CETA 79-5 (AD-AOTT S06) Estimating Nearshore Significant Wave Height for Irregular Waves wHO! * DOCUMENT } . COLLECTION by William N. Seelig COASTAL ENGINEERING TECHNICAL AID NO. 79-5 OCTOBER 1979 Approved for public release; distribution unlimited. , U.S. ARMY, CORPS OF ENGINEERS , aco COASTAL ENGINEERING 330 RESEARCH CENTER Ug Kingman Building ne. og Fort Belvoir, Va. 22060 x Reprint or republication of any of this material shall give appropriate credit to the U.S. Army Coastal Engineering Research Center. Limited free distribution within the United States of single copies of this publication has been made by this Center. Additional copies are available from: National Technical Information Service ATTN: Operations Division 5285 Port Royal Road Springfield, Virginia 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. UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) READ INSTRUCTIONS REPORT DOCUNENTATION PAGE T. REPORT NUMBER 2. GOVT ACCESSION NO.| 3. RECIPIENT'S CATALOG NUMBER CETA 79-5 4. TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED ESTIMATING NEARSHORE SIGNIFICANT WAVE HEIGHT ies jaa FOR IRREGULAR WAVES echnical Ai 6. PERFORMING ORG. REPORT NUMBER 8. CONTRACT OR GRANT NUMBER(e) 7. AUTHOR(s) William N. Seelig 9. PERFORMING ORGANIZATION NAME AND ADDRESS Department of the Army Coastal Engineering Research Center (CERRE-CS) Kingman Building, Fort Belvoir, Virginia 22060 ROJECT, TASK MBERS 12. REPORT DATE October 1979 13. NUMBER OF PAGES WIS” 15. SECURITY CLASS. (of thie report) UNCLASSIFIED 11. CONTROLLING OFFICE NAME AND ADDRESS Department of the Army Coastal Engineering Research Center Kingman Building, Fort Belvoir, Virginia 22060 14. MONITORING AGENCY NAME & ADDRESS(if different from Controlling Office) 1Sa. DECL ASSIFICATION/ DOWNGRADING SCHEDULE 16. DISTRIBUTION STATEMENT (of this Report) Approved for public release, distribution unlimited. 17. DISTRIBUTION STATEMENT (of the abstract entered in Block 20, if different from Report) 18. SUPPLEMENTARY NOTES 19. KEY WORDS (Continue on reverse side if necessary and identify by block number) Design curves Irregular wave conditions Analytical model Computer program 20. ABSTRACT (Continue en reverse side if neceasary and identify by block number) Design curves for predicting nearshore significant wave height for irregular wave conditions, given deepwater wave conditions and the nearshore bottom slope, are presented. Examples of the curves used are given. The design curves were developed using the analytical model of Goda (1975). FORM DD 1. jan 73 1473 = EDITION OF ? Nov 65 1S OBSOLETE UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) i Fi ne ieee wm y fran te a An arteries wilern sr pelememmnntee opty ot ir =: eee een mice hirmereeay 9 ire etm te tener ity saiscaimeaamlig og me a ee - i i . wananryrey dn ae poral a ‘ ‘at, 7 agri ao lent ‘ge ‘Laat iytame, ty emetiinnes emer telugettt ! ——“_e ee eee tot syle’ evew maeaattivgly wrote sk goetgihs sidsetsen oft oe extitfhuas ovenw “S6taucne Revie oft .aotlg ove beew eovtts eda to polquend f2i@.) shod 2a Johom Jotiyians wit pact PREFACE This report presents procedures developed by Goda (1975) for esti- mating nearshore significant wave heights for irregular wave conditions, using known offshore (deepwater) wave conditions and the nearshore bot- tom slope. Goda's methods represent an important increase in the eng},- neering community's ability to predict waves propagating into shallow ~ water. The method is based on a number of simplifications and empirical adjustments but appears to represent laboratory and limited field data reasonably well. It is suggested that the method be used; however, the results should be carefully evaluated to confirm that the method is not used outside of its range of applicability. Procedures for predicting design wave conditions for irregular waves are not discussed in the Shore Protection Manual (SPM) (U.S. Army, Corps of Engineers, Coastal Engineering Research Center, 1977). The selection of design waves in the SPM (Section 7.12) is based on monochromatic wave theories. This work was carried out under the offshore breakwaters for