Coast. Gre. Res. Ct CETA 81-16 A Method for Estimating Depth-Limited Wave Energy by C. Linwood Vincent COASTAL ENGINEERING TECHNICAL AID NO. 81-16 NOVEMBER 1981 DOCUMENT COLLECTION Approved for public release; distribution unlimited. U.S. ARMY, CORPS OF ENGINEERS COASTAL ENGINEERING 330 RESEARCH CENTER Us Kingman Building ne G(-Ib Fort Belvoir, Va. 22060 of this material republication of any Army Coastal Reprint or shall give appropriate credit to the U.S. Engineering Research Center. made by Limited free distribution within the United States publication has been of single copies of this this Center. Additional copies are available from: Nattonal Technical Information Service ATTN: Operattons Diviston 5285 Port Royal Road Springfteld, Virginia 22161 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. = i) I i O ut UT UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) REPORT DOCUMENTATION PAGE BE ROE e Cone ee aon T. REPORT NUMBER 2. GOVT ACCESSION NO] 3. RECIPIENT'S CATALOG NUMBER CETA 81-16 4. TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED Coastal Engineering A METHOD FOR ESTIMATING DEPTH-LIMITED Technical Aid 7. AUTHOR(s) 8. CONTRACT OR GRANT NUMBER(8, C. Linwood Vincent 9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT, PROJECT, TASK AREA & WORK UNIT NUMBERS Department of the Army Coastal Engineering Research Center (CERRE-CO) A31592 Kingman Building, Fort Belvoir, Virginia 22060 11. 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 this report) UNCLASSIFIED 15a, DECL ASSIFICATION/ DOWNGRADING SCHEDULE 16. DISTRIBUTION STATEMENT (of this Report) Approved for public release; distribution unlimited. DISTRIBUTION STATEMENT (of the abstract entered in Block 20, if different from Report) SUPPLEMENTARY NOTES KEY WORDS (Continue on reverse side if necessary and identify by block number) Monochromatic waves Spectral waves Wind wave energy ABSTRACT (Continue on reverse side If necesaary and identify by block number) A method for estimating an upper limit of wind wave energy in shallow water is presented. The method requires knowledge of the depth, the peak frequency of the sea, and the windspeed in order to predict a depth-controlled wave height, H, defined as 4(E)!/2, with E the energy of the wind sea. In the shallow limit, H is shown to be approximately proportional to the square root of depthe The method is recommended for predictions in storm seas and not for swell (ieee, nearly monochromatic waves). DD (1 2n", 1473 Eprtion oF t Nov 65 1S OBSOLETE UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) che Dy ane anes Ne Wal Put te mae tte Geel sent ini ge |) ian nnpncamen Cy ai io * ’ Maths ¥ a mca. ae hh a ui “sch Yay 7 : fe eis ey ee oj ie gloat, toe a aulye et ahenn ei — Te Gl ’ ‘ eye a ei ‘ A ; eh’ t re x aie pe sar i: i ; heen. i rn op uw F wo 1 oe | : —— ‘iy a - t fat q - , we vt Aut ‘ 4 i, & * T T oy UR toy 7 a - 7 i 7 WV y 7 t - iG ; : : - & ey Cae ates ya ‘ : PREFACE This report presents a method for estimating an upper limit on wave energy in shallow water as a function of depth and parameters of the wave spectrum. The research was carried out under the coastal waves and flooding program of the U.S. Army Coastal Engineering Research Center (CERC). The report was prepared by Dre C. Linwood Vincent, Chief, Coastal Oceanography Branch, under the general supervision of R.eP. Savage, Chief, Research Division. J.-E. McTamany prepared the computer integration scheme; WeNe Seelig and LeL. Broderick provided the laboratory data. 