MAXIMUM WAVE HEIGHTS AND CRITICAL WATER DEPTHS 

 FOR IRREGULAR WAVES IN THE SURF ZONE 



by 

 Wilt-lam N. Seet-ig 



I. INTRODUCTION 



The Shore Protection Manual Q'-S. Army, Corps o£ 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. 



II. DESIGN CURVES 



Calculations of nearshore wave conditions using Goda's (1975)^ model show 

 that wave height parameters reach a maximiom 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, 1 , has a 

 peak value of significant wave height, Hg ^oa; at a water depth, d* (Fig. 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. Wi shown in the figures is defined as the 



^U.S. ARMY, CORPS OF ENGINEERS, COASTAL ENGINEERING RESEARCH CENTER, Shore 

 Froteotion Manvial , 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. 



^GODA, Y., "A Synthesis of Breaker Indices," Transactions of the Japanese 

 Society of Civil Engineers, Vol. 2, Pt. 2, 1970. 



^GODA, Y., "Irregular Wave Deformation in the Surf Zone," Coastal Engineering 

 in Japan, Vol. 18, 1975, pp. 13-26. 



'^SEELIG, 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). 



^GODA, Y., op. cit. 