shore stabilization program of the U.S. Army Coastal Engineering Research Center (CERC). This report was prepared by William N. Seelig, Hydraulic Engineer, under the general supervision of Dr. R.M. Sorensen, Chief, Coastal Structures Branch. Comments on this publication are invited. Approved for publication in accordance with Public Law 1966, 79th Congress, approved 31 July 1945, as supplemented by Public Law 1972, 88th Congress, approved 7 November 1963. ED E. B Colonel, Corps of Engineers Commander and Director CONTENTS CONVERSION FACTORS, U.S. CUSTOMARY TO METRIC (SI). SYMBOLS AND DEFINITIONS. I. INTRODUCTION . II METHODS FOR USING THE DESIGN CURVES. III EXAMPLES FOR USE . IV SUMMARY. FIGURES Selected nearshore wave records . Conditions in the nearshore zone. Nearshore slope of Nearshore slope of Nearshore slope of Nearshore slope of significant wave height diagram for 1 on 100. significant wave height diagram for ono Oe significant wave height diagram for 1 on 20 . significant wave height diagram for i om 1@ . a bottom a bottom a bottom a bottom 15 16 10 12 13 14 CONVERSION FACTORS, U.S. CUSTOMARY TO METRIC (SI) UNITS OF MEASUREMENT U.S. customary units of measurement used in this report can be converted to metric (SI) units as follows: inches iei5e4 millimeters 2.54 centimeters. square inches 6.452 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 259.0 hectares knots 1.852 kilometers per hour acres 0.4047 hectares foot-pounds 1.3558 newton meters millibars 1.0197 x 1073 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! lTo 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. SYMBOLS AND DEFINITIONS stillwater level or water depth that would be found if the waves were not present acceleration due to gravity nearshore breaker height predicted by monochromatic wave theory unrefracted deepwater significant wave height (this is the equivalent wave height that would occur with refraction accounted for at the point of interest) nearshore significant wave height deepwater wavelength the average beach slope approximately one-half to one wavelength seaward of the point of interest wave setup or increase in effective water level that occurs due to radiation stress (S, can be negative; when S, is negative it is referred to as setdown) wave period (for irregular waves use the period of peak energy density) ESTIMATING NEARSHORE SIGNIFICANT WAVE HEIGHT FOR IRREGULAR WAVES by Willtam N. Seeltg I. INTRODUCTION The selection of design waves, as discussed in Section 7.12 of the Shore Protection Manual (U.S. Army, Corps of Engineers, Coastal Engineer- ing Research Center, 1977), is based on monochromatic wave theories. The monochromatic wave theory assumption that waves have a constant height and period is best applied to swell (i.e., waves generated far from the point of interest). However, wind waves and waves generated by nearby storms are often irregular (i.e., height and period vary from one wave to the next), as evidenced by numerous wave records taken along the coasts of the world (see Fig. 1 for two examples). This report presents design curves for the prediction of nearshore significant wave height that include effects of wave irregularity, based on the procedures devel- oped by Goda (1975)2, using known offshore (deepwater) wave conditions and the nearshore bottom slope. This report does noc address factors such as refraction, diffraction or nonbreaking forms of wave energy loss. A method of accounting for wave refraction for irregular waves is dis- cussed in Seelig and Ahrens (in preparation, 1979)°. The analytical model requires the following assumptions: (a) the deepwater unrerracted significant wave height, Hj, and period, T, are known; (b) the bottom depth is continuously decreasing from deepwater shoreward; (c) the deepwater wave heights have a Rayleigh distribution; (d) surf beat, wave setup, and breaking limits can be described by em- pirical formulas; (e) shoaling is nonlinear; and (f) broken waves re-form at lower heights. Larger waves are assumed to break in deeper water and re-form, so that nearshore waves have a non-Rayleigh distribution. The significant wave height nearshore cannot be used to predict other near- shore height parameters, such as the mean height, because the height distribution is non-Rayleigh. lu.S. ARMY, CORPS OF ENGINEERS, COASTAL ENGINEERING RESEARCH CENTER, Shore Protection Manual, 3d ed., Vols, I, II, and III, Stock No. 008- 022-00113-1, U.S. Government Printing Office, Washington, D.C., 1977, IL, AGA, j3}de 2GODA, Y., "Irregular Wave Deformation in the Surf Zone," Coastal Engi- neering tn Japan, Vol. 18, 1975, pp. 13-26. 