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. TED Ee BISHOP Colonel, Corps of Engineers Commander and Director CONTENTS Page CONVERSION FACTORS, UeSe CUSTOMARY TO METRIC (SL)ecccceccccccocce 5 SYMBOLS AND DEFINITIONS clevctsreroioxess ci6 eicle.6\ 0100's! eierele eleele:0,0)0\ 0 0: 60 (e\e10.0 16)8 6 I TNE ROD WU CIEWON eivetererelisteiteieelove:eepeiele'es siete sieleleleiel sie exelesele!e-01s jele 0 oie eloisieve eileisiels I ime BACKGROUND ctertsteretsie exe steve era) clelicl sieve) oie) cl ocerevelevelorele esis ee ee) ejele! eles ereleleieiclere 8 IE SIMPLIFIED MIM ODA COG ROObORO OOD OOO DOODDODUOUUDOUDUOOUODUDUODUOUOG 10 lS Selection of fcc cccccccccccccccccccscccvcescccecccscseces 10 De Selection of Aeoossecsccecrrcrcvvsserrsvs20eFcL2e22e2 2222002020000 000 10 IV EXAMPLE BROBIREMSievetelereleteleieicleteloieieiere: eves) eiel'e eles) erelsie/elel el clelellesalelotelevolelelelers Meal V DIEKCWSSILONS GOO 5 OD OOO OUD OOUODUDUDOODUUOODDOODUUOUDUGUUUOUDOUODOOOG 13 VI SUMMARY ects cheislolcloveseietelel sl clcfolelojoleilelelels cvelelelece!eleletelele tele ele lenevelereleicle a ecelelevete 13 APPENDIX A PREDICTION CAPABILITY OF METRE OD Siereietereieseie:eteieitereye)6: 1 e'e /o\ehele 16 eels! ele) etorera 15 B METRIC VERSION OF TEXT WAI IEE Sietetelelenetoleieroretelevereiereielarcreleteretelersiererstereneiers 20 TABLES 1 Depth-controlled height, H (f,, h, 0.0081), as a function of lower frequency cutoff, f., period, T, and depth, heeesceecccvcee 9 2 Values of (a/0.0081)!/2 as a function of spectral peak frequency, fo» period, al, (and! wilndspeed;. | (Ue sislcs:s s1c)01e1s 10016 6 'sieie os\n'eieleis e's'ee/e clciclenm le CONVERSION FACTORS, U.S. CUSTOMARY TO METRIC (SIL) UNITS OF MEASUREMENT U.S. customary units of measurement used in this report can be converted to metric (SI) units as follows: Multiply by To obtain inches 2564 millimeters 2624 centimeters square inches 66452 Square centimeters cubic inches 16.39 cubic centimeters feet 30.48 centimeters 0.3048 meters square feet 0.0929 square meters cubic feet 0.0283 cubic meters yards 0.9144 meters square yards 0.836 square meters cubic yards 0.7646 cubic meters miles 1.6093 kilometers square miles 259/50 hectares knots L852 kilometers per hour acres 0.4047 hectares foot-pounds 1.3558 newton meters Pe bane 10197 x 1072 kilograms per square centimeter ounces 28.35 grams pounds 453.6 grams 0.4536 kilograms ton, long 1.0160 metric tons ton, short 0.9072 metric tons degrees (angle) 0.01745 radians Fahrenheit degrees 5/9 Celsius degrees or Kelvins! 1To obtain Celsius (C) temperature readings from Fahrenheit (F) readings, use formula: C = (5/9) (F -32). To obtain Kelvin (K) readings, use formula: K = (5/9) (F -32) + 273.15. OH SYMBOLS AND DEFINITIONS total variance in wind sea upper bound on energy density in a frequency, frequency low-frequency cutoff peak frequency of the spectrum gravitational acceleration depth-controlled wave height (spectral) linearly shoaled wave height breaker height depth-limited wave height (monochromatic) significant wave height depth refraction-shoaling coefficien windspeed Phillips’ equilibrium coefficient pi dimensionless function describing deviation from deepwater equilibrium range dimensionless combination of t 8» f, and h f A METHOD FOR ESTIMATING DEPTH-LIMITED WAVE ENERGY by C. Linwood Vineent I. INTRODUCTION This report presents a method for calculating a limit on the total energy of a storm sea in finite-depth water based on characteristics of irregular wavese The total variance, E, in the wave field is parameterized by a wave height parameter, H, defined as H = 4.0(E)1/2 (1) The energy in the wave field is directly related to E. H_ should be recog- nized as the estimate, based on a Rayleigh distribution, of the significant . wave height in deep water. H, defined in this way, is often given as an approximation to the significant wave height (average of highest one-third waves) in shallow water as well, although there is some evidence that the significant wave height may be slightly larger than this estimate. The method presented for estimating H is believed valid for wave conditions where there is spread in the spectrum similar to what might be expected under storm condi- tions. Estimates