j^d/ioo) ^ ^j- takes about 100 component waves to stay within 10 percent of a 

 Rayleigh h^^'^°°^ . Beyond a certain bulk spectral bandwidth, the parameters 

 do not appear to approach Rayleigh parameters, no matter how many component 

 waves are used in the spectral definition. This is most clear for the widest 

 case investigated here, Af/fc =1.60 , but is also slightly evident in the 

 next- to-widest case Af/f,, = 0.80 . It is notable that even the mean wave 

 height H'^'-'-^ and the average of the highest one-third waves H^^'^' show 

 some effect of spectral broadening. 



86. The Modified Rayleigh pdf and exceedence curves clearly represent 

 the synthetic data better than the Rayleigh curves. With roughly the same 

 constraints on numbers of component waves as for the Rayleigh comparison, 

 averages of synthetic wave height distributions were within 2 percent of 

 averages from the Modified Rayleigh model for all bandwidths and for averages 

 out to h'-^'^°°' . This result suggests that the Modified Rayleigh curve is a 

 better model for broad spectra if the added parameter H^^^ can be determined 

 directly from the spectra. It is not yet evident that this determination can 

 be made, and further research is required to characterize H^^^ in terms of 

 spectral shape. 



87. The primary part of this investigation is examination of wave 

 height distributions in wave signals derived from multimodal spectra. To keep 

 the study simple, only bimodal cases are considered. Using criteria es- 

 tablished in the unimodal tests, bimodal spectra are constructed from two 

 unimodal spectra, each of which yields a Rayleigh wave height distribution by 

 itself. Given this characteristic, the details of the mode structure 

 (bandwidth and number of component wave trains) are no longer important. The 

 two primary variables in these bimodal tests are a measure of modal separation 

 in the frequency domain and the relative amount of energy in one mode compared 

 with the other. 



88. Modal separation is characterized by differences between modal 

 center frequencies normalized by the mean of the two modal center frequencies. 

 In the present tests, the smallest modal separation is zero, corresponding to 

 modes coincident in the frequency domain and representing a directional wave 

 field where the modes have two different peak directions. The largest modal 

 separation has one mode center frequency at 0.05 Hz and the other at 0.25 Hz, 

 corresponding to wave periods of 20 and 4 sec, respectively, and considered to 

 be a practical limit for wind waves. Five levels of relative energy have been 



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