PART V: BIMODAL TESTS 



Test Conditions 



68. A total of 55 cases have been examined for the bimodal tests. 

 Table 2 lists the parameters used in the tests. The primary variables are 

 modal separation, as defined by Equation 69, and relative modal energy, as 

 defined by Equation 70. Each mode has been constrained to a width of 0.01 Hz 

 by adjusting the parameter Af/f^ along with the parameter f^ so that their 

 product yields the desired bandwidth. With a time step At = 0.5 sec and the 

 time series length of 65,536 points, the raw spectral bandwidth is about 

 0.0000305 Hz. With this raw bandwidth, a modal bandwidth of 0.01 Hz contains 

 about 328 spectral lines. Each mode is independently a Rayleigh process, as 

 determined from the results of Part IV. 



69. Modal separation has been allowed to vary from zero to about 1.33. 

 At zero separation, the two modes coincide on the frequency axis. In this 

 case, the resulting process should be Rayleigh for all values of relative 

 modal energy because the effective spectrum is unimodal and narrow, and 

 contains enough spectral lines. It is no longer a white spectrum, however, 

 because there are now two randomly phased waves at each frequency. Two waves 

 at the same frequency can interfere constructively or destructively, depending 

 on their relative phases, so that the resulting wave amplitude can vary from 

 zero (destructive interference with waves of equal amplitude) to the sum of 

 the two component wave amplitudes (constructive interference with the waves in 

 phase) . Corresponding wave energy will vary from zero to a number proportion- 

 al to the square of the sum of the two component wave amplitudes. In the 

 derivation by Longuet-Higgins (1952) , there was no constraint on the distribu- 

 tion of energy within the narrow band process. Hence, coincident modes in the 

 test spectra are expected to yield wave height distributions that follow the 

 Rayleigh model. 



70. The largest modal separation has one mode center frequency at 

 0.05 Hz and the other at 0.25 Hz. These frequencies are near the limits of 

 the overall band normally associated with wind waves, corresponding to wave 

 periods of 20 and 4 sec, respectively. This separation is considered to be a 

 practical limit for wind waves. Such a case might occur where young or short- 

 fetch waves are riding on longer, swell -like waves. 



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