for nearly monochromatic swell should follow monochromatic wave theory as discussed in Section 7.11 of the Shore Protection Manual (SPM) (U.S. Army, Corps of Engineers, Coastal Engineering Research Center, 1977)!. This report represents a major departure from the SPM methods which are based on regular (monochromatic) waves. There is no clear parallel to this method in the SPM. It is important to differentiate H from other commonly defined wave parameters in shallow waters H, which will be called the depth-controlled wave height (spectral), simply parameterizes the total wave energy in a spec- trum. The significant wave height, H,, is traditionally defined as the average of the one-third highest waves and is approximately equal to H in deep water.e H is the breaker height and H is the largest individual wave that can exist at a given depth. It should normally be expected that, in an irregular sea, H and H, will be less_ than Hy and Hg. Hq will be called the depth-limited wave height (monochromatic) to differentiate it from He Hy is expected to be an estimate of the largest single wave that can occur in a spectrum in water of depth d. Engineering designs that require the largest single wave that can occur should use the SPM methods. The technical background and an evaluation of this method will be provided in a forthcoming CERC report. A comparison of this method to field data is described in Appendix A. 1U.S. ARMY, CORPS OF ENGINEERS, COASTAL ENGINEERING RESEARCH CENTER, Shore Protection Manual, 3d ede, Vols. I, II, and III, Stock Noe 008-022-00113-1, U.S. Government Printing Office, Washington, D.eC.e, 1977, 1,262 pp. Il. BACKGROUND Research by Kitaigorodskii, Krasitskii, and Zaslavskii (1975)2 has pro- vided an equation for the maximum energy density in a frequency component of a wave spectrum in finite depth ig ag? 2f ° (u,) E_(£) (2) = (21)* where T = 3.1415 iE = frequency g = gravitational acceleration h = depth Wp Ss dimensionless parameter defined as h\i/2 - ae (2) Wh mE\ (3) co) = dimensionless function of uw, which varies monotonically from 0 tom) o = a function of the wave field Equation (2) has been shown in a number of studies to be an excellent estimate of the upper bound on energy density as a function of f- E, represents an upper bound for energy density as a function of fre- quency. An estimate of an upper bound on the total variance or energy in the wave field can be obtained by integrating equation (2) over the frequencies containing wave energye This estimate of total energy can be used in equation (1) to obtain an estimate of H. If f denotes the lower frequency bounding e the energy containing frequencies, then oO H = aE: EL (2) ve” (4) (es For practical purposes the high-frequency bound for integration in equation (4) is taken as 1 hertz rather than infinity, because for most cases there is little energy beyond 1 hertz in comparison to that below 1 hertz. Clearly, H will vary with depth, h, the lower cutoff frequency, f,, and the spectral parameter, a; therefore, the notation H(f,, h, a) will be used. Table 1 presents values of H(f£.; h, a) in feet for values of f, from 0.05 to 0.34 hertz in steps of 0.01 hertz and for depths of 3 to 60 feet (1 to 20 meters) in 3-foot (1 meter) intervals for a fixed value of a= 0.0081. (A metric 2KITAIGORODSKII, S.A-, KRASITSKII, V.eP., and ZASLAVSKII, M.M., “Phillips Theory of the Equilibrium Range in the Spectra of Wind-generated Gravity Waves," Journal of Physical Oceanography, Vol. 5, 1975, ppe 410-420. version of the table is in Appendix B.) The parameter a is related to dimensionless fetch and can be either obtained from a measured deepwater spectrum or can be inferred as a function of a peak frequency of a spectrum and windspeed. The adjustment of H(t. hy. 0.0081) “for variation initja@ jis discussed in the next section. If the parameter, Wh» defined in equation (3) is one or less for the main energy containing frequencies in a sea state, the H(f,, h, 0.0081) can be approximated by 0.161 hi/2 HCE. h, 0.0081) ve re for h in feet c (5) 0.089 h!