Ogilvie 



which is usually used by oceanographers that define the spectrum only on 

 -^+co range of co is inconvenient. The spectrum of the waves, |h (w)!^^ 

 ^0o*o' ^i 4> ^^^ ^^^° ^^^ convolution S are shown in Figs. 17, 18 and 19. 

 From Fig. 19, we can see the character of single and double convolutions. In 

 the single convolution, a large power appears at w = o and at the frequency 

 twice of that of the peak. In the double convolution, the large power appears 

 again at the frequency of the peak of the original spectrum, and at the triple of 

 that frequency. Because of the large decay of |H(<ij) p at these high frequencies, 

 the latter peak did not modify the spectrum. From these results, s^j.^^ was ob- 

 tained as in Fig. 20. This is a pretty reasonable example of the effect of non- 

 linear damping, which reduced the height of the peak that appeared in the spec- 

 trum of zero order approximation. There is the possibility that when the linear 



Fig. 17 - Spectra of wave, roll, 

 and roll angular velocity 



122 



