbances of the field of wind speed having been avoided as far as possible. The measurements of Wust, Bruch and of the Altair voyage, however, show departures in the sense of greater roughness parameters above the level of 50 - 100 cm. By a discussion of the possible source of error and by comparative neasure- ments it was made probable that these differences are not due to fundamental causes but to inaccuracies in the technique of measuring. In particular it appeared that the measurements of wind on the bow of an anchored ship may yield results that are 50 - 100 cm/s to high. "The Application of Conformal Transformations of Ocean Wave Refraction Problems," New York University, Leon S. Pocinki, April 1950. If the bottom contours are considered straight end parallel, and if the usual assumptions are made, a simple differential equation for the orthogonals can be derived from Snell's Law. Solutions to the equation are easily obtained. Conformal transformations may be applied to change the contours in the complex Z plane into several different configurations in a complex W plane. In each case an orthogonal in the Z plane maps into a new orthogonal in the W plane and thus a solution to the problem of wave refraction over the contour configuration in the W plane is obtained. An expression for Kj is then derived from the orthogonal pattern. Cases treated include a circular island, a reef and a bay with parabolic contours, and twin islands. 51