13. (Concluded) . 



from idealized, synthetic time series having spectra with variable widths, 

 modes, and modal separations. The Modified Rayleigh model is the two- 

 parameter, deepwater asymptotic form of the Beta-Rayleigh distribution. 



The first part of this report involves determining some of the limits 

 implied by the phrase "unimodal, narrow spectrum" in the synthesis of time 

 series having Rayleigh distributions of wave heights. It is found that for 

 unimodal, band-limited, white spectra, there are constraints on both the 

 overall bandwidth and the number of component waves for a close approxima- 

 tion to a Rayleigh process to occur. 



The primary part of this investigation is examination of wave height 

 distributions in wave signals derived from multimodal spectra. Using cri- 

 teria established in the unimodal tests, bimodal spectra are constructed 

 from two unimodal spectra, each of which yields a Rayleigh wave height 

 distribution by itself. 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. 



Spectra with broad ranges of modal separation parameter and with a 

 ratio of low-frequency modal energy to high-frequency modal energy roughly 

 greater than 1.0 have wave height distributions that are well-represented 

 by the Modified Rayleigh model. The Rayleigh model tends to overpredict 

 wave height averages for these parametric ranges in much the same way as 

 was found for time series derived from broad-banded spectra and as have 

 been found frequently in natural observations. For large modal separations 

 and small high-frequency modal energy relative to low-frequency modal en- 

 ergy, synthetic data deviate strongly from the Rayleigh model and deviate 

 significantly from the Modified Rayleigh model. Further study is needed 

 to determine the relative importance of such conditions. Further research 

 is also required to determine the parameters of the Modified Rayleigh 

 model in terms of spectral parameters. Finally, these conclusions need to 

 be tested with natural data to ensure that the artifice of synthesis has 

 not biased the results. 