3SEELIG, W., and AHRENS, J., "Estimating Nearshore Conditions for Irregular Waves,'' U.S. Army, Corps of Engineers, Coastal Engineering Research Center, Fort Belvoir, Va., (in preparation, 1979). ip) (o) > = |-______—— 50 5-________=| Nags Head, N.C., 1840, 20 Sept. 1972 |}+—___—100 | Huntington Beach, Calif. 1800, 13 Mar. 1973 Figure 1. Selected nearshore wave records. Figure 2 illustrates some conditions assumed to occur nearshore. The local significant wave height (Hg defined as the average height of the highest one-third waves) 1s one of the most important parameters to de- Signers. For design curves that give the maximum, mean, or root-mean- SUES wave height or wave setup, see Seelig and Ahrens (in preparation, UGI/S)))\ II. METHODS FOR USING THE DESIGN CURVES The design curves (Figs. 3 to 6) are plots of local significant wave height divided by the stillwater depth, H,/d, versus the ratio of d/gT*. Curves are given for various deepwater wave steepness, H}/gT. The bottom slope, m, is the average slope one-half to one wavelength seaward of the point of interest. The location of the transition between wave setup and setdown is shown on each curve (where S, changes from positive to negative). The ratio Hg/d may be large because the effec- tive water depth may be greater than the stillwater depth due to wave setup. Where setup is positive the effective water depth is greater than the stillwater depth. The method of presenting the data was selected because nearshore wave height can be predicted from deepwater wave con- ditions (method 1, described below) or alternatively, waves measured in finite depth water can be used to estimate wave height at other shallower depths (method 2, described below). For values that fall between the curves use linear interpolation; for bottom slopes flatter than 1 on 100 use Figure 3. In some cases more detailed calculations or examination of wave height distribution may be necessary. If so, the computer program GODAS (720X1R1CBO) may be used to predict wave height distributions. This program may be obtained from the Coastal Engineering Research Center, Automatic Data Processing Coordinator, Kingman Building, Fort Belvoir, Virginia 22060. The computer program assumes that deepwater wave heights have a Ray- leigh distribution. If in a design situation the deepwater waves are known to be non-Rayleigh, which may occur with multipeaked spectra, the deepwater height distribution in the computer program can be changed to the assumed distribution function and the program used directly to make predictions. The analytical model assumes that the water depth is continuously decreasing from deepwater shoreward, and it is not shown what effects offshore bars have on nearshore wave height. As a first approximation for coasts with offshore bars, the wave height shoreward of the bar should be taken as equal to the predicted height at the bar crest location (Y. Goda, Port and Harbour Research Facilities, Tokyo, Japan, personal communication, 1978). At locations shoreward of the bar where the water depth is less than the depth at the bar crest, the methodology can be used to predict wave heights. 