combinations. Thompson (1980) discussed several coastal gage records with large 

 ratios of Hg/d that have n^/Hg ratios on the order of one for the highest 

 crest observed, while n(,/d for the largest crest is somewhat less than one. 

 Jahns and Wheeler (1973) found similar extremes for hurricane and storm waves 

 in the Gulf of Mexico. Large values of H^^/Hg can be obtained if the signif- 

 icant wave height is small compared to the water depth and the wave steepness 

 is low. Individual wave crests with elevations greater than 1.5 times the 

 significant wave height were observed in a number of the laboratory experiments, 



where H^/d <0.3 and d/(gT2) < 0.005 for m = 0.0. 

 ° P 



Similar values of maximum wave crest elevation were found for irregular 

 waves shoaling on a 1 on 30 laboratory smooth slope. An examination of a typi- 

 cal set of results showed that crest elevation increases as the wave shoals, 

 then decreases as the wave breaks (Fig. 17). Note that in this figure both the 

 crest elevation and the Stillwater depth have been normalized by the deepwater 

 equivalent significant wave height, Hq. Typical values of the single highest 

 crest observed during an irregular wave test of 260 seconds for model time are 

 presented in Table 7. Water level time histories at several gages at various 

 depths along the 1 on 30 slope are given in Figure 18 for an irregular wave 

 condition. 



Jahns and Wheeler (1973) suggested a method for predicting irregular wave 

 crest statistics, using the dimensionless parameter (ri(;.)/Hs. A Rayleigh-type 

 distribution is assumed, then an empirical correction factor is recommended 

 to increase the probability of occurrence of crests. One of the disadvantages 

 of this approach is that the data often dramatically differ from a Rayleigh 

 distribution because actual probabilities are orders of magnitude larger than 

 predicted. For example. Figure 19 compares crest height distributions for the 

 wave records A, B, and C shown in Figure 16 with the Rayleigh distribution. 



The approach taken in this report is to predict crest elevations in terms 

 of local parameters for a given probability level in terms of Hg, d, and 

 Tp. Figure 20 shows values of n^/d for wave records A, B, and C illustrated 

 in Figure 16. 



The suggested method for predicting irregular wave crest elevations is to 

 use the stream-function results to determine the general form of the equation 

 and laboratory results to calibrate the prediction technique for various prob- 

 ability levels. The equation used is 



(nc)i 



..0 + tanh (-A2 l-nik^ it)) 



(8) 



where the parameters A2 and A3 are taken from stream-function results 

 (Fig. 8 and Table 2), and A* is an empirical parameter determined from the 

 experimental data. The laboratory data (App. C) indicate that Af is a 

 function of the probability of exceedance, with A* increasing as the prob- 

 ability, p, decreases (Fig. 21, Table 8). Equation (8) shows good correla- 

 tion with the laboratory data as indicated by the small standard deviation of 

 A* about the mean for values of p = 0.01 and greater (Tables 8 and 9). Af at 

 p = 0.005 has poor resolution because the data collection runs had only a few 

 crests more than 200 crests per run. Figure 22 gives observed and predicted 

 crest elevations at the 2-percent probability level of exceedance. 



32 