/2 = ———————- for h in meters f. This equation predicts that in areas where the wave energy is controlled by depth, H varies with the square root of depth, not approximately linearly with depth as does the monochromatic Hae III. SIMPLIFIED METHOD To use Table 1 or equation (5), estimates of f, and a are necessary to estimate H in depth, h. 1. Selection of fae f,. is defined as the lowest frequency in which there is appreciable wave energye Typical storm spectra in shallow water (60 feet or less) have very sharp peaks. If there is a given spectrum offshore where the values of H are desired in a depth, h, it is recommended that oe be set to 90 percent of Eos the peak frequency of the sea spectrum. £, = 0.9 f 5 (6) If more conservatism is required, fe can be set lower. If no spectral data are available at a site, then f, can be estimated either by estimating f via hindcast curves or by selecting a reasonable but conservative value of fe based on similar conditions elsewhere. 2- Selection of a. The parameter of a can be directly estimated from measured spectrum by fitting equation (2) to the spectrum. If measurements are unavailable, a can be estimated by fitting equation (2) to good quality hindcast spectra. If neither hindcasts nor measured data are available, then a can be estimated from Hasselmann, et ale (1973)3 ‘ gF V0. 22 (0 0.076 Saat (32) 3HASSELMANN, Ke, et al., “Measurements of Wind-Wave Growth and Swell Decay During the Joint North Sea Wave Project JONSWAP,"” Deutsches Hydrographisches Institut, Hamburg Germany, 1973. 10 where f£ is fetch and u is windspeed. For a # 0.0081 H(f Cc? 1/2 h, a) = H(fc, h, 0.0081) (—_) (7) An alternate way to estimate (a/0.0081) 1/2 is to use Table 2 where (a/0.0081)1/2 is provided for peak frequencies from 0.05 to 0.34 and windspeeds from 10 to 100 miles per hour (5 to 50 meters per second). (See Appe B for metric version of tables.) Appendix A describes the comparison of this method to field data. IV. EXAMPLE PROBLEMS k kk RR kk Ok & OK OK Ok & & & * EXAMPLE PROBLEM 1 * * * * * * * K % KR RR RK GIVEN: A wave spectrum measured offshore has a significant height of 18 feet (6 meters) with a peak frequency fp = 0.08 and a value of 0.0101. FIND: The depth-controlled wave height (spectral) H in 45, 30, 15, and 3 feet (15, 10, 5, and 1 meter) of water. ; SOLUTION: Calculate f, = 0.9 ft = 0.072, using 0.07. From Table 1 using, a= 0.0081, find = 14.9 feet (4.5 meters) in 45 feet 12.3 feet (3.8 meters) in 30 feet 8.9 feet (2.7 meters) in 15 feet 4.0 feet (1.2 meters) in 3 feet i za nt at WW These values must be adjusted to (a/0.0081) 1/2 = 1.11, but the correction is very small in each casee Examination of field data indicates that in depths less than 13 feet (4 meters), wave spectral densities in frequencies less than 0.1 hertz can be substantially smaller than the upper bound value in equation (2), probably due to frictional effects and turbulence; H(f os h, a) can be an overestimate. Also note that h representing actual water depth including tide, surge, and wave setup is used. kok RR RK Kk Rk kok & kok ok & *& EXAMPLE PROBLEM 2 * * * ®& ¥ ¥ * RR RR RRR GIVEN: Hindcasts on a lake indicate that under design storm conditions, peak frequencies were not expected to be any lower than 0.17 hertz for windspeeds of 68 miles per hour (30 meters per second). FIND: The depth-controlled (spectral) wave heights in 30, 15, 10, and 3 feet (10, 5, 3, and 1 meter) of water. SOLUTION: Calculate f, = 0.9 fy = 0.9(0.17) = 0.153, using 0.15. From Table 1 using a = 0.0081, find H = 5.1 feet (1.6 meters) in 30 feet H 3.9 feet (1.2 meters) in 15 feet H = 3.2 feet (1.0 meter) in 10 feet H 1.8 feet (0.6 meter) in 3 feet i] a Values of (a/0.0081)!