Ud s.frm on Coast. Eng RAS SEEDY CETA 7 CETA 80-1 Maximum Wave Heights and Critical Water Depths for Irregular Waves in the Surf Zone by William N. Seelig COASTAL ENGINEERING TECHNICAL AID NO. 80-1 FEBRUARY 1980 Approved for public release; distribution unlimited. U.S. ARMY, CORPS OF ENGINEERS Te COASTAL ENGINEERING P22 RESEARCH CENTER Ue Kingman Building uo, S0-| Fort Belvoir, Va. 22060 Reprint or republication of any of this material shall give appropriate credit to the U.S. Army Coastal Engineering Research Center. Limited free distribution within the United States of single copies of this publication has been made by this Center. Additional copics are available from: National Technical Information Service ATTN: Operations Division 5285 Port Reval 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. MBL/WHOI QM 0 0301 0089713 & UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE. (When Data Entered) READ INSTRUCTIONS REPORT DOCUMENTATION PAGE 1. REPORT NUMBER 2. GOVT ACCESSION NO. 3. RECIPIENT'S CATALOG NUMBER CETA 80-1 4. TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED MAXIMUM WAVE HEIGHTS AND CRITICAL WATER DEPTHS aa ae ie Bs FOR IRREGULAR WAVES IN THE SURF ZONE oC eee 6. PERFORMING ORG. REPORT NUMBER 7- AUTHOR(s) 8. CONTRACT OR GRANT NUMBER(s) William N. Seelig ELEMENT, PROJECT, TASK ORK UNIT NUMBERS 12. REPORT DATE February 1980 13. NUMBER OF PAGES 11 15. SECURITY CLASS. (of this report) UNCLASSIFIED 9. PERFORMING ORGANIZATION NAME AND ADDRES3 Department of the Army Coastal Engineering Research Center (CERRE-CS) Kingman Building, Fort Belvoir, Virginia 22060 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) DECL ASSIFICATION/ DOWNGRADING SCHEDULE 15a. 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) Design curves Wave heights Irregular waves Waves ABSTRACT (Continue om reverse side if necessary and identify by block number) The nearshore irregular wave deformation model of Goda (1975) is used to develop prediction curves for the magnitude and location of peak wave heights in the surf zone as a function of profile slope and offshore wave steepness. An example that demonstrates the use of these curves is presented. 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This report presents similar curves for the magnitude and location of peak wave heights for irregular waves, based on the model of Goda (1975). This work was carried out as a part of 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 Processes and Structures Branch. 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. Colonel, Corps of Engineers Commander and Director CONTENTS CONVERSTONSFAGTOR SS.) eUSin CUSTOMARY) sTORMET RI Gia (Sip) sume een rennet ns ncunreiars fer SLIMUTOVS) ZNNID) IOVS IINUEINIOINISS GG 5010 6 0 06 0 6 0 606 0 60 6 8 6 The elNTRODUCTIONstasy ys) Sate ys dager gf nee Fee WO Reis aseue kOe SeheT: “eee 7 JE W)DISSINE | HQU MES Ge Go Goo) Clo OG lGnonotD 6 6 0 OG 6 1b 616 6 © 0 6 oc 7 GE ONION Groot goo 6 cHOMorolo (0.0 ob 'o| G onal 6 O10 0,5. 0 co 8 TW: SUMMARY: Xo a me he See Felt eels ies ven! les 8) ey Regine). ca) ts cree 0) > ts) ge Oe TABLE Predicted peak wave heights using irregular and monochromatic theories .. ll FIGURES 1 Predicted nearshore wave heights using Goda's model .......... 8 2 Peak values of wave height in the nearshore zone. ........... 9 3 Water depth for the peak significant wave height: =~ 29. 4 =<) 3 = alo 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: Multiply inches square inches cubic inches feet square feet cubic feet yards Square yards cubic yards miles square miles knots acres by To obtain ooo eeOOeeeeeeeeeeeeeeeoooeoeoeeeswweweaeaeaeaeaeasa( aS OOMnNMMN(R(ae 25.4 millimeters 2.54 tentimeters 6.452 square centimeters 16.39 cubic centimeters 30.48 centimeters 0.3048 meters 0.0929 square meters 0.0283 cubic meters 0.9144 meters 0. 836 square meters 0.7646 cubic meters 1.6093 kilometers 259.0 hectares 1.852 kilometers per hour 0.4047 hectares. 1.3558 newton meters foot-pounds millibars ounces pounds ton, long ton, short degrees (angle) Fahrenheit degrees 1.0197 x 1073 28.35 453.6 0.4536 1.0160 0.9072 0.01745 5/9 kilograms per square centimeter grams grams kilograms metric tons metric tons radians Celsius degrees or Kelvins! ee lITo obtain Celsius (C) temperature readings from Fahrenheit (F) readings, use formula: C= (5/9) (8 =22)- To obtain Kelvin (K) readings, use formula: K = (5/9) (F -32) 2 SSE d* SYMBOLS AND DEFINITIONS water depth where H Ss max occurs acceleration due to gravity maximum breaker height for monochromatic waves average height of highest 1 percent of all waves for a given time period peak value of Hy deepwater significant wave height significant wave height defined as the average of the highest one-third waves peak value of Hg wave period defined as the period of peak energy density for irregular waves slope of the bottom MAXIMUM WAVE HEIGHTS AND CRITICAL WATER DEPTHS FOR IRREGULAR WAVES IN THE SURF ZONE by