effect on average heights is similar to results from the broad, unimodal cases 

 of Part IV. In fact, the cases in Figure 10 with energy ratios of 1.0, 2.0, 

 and 4.0 have properties very much like the two broadest unimodal cases (Af/f^, 

 = 0.80 and 1.60) in Figure 3. Mean wave heights H''"''^^ are higher than 

 Rayleigh predictions by 2 to 3 percent; the H''"''^^ are smaller than Rayleigh 

 by 2 to 3 percent; the h'^'^°' are smaller by 3 to 5 percent; and the h'^'^°°' 

 are smaller by 3 to 10 percent. The evident conclusion is that from some 

 bimodal spectra with intermediate and large peak separation, the effect on 

 wave height averages is the same as for broad, unimodal spectra. 



76. For bimodal spectra with low energy ratios (energy in the high- 

 frequency mode somewhat smaller than that in the low- frequency mode) , average 

 wave height behavior is very different at large peak separations. Here, 

 again, short waves are being carried on longer waves, but now the short waves 

 tend to have less amplitude than the long waves. This situation leads to the 

 condition that at the crests and troughs of the long waves, there are a number 

 of short waves whose extrema do not cross the line of zero displacement. 

 There tend to be higher crests because short wave crests add to long wave 

 crests, and deeper troughs because short wave troughs drop below long wave 

 troughs, but fewer waves overall because the short waves do not have as many 

 zero crossings as when they have higher energy. In regions of the time series 

 near nodes (zero-crossings) of the low-frequency waves, the number of zero 

 crossings is about the same as for higher levels of high-frequency energy. 

 Hence, there is a relative reduction in the number of waves of intermediate 

 height, those which would occur if the high-frequency waves reached zero level 

 from extrema of the low-frequency waves. There becomes a relative abundance 

 of both large and small waves, at the expense of the number of waves of inter- 

 mediate height. 



77. This redistribution of wave heights also affects the value of 

 Hj^5 , a parameter used to normalize all distributions and parameters in this 

 study. The net results of this alteration of H^^^ (relative to H^^, , the 

 parameter used to govern total spectral energy and to generate the time 

 series) and the redistribution of wave heights are shown as the normalized 

 wave height averages in Figure 10. The higher wave height averages are very 

 much higher than the Rayleigh prediction. For the lower averages, H'-"^'-^' 

 hovers near the Rayleigh prediction, and the average wave height H'^'^' tends 

 to be less than the Rayleigh value. 



46 