/2 as function of spectral peak frequency, windspeed, ue Table 2. ah fy T Ghz. Cs) 10 0.05] 20.0 | 0.582 0.06 | 16.7 | 0.618 0.07} 14.3 | 0.650 0.08 | 12.5 | 0.679 0.09; 11.1 | 0.706 0.10} 10.0 | 0.731 0.11 9.1 | 0.754 0.12 8.3 | 0.776 0.13 7.7 | 0.797 0.14 7-1 | 0.817 0.15 6-7 | 0.836 0.16 6-3 | 0.854 0.17 52.9 | 0.871 0.18 506 | 0.887 0.19 523 | 0.903 0.20 D0 (105919 OR 21 4.8 | 0.934 0.22 4.5 | 0.948 0.23 4.3] 0.962 0.24 4.2 | 0.976 0.25 4.0] 0.989 0.26 3.8 | 1.002 0.27 Jef Velo O15 0.28 3.6 | 1.027 0.29 3.4 | 1.039 0.30 323} 1.050 0.31 3.2{ 1.062 0.32 Sell .073 0.33 3.0} 1.084 0.34 Ze leO95 period, 20 0.731 0.7/6 0.817 0.854 0.887 0.919 0.948 0.976 1.002 1.027 1.050 1.073 1.095 1.116 1.136 1.155 1.174 1.192 1.210 1.227 1.243 1.260 W275 We 2911 1.306 1.320 16335 1.349 1.363 1.376 T, 30 0.836 0.887 0.934 0.976 1.015 1.050 1.084 1.116 1.145 1.174 1.201 1.227 1251 1.275 1.298 1.320 1.342 1.363 1.383 1.402 1.421 1.440 1.458 1.475 1.493 1.509 1.526 1.542 1.558 1.573 Windspeed, 40 50 0-919 0.989 0.976 1.050 VeO027 * Vol05 L073 y dyel55 Wooo 2011 1.155 1.243 Tol92 7 se 285 1.227 1.320 1.260 1.356 1.291 1.389 1.320 1.421 1.349 1.452 1.376 1.481 1.402 1.509 1.438 1.537 1.452 1.563 1.475 1.588 1.498 1.613 1.520: 1s637 1.542 1.660 1.563 1.682 1.583 1.704 15603 16726 1.622 1.746 1.641 1.767 1.660 1.787 1.678 1.806 1.696 1.825 1.713 1.844 1.730 1.862 12 u-- (mi/hr) 60 1.050 1.116 1.174 16207 15275 1.320 1.363 1.402 1.440 1.475 1.509 1.542 1.573 1.603 1.632 1.660 1.687 jy ale 1.738 1.763 1.787 1.810 1.833 1.855 1.876 1.897 1.918 1.938 1.958 1.977 70 1.105 1.174 1.235 1.291 1.342 1.389 1.434 1.475 1.515 1.552 1.588 1.622 1.655 1.687 1/17 1.746 1.775 1.802 1.829 15855 1.880 1.904 1.928 195i 1.974 1.996 22018 22039 2.060 2-081 1.201 Ves 2 1.342 1.402 1.458 1.509 1.558 1.603 1.646 1.687 1.726 1.763 1.798 1.833 1.866 1.897 1.928 1.958 1.987 2.015 2.042 2-069 22095 22120 2.145 22169 22.193 22216 22238 22261 100_| 1.243 1.320 1.389 1.452 1.509 1.563 1.613 1.660 1.704 1.746 1.787 1.825 1.862 1.897 1.932 1.965 1.996 2027 2.057 22086 20115 22142 2.169 2ieh9'5 22221 2246 22270 22294 2.318 2.340 To adjust for the proper value of a use Table 2 which indicates that (a/ 0.0081)!/2 for £ = 0.17 hertz and u = 68 miles per hour is 1.63. The above wave heights must be multiplied by 1.63 yielding 8.3, 6.3, 5.2, and 2.9 feet (2.6, 2.0, 1.6, and 0.9 meter). Ve DISCUSSION The two example problems indicate that the depth-controlled wave height (spectral) depends significantly on the values chosen for a and f,. On the lake, the waves have a higher a value but because of fetch limitations, f cannot be very lowe As a result, there is less spread in energy over the spec- trum and the limiting form (eq 2) is only integrated over frequencies where the energy density is relatively small compared to cases where f is lower and E, is much larger. The method presented here indicates that the upper bound on wave energy and an estimate of the significant height, H,, by H varies with depth (nonlinearly), the peak frequency associated with the waves, and a parameter a associated with the wave generation process. The method allows an estimation of the depth-limited conditions of H = 4(E)!/2 to be based on an analysis of the wave generation conditions. The difference between H (directly related to the energy) and Hy (based on the largest single wave that can occur) is significant for most wave condi- tions and especially when the site has short fetches. It is recommended that Hq only be used where it is necessary to determine the largest individual wave or if the wave conditions are nearly monochromatic. In all other cases, and in particular, where an estimate of the energy of the wave field is required, the method in this report may be expected to provide a more accurate (though less conservative) estimate. VI.