from synthetic data are compared with Rayleigh and Modified Rayleigh model 

 predictions of these statistics. Percentage differences are then computed 

 following the pattern of Equation 71, and comparisons are done among these 

 percentages . 



Test Results 



73. Figures 10 and 11 summarize the results of the bimodal tests. 

 Figure 10 shows percentage differences of synthetic data from the Rayleigh 

 model. Figure 11 shows synthetic data compared with the Modified Rayleigh 

 model. In both figures, peak separation (defined by Equation 69) is along the 

 abscissa. Symbols denote points of constant relative energy ratio (defined by 

 Equation 70) . 



74. In Figure 10, the synthetic data clearly approximate the Rayleigh 

 model for small modal separations, as expected. Synthetic data begin to 

 deviate from the Rayleigh model when the peak separation parameter reaches 

 about 0.40, especially for averages on the high-wave tails of the distribu- 

 tions, e.g., H<^'^°°Vh^^ and H'^'^VH^s • Curves for all values of the 

 energy ratio behave similarly up to peak separations of about 0.60, and then 

 diverge radically depending on the energy ratio. At the largest peak separa- 

 tion, and for a small energy ratio, i.e., where the energy in the high- 

 frequency mode is small relative to that in the low- frequency mode, the 

 average of the highest 1 percent of the waves exceeds the Rayleigh prediction 

 by almost 20 percent. This result suggests a rather severe problem in 

 structural design if the Rayleigh model is used for estimating extreme waves, 

 since it will be low by 20 percent under these conditions. For intermediate 

 and large energy ratios and for large peak separations, the statistics of the 

 higher wave averages are less, by up to 7 percent, than the Rayleigh model 

 prediction. 



75. The reasons for this severe dichotomy in the extreme average wave 

 heights at large modal separations are not immediately obvious. Part of the 

 explanation is how H^^^ behaves relative to the absolute average heights in 

 the various test conditions. If waves in the high-frequency mode are as 

 energetic or are more energetic than those in the lower frequency mode (energy 

 ratio > 1), the effect is simply to broaden the spectrum. High-frequency 

 waves are carried by lower frequency waves of comparable energy, and the 



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