0.6 
0.5 
0.4 
0.3 
02 
0.1 
_——— SS = 
01234567 8 910111213 141516171819 20 
0.0003 
0.0002 
0.0001 
012345 67 8 9101112131415161718 19 20 
S2(@) for s;(@) = 18 x 104, |a@| > Wp 
Fig. 9.1. The second order spectra. 
(From Tick.®) 
sD@)=C ate, w<2 
and showed s®(w) as in Fig. 9.2. In this case, even when the water depth h = 32.2 ft, the 
effect of nonlinearity is small. 
He pointed out the necessity for computing the bispectrum to show clearly the 
quadratic effect of the waves as will be discussed in Section 9.2.2. 
On the nonlinearity of the waves M. S. Longuet-Higgins™ © and D. M. Phillips® 
discussed work along the same lines, and M. Hineno®’ referred these works and showed 
clearly the quadratic effect, as in Fig. 9.3, that was calculated for a modified Moskowitz— 
Pierson type spectrum. In Fig. 9.4, the quadratic and linear parts of the spectrum 
produced in the experimental water tank are shown. 
Hineno®’ also showed the quadratic kernel functions g(t), T2) as Fig. 9.5, that is, the 
Fourier transform of quadratic frequency responses G2(w), w2), equivalent to the 
Q(w,w’) by L. Tick, as 
270 
