G2(@ 1,2) = os (03 a 3) 
G2(@1,-@2) = pols (0? - 3) 
with the linear response assumed as G;(m) = 1. 
Fig. 12.13. Probability density function of the maxima of waves. 
(From Hineno.®7) 
Figure 12.13 shows the probability distribution density function for maxima of the 
waves compared with the experimental data by a certain research worker for model 
waves with a wave spectrum that is almost of the Pierson—Moskowitz type. In Fig. 12.13, 
the + marks indicate the experimental data analyzed as nonlinear waves and the other 
marks (A, O) are experimental data analyzed on the assumption of linear waves, the solid 
line being the theoretical relations as linear for this model waves. Results computed by 
Eq. 12.123 are shown by a dotted line, and the agreement with + signs is quite good, 
especially in the larger amplitude range, which is important practically. 
Figures 12.14, 12.15, and 12.16 illustrate the calculated results for nonlinear waves, 
using a modified Pierson—Moskowitz wave spectrum with H/3 = 11.6 m, To = 16.1 
sec as the input. From these figures, we can find the extent of nonlinearity of the waves 
and also the effects of nonlinearity or the effect of the distortion of the wave forms on the 
difference of the probability distribution function for maxima and minima. 
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