- SUMMARY A method has been presented for calculating a maximum value for H = 4(E)1/2 for wind sea situations where depth is the controlling factor. Estimation requires input of depth, a lower bound frequency, and parameter a typical of storm spectra at the site. Methods for estimating the latter two parameters are also provided. The results indicate that, in the shallow-water limit, H (which is also an approximation to the shallow-water value H,) is propor- tional to the square root of depth. The values obtained can be significantly less than the monochromatic depth-limited wave height, Hy, which is taken to be the upper bound of individual single waves in the spectrum. Again it is important to emphasize that the H defined here is directly related to the total energy of the wind sea and approximates the average of the highest one- third waves. The monochromatic value H, defined in SPM better approximates the highest individual wave that might be expected in that depth. The selec tion of which approximation to use will depend on the design application. 13 poe. Pe aie oa e a ys % ean ’ ae gt Ae bs BO, F Seal a “i Sige UK WEN . a yal ae 7 = APPENDIX A - PREDICTION CAPABILITY OF METHOD Because the method presented in this CETA is significantly different from the procedures in the SPM, summarized data are presented here to illustrate the method's prediction capability. Irregular wave conditions with a spectral shape similar to wind sea spectra were mechanically generated in a wave tank at CERC. The waves were allowed to propagate up a 1 on 30 slope and break. Wave staffs located along the tank were used to measure the waves. Wave spectra and the wave height H = 4o = 4(E)!/2 were calculated. Figure Al provides an example showing measured H (H obtained using this CETA) and the value of H projected by linear shoaling theory, H' = KH,» The SPM methods would predict the value H'. The method in this CETA appears to be a better estimate of the quantity He. Figure A-2 provides data from a storm of 25 October 1980 at the Field Research Facility (FRF) in Duck, North Carolina. The measured values of H = 40 are plotted against the square root of water depth, (h)l/2, Also plotted are (1) the upper limit for H for the maximum a and f, condition observed, and (2) a monochromatic determined breaker height which considers the shore steepness, water depth, and wave period. In most cases Hj is greater than H. A suggested approximation of H = 0.5h is also plotted. This relationship is adequate at the deeper end of the pier but is an underestimate at the shallower depths. The bathymetry under the pier is somewhat distorted (Fige A-3,a). A refraction and shoaling analysis of a 12-second wave approaching from the primary direction of waves of the October storm was performed and the joint refraction-shoaling coefficient, KpK,, is shown in Figure A-3(b).- Refrac- tion and shoaling create regions of higher waves to either side of the pier. However, shoaling predominates and even under the pier, Kpk, is greater than 1.1. During the part of the October storm plotted in Figure A-2, waves off- shore were in excess of 4.2 meters, and waves along the pier would be expected to reach the monochromatic breaking limit unless some other process is acting. Figure A-4 provides plots of spectra at 36-, 8-, 7-, 4- and 2-meter depths during a storm at the FRF in December 1980. The expected upper bound on spectral density for the 7-, 4-, and 2-meter depths are plotted also. The figure indicates the degree and location of energy loss in the spectrum and the degree of approximation of the theory used in development of this CETA. The method in this CETA represents a simple approximation of estimating depth-controlled wave energye The method does not consider any of a number of mechanisms important to predicting precisely the shape of the wave spectrum but still provides what appears to be a useful approximation to the quantity He 4¢ = 4(e)*/2. 