0.60 
0.40 
0.30 
SPECTRAL DENSITY (ft)? -sec. 
0.20 
0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 
FREQUENCY, rad/sec 
Fig. 9.2. The second order spectra s®(w) for varying depth h = 32.2, 46.4, and 72.5 ft. 
(From Tick.®) 
1 
G2(@1,@2) = ap (wt + w3) for the sum (@ + @2) frequency component 
1 
=— Oe lot = w3! for the difference frequency component. (9.10) 
Figures 9.3 and 9.4 indicate that the quadratic effect on the spectrum computations 
is very small for ordinary cases. M. Hineno® extended this result and calculated the prob- 
ability distribution of the maximum and minimum of the waves. The results are intro- 
duced in Section 12.7, and from the results we find that the effect of the nonlinearity is 
not large. 
92.2 Bispectrum of Waves 
L. Tick® suggested the need for bispectrum analysis for ocean waves. Such an anal- 
ysis was performed by K. Hasselman et al.°* as shown in Fig. 9.6. The exposition on the 
bispectrum is given in Section 11.3. Here, one bispectrum for shallow waves is given as 
an example, and it indicates that the nonlinearity is not large in this analysis either. 
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