Willtam N. Seeltg I. INTRODUCTION The Shore Protection Manual (U.S. Army, Corps of Engineers, Coastal Engi- neering Research Center, 1977)! gives methods for estimating wave height near- shore due to monochromatic waves, based on the work of Goda (1970)%. However, the action of irregular waves in the surf zone is very complex, involving the interaction of wave shoaling, breaking, and setup; re-formation of broken waves; surf beat; and other mechanisms. Goda (1975) % proposed a model for predicting wave height distributions and wave height parameters in the nearshore zone for the case of continuously shallowing profiles. Goda's model assumes that the (a) equivalent deepwater significant wave height and period are known; (b) deep- water wave heights have a Rayleigh distribution; (c) average beach slope one- half to one wavelength seaward of the point of interest is known; (d) surf beat, wave setup, and breaking limits can be described by empirical formulas; (e) wave shoaling is nonlinear; and (f) broken waves re-form at lower heights. Using these assumptions, a numerical procedure was developed to predict nearshore wave heights (see Seelig and Ahrens, 1979)*. Limited testing of the model with field and laboratory data suggests that Goda's model gives useful estimates of near- shore wave heights. Il. DESIGN CURVES Calculations of nearshore wave conditions using Goda's (1975)° model show that wave height parameters reach a maximum or peak value at one point along the profile. For example, an irregular wave condition with a deepwater sig- nificant wave height, H,, and a period of peak energy density, T,, has a peak value of significant wave height, Hg, max, at a water aeoen, “Ge (rig. 1). This would be an especially poor location to build a structure or site any other activity sensitive to wave height, because the significant wave height reaches its largest value at this point. H, shown in the figures is defined as the 1y.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, 1,262 pp. 2GODA, Y., "A Synthesis of Breaker Indices," Transactions of the Japanese Soctety of Civtl Engineers, Vol. 2, Pt. 2, 1970. 3GODA, Y., "Irregular Wave Deformation in the Surf Zone," Coastal Engineering in Japan, Vol. 18, 1975, pp. 13-26. 4SEELIG, W.N., and AHRENS, J., "Estimating Nearshore Conditions for Irregular Waves,'' U.S. Army, Corps of Engineers, Coastal Engineering Research Center, Fort Belvoir, Va. (in preparation, 1980). HEN, Win Gdn eile 5 Wave Height SWL Intercept SSS Distance Offshore Water Depth Figure 1. Predicted nearshore wave heights using Goda's model. average of the highest 1 percent of the waves and is the wave height with an exceedance probability of approximately 1/260. Goda's model predicts that the peak value of H, occurs just seaward of d* (Fig. 1). Figure 2 gives the design curves for Hg mg, amd Hi max as a function of deepwater wave steepness and beach slope. These curves show that the peak wave heights decrease as the wave steepness increases and the beach slope becomes flatter. The dimensionless water depth where the peak significant wave height occurs becomes smaller as the beach slope or wave steepness increases, except for the steepest waves (Fig. 3). III. EXAMPLE PROBLEM GIVEN: Wave conditions of Ho = 6.56 feet (2.0 meters) and Tp = 10 seconds with a beach slope, m, = 1/100. FIND: The peak significant and maximum wave heights in the surf zone and their locations. SOLUTION: For this example: Ho/8Tp = 2.0/(.8 *) 102) =) 0.002" From Figure 2, Hs max Hp = 1.18 or Hg may = 7.7 feet (2.3 meters), and H ara = 1.81 or Hy mgx = 11.8 feet (3.62 meters). (a) Dimensionless Maximum Wave Height 0.001 0. 4.0 3.5 Oo oO iS) wn ine) oO on 0.000! 0.002 004 0.006 Ho /Tp* (m2 /s) 0.004 0.006 0.01 0.02 0.04 0.06 (ft2/s) 0.01 0.02 0.04 0.06 0.1 0.2 m=1/100 0.0002 Figure 2. 0.0004 0.001 0.002 0.004 0.006 Ho/g ipa Peak values of wave height in the nearshore zone. 0.1 0.3 0.01 Ho/ Tp? (m2/s) 0.001 0.002 0.004 0.006 0.0! 0.02 0.04 0. a AR ACT AT a Ne. Cah. LA (147s) 2 04 0.06 _—O.! Oa) Os 4.0 0.004 0.006 0.0! 0.0 m=1!/!100 a*/ Ho 0.001 0.002 0.004 0.006 0.0! Ho/a1p- Water depth for the peak significant wave height. 0.000! 0.0002 0.0004 Figure 3. From Figure 3, —— = 2.36 or d* = 15.5 feet (4.72 meters) which occurs 1,550 feet (472 meters) offshore of the beach stillwater level (SWL) intercept for a 1/100 slope beach. Note that monochromatic theory predicts a breaker height, H,, (Fig. 7-3 in U.S. Army, Corps of Engineers, Coastal Engineering Research Center, 1977)® that occurs between the peak significant and maximum one percent heights (see Table). Table. Predicted peak wave heights using irregular and monochromatic theories (T = 10 seconds; m = 1/20). Hs max H Ay mas Ho b (ft) @) (ft) () (ft) () (ft) (m) 5.28 GLO) Sosy So Ge) 754 CS) 6.56 @.0) 8.88 @.6) 10.2 Gel) 12.5 G8) Io CG.O) 15.8 MsP) i6o7 (oN) 21.8. G5) LOROME (SRS 28.0 (WoO) 30.8 (9.2) IV. 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