1h) Wave Height (cm) ) Figure A-l. Estimated Breaker Height Hy 7. x’ Shoaled Wave Height H' i} ae pa is Va Predicted H Measured H=4 | Z %) 4 Square Root of Depth Gree Laboratory data. The wave height parameter H = 4o measured in a CERC wave tank along a 1:30 slope is compared to predicted value H as a function of (h)!/%. Also shown is the linearly shoaled wave height H' and the breaker height Hye The maximum indi- vidual measured wave height, Haax» is shown and appears to follow Hype 16 Figure A-2. @ 4 e e e @ @ e e | 2 3 Square Root of Depth Field data, 25 October 1980. H = 40, measured at the FRF, is plotted against the square root of water depth, (h)!/2, Also plotted are the values of H estimated by the method of this CETA given a at 36 meters (line A) and a at 9 meters (line B)- The breaker height, H,, is plotted (line C) with bottom slope variations accounted for. An estimate of H = 0.5h is also given (line D). During the storm, maximum wave heights of 5.6 meters were observed in 7- to 9-meter depths. IL 7 °pez103STp St JoTd sy} Jo eTeos X-x ay], °3seea eNp WOIZ soaAeM puUOdeS-—7] 1oJ uUMOYS ST JUSTOTJJIO0I BSutTTeoys—uoTjoeAjer ayy (q) UL cuMOYS sie AYA 3u3 punoie sinojuod woz}0q (ke) UT UOI}IOIIG BADM Juapioul °TUd SUR Je sursqzjzed ButTTeous pue uot oIeIzZOyY *E-y eAN3Ty yud!d13Ja09 $iNOJUO) WO0G BuljD0ys puod uoljr0Ijay 18 gay SOK Normal —E 90° eee Wave Direction Wave Spectra 50 Gage 630 H,=5.8m h=|8m 45 40 \ \ 35 \ \ Gage 635 Hs=!.3m h=2m \ E(f),m2/s [o) fee} = 30 h=2m Ee 0.4 aco : 0) 0.1 0.2 0.3 0.4 0.5 0.6 Frequency (hz) 20 IS XERB He=5.0m h=36m ae Ss 10 5 Gage 621 Hys= 3.8m h=7m SAN yee Ve >“ Gage 645 H,=!.7m h=4m 0) A — 0 0.05 0.10 OS 0.20 0.25 0.30 @:35 0.40 0.45 Frequency (hz) Figure A-4. Wave spectra during storm of 28 December 1980. Wave spectra from 36-, 7-, 4-, and 2-meter depths are plotted with the predicted value of Ef) for depths of 7 meters or less. The value of E, &ppears to be an estt- mate for parts of the spectrum with frequencies less than 2f a> where f£, 1s the peak of the spectrum. Above 2f,, the value often tends to be an underestimate because the spectral values are related to harmonics of the dominant wave. However, the differences tend to be small. The wave direction 6 at 36-meter depth is plotted by frequency. 19 APPENDIX B METRIC VERSION OF TEXT TABLES 20 ‘yyoqnd Aduenbeiz AVMOT Jo uoT}OUNZ se “(180070 *4 Pa) uy at) 6 yjdep pue ‘1 ‘potzed 6%; H *jyu3TeYy peTToaquoo yjdaqg “T-d@ PLIFL 21 Table B-2. frequency, f (hz) (s) 5 0.05 0.06 0.07 0.08 0.09 0.10 0-11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 | 0.34 20.0 | 16.7 14.3 12.5. Hapa 10.0 9.1 8.3 Ted el 6.7 6.3 5.9 526 5.3 5.0 4.8 4.5 4.3 eo) 4.0 3.8 a) 3.6 3.4 BS 362 eal 3.0 29 0.60 0.64 0.67 0.71 0.73 0.76 0.78 0.81 0.83 0.85 0.87 0.89 0.90 0.92 0.94 0.95 0.97 0.98 1.00 1.01 1.03 1.04 1.05 1.07 1.08 1.09 1.10 1.11 1.13 1.14 US) 0.87 0.92 0.97 1.01 1.05 1.09 els 1.16 1.19 WAya2 1.25 1.27 1.30 1.32 1.35 1.37 1.39 1.41 1.44 1.46 1.48 1.49 Leal 1.53 1.55 1.57 1.58 1.60 1.62 1.63 period, Windspeed, 20 25 0.95 1.03 1.01 1.09 MOF melts V5 Vell te20 Velo 1 We.25 We 2OR iei29 1.24 1.33 Ve27 ~ le 37 1.31 1.41 1.34 1.44 1.37 1.48 1.40 1.51 1.43 1.54 1.46 1.57 1.48 1.60 1.51 1.62 Iiea3) 31.65 1.56 1.67 1.58 1.70 ‘1.60 1.72 Us62> 71375 1.64 1.77 ¥.66 41.679 1.68 1.81 1.70 1.83 U.72. 1.85 1.74 1.87 1.76 1.89 1.78 1.91 1.80 1.93 u_ (m/s) 35 1.15 1.22 1.28 1.34 1.39 1.44 1.49 153 1.57 1.61 1.65 1.68 1.72 1.75 1.78 1.81 1.84 1.87 1.90 1.93 1.95 1.98 2.00 2203 2205 2207 2.10 2012 2014 2.16 Ue Values of (a/0.0081)1/2 as function of spectral peak T, and windspeed, aM wie . sa Br: L029 9T=18) = Pete 43 = ay a a) a . ee cies es a re pene ag 7 ci a ' ty 7 a iP - man yy » 7 av n 1 on a ' 5 - : go - o ot re iid iA ie : i - a oe ot Ti ; ae A Uae oe ro a " ua A 7 ey > 7 : a f Ors ty a my nee (oS : 7 : v 7 7 z P yy 7 a i Th RUARE I 5 OE