4SEELIG, W., and AHRENS, J., op. cit., p. 7. *9u0Z SLOYSIVSOU dy} UT SUOTJIpUOD “7 oLnsTy UOIENGI44S1Q $y61aH aADM 4J9a40Mda0eqG UOIINgIs4SIg yybIaH @ADM [0907 $4618H OADM v0 $4y610H aADM Bs 3 3 2 S yBbiajAoy =| = ybiajAoy —uoN |= < < 4SaJajul Jo yuiod ayy JO psOMDeS y4bua} -—9ADM 9U0 Of J/DY—aU0 adojs wojjoqg abosany ‘w fSosazul JO yulog uMOpLaS JOLDM 8AIL99) 3 Ja40M daag me) “Q00T uo T FO edoTs woz}0q @ IOF wesrsetp IYysTOY sAeM qURoTFTUBIS OZOYSTeeN “¢ OANdTY ,16/p 100 1000 10000 ¢100 #9000 z€000 91000 080000 2£0000 cae H anizobeu “cs (oif0) anigisod “cs ae ag 0! p/SH Gl (001 U0 |) 1OO0= W edojs LOA °0S¢ uo T FO ddoTs wo2110q B LOF WeAlseTp YYSTOY S9AEM JULITFTUSTS oTOYSIeON ‘p orn3TYy 9) 10° z-L5/P 1000 1000°0 16 ¢100 v9000 2£000 91000 080000 220000 = S— | 8Ai,0beu = le anizisod Mc 0! cu p/5H (OS U0}]) ZOO= wW adojs O72 Ge O€ 12 0 °0Z uo T FO odoTs woq.0q B OF WerseTp ZYBTOY eAeM JULITJTUBTS eLoYSIeEN ‘Ss oan3Ty z6/p 10:0 1000 1000°0 16 A €100 79000 2£000 91000 080000 z2e0000 = Or anizobau ™ t anizisod Mc (02 U0!) GO'O=W eadojs 13 "QT uo TT FO odoTs wozW0qG eB IOF WeaiseTp IYSTOY SAM JULITFTUSTS aTOYySIeeN *9 OINdTYA _ L6/p 10 100 1000 1000°0 216 €10'°0 +9000 z£000 91000 080000 z2£0000 = >— 'H on@) anizpbeu ™ 0! @Al}ISOd Is G'| p/SH O02 G2 (O01 UO|) O] 0 = Ww adojs ¢ Ge 14 Method 1 If the deepwater wave conditions, Hi and T, and bottom slope, mn, are known, use the following procedure for predicting nearshore signifi- cant wave height: a. Determine the ratios, H3/gT2 and d/gT*, where d is the stillwater depth at the point of interest. b. Enter the appropriate graph corresponding to the bottom slope, m, with the value of d/gT? on the ordinate. Find the point where d/gT2 and H3/gT2 intersect and read the value of (Hg/d) off the abscissa. c. Finally, Hg, = d(H¢g/d). Method 2 If local conditions at one location are known ((Hg)j, dj, m, T) the Significant wave height, (Hs), at another shallower depth, d,, can be determined: a. Compute (Hg),/d,; and dj,/gT?, enter these values on the abscissa, ordinate, and determine where they intersect. b. Determine the H$/gT* where the values intersect. Hj can be found directly; (Hg/d), and (Hg)> can be found as illustrated in method 1. TII. EXAMPLES OF USE kok eK kK KK RK KK RK RK KK KK SUNMDINS T «2 OS ee Go Ge te ee ee GIVEN: The conditions m = 0.02 (1 on 50 slope), T = 9 seconds, and Hi = 8.2 feet (2.5 meters). FIND: The significant wave height where d = 6.56 feet (2.0 meters). SOLUTION: Using method 1, 8.2 !/gT2 = —?-4—— = 0.0031 Ho/8T" = 37 2(9)2 and d/gT2 = —6-56 — = 9.0025 - 32.2(9) From Figure 4, (Hg/d) = 0.75; therefore, Hg = d (Hg/d) = 6.56(0.75) = 4.9 feet (1.5 meters) This nearshore predicted significant wave height is lower than if waves were monochromatic. If the SPM monochromatic design breaker height | curves (Fig. 7-4 in the SPM) were used with this example, the predicted breakwater height, Hp, would be: Hp = 6.23 feet (1.9 meters) . ke kK ke kOe RK RK KOK KK ® *® EYAMPLE 2 * * % * 4 KOK ROK RK RK RH GIVEN: Wave conditions were measured as T = 16 seconds and (Hs); = 6.56 feet (2.0 meters) where the bottom slope was m = 0.05 (1 on 20) and water depth was d, = 13.1 feet (4.0 meters). FIND: The significant wave height at a second location where do = 3.28 feet (1.0 meter). SOLUTION: Using method 2, (a) (Hg) 1/41 = TS aie = 0.5 and 1G de eae pee 1/8 32.2(16)2 = 0.0016 . (b) The abscissa and ordinate values in (a) intersect where H8/egT? = 0.00048 on Figure 5 3.28 —---_. = 0.0004 32.2(16)2 (c) At location (b), do/gT? = (d) At do/gT* = 0.0004 and H3/gT? = 0.00048, (Hg/d)o = 0.83 (e) Finally, the predicted significant wave height at location (b) is (Hs)2 = dg (Hg/d)o = 3.28(0.83) = 2.7 feet (0.83 meter) WKS I es he) Te) ei ae ke) ey ik) eae ak, Re eck CRD uke ae ee ep) ok) ee ck Kem eek IV. SUMMARY Curves for estimating nearshore significant wave heights for irregular waves using the analytical model of Goda (1975) are presented with exam- ples for use. 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yeopqATeue oy} Butsn pedoTeaep 210M seaino ustTsep ey], ‘“UeATS ole pesn sesino oy Jo setdwexqg *pejueseid ere ‘oedoTs woj}0q et0ysie9u ay} pue suoTE_puoD aAeM AezeMdsep UsATS ‘SUOTITpUOD sAEM AeTNZe1IT ZOF AYSTEey aaeM JueoOTFFUSTS sLoysieeu BuTIOTperd 1z0y seaano ustseq *O9TIFI 128A00 (S-62 VLU) : PES TeoFUyoe] BuzaseuTsue Teqyseop) — ‘wo /z $ “TTF : *d OL "6161 ‘80FAZeg uoTFeWAOFZUT TeopPUYyoe], TPUCTIEN WorZ oTGeTTeAe : ‘ep ‘pTeTF3utads £ 1equeD yorPesey SupTiseuTZug TeqseoD *S°M : “eA SAFOATEG JA0q — “3TTeeS *N WETTTEM Aq / seaem ieTNBerIT JoOF JYyBpPeYy eAeM QUeDTFTUSTS eToysiesu SuTIeUTISY ‘N WETTTEM ‘3TTeeS »