600 



400 



200 





\^ / 



/ 

 / 



• South Haven 

 o Columbia Light 

 X South Pass 



200 



400 



5 00 



Tmod ( S 



Figure 40. Comparison of modulation period estimated from 

 LVTS and from wave steepness. 



Figure 41. The relationships predicted by the BF theory and by Longuet- 

 Higgins (1980) are also shown. Scatter in the field data is greater than in 

 Lake and Yuen's laboratory data. A more definitive comparison of field data 

 and theory is obtained by computing a mean dimensionless modulation frequency 

 for each field record which has five or more T^u-pS values. The comparison 

 (Fig. 42) indicates that the field data correspond more closely with the 

 Longuet-Higgins (1980) prediction of modulation frequency than with the BF 

 prediction. 



Constituents obtained by MRS analysis of the squared time series for 

 Columbia Light, 1300 to 1317, were presented in Figure 37. Two constituents 

 have considerably higher amplitude than the others. They occur at frequencies 

 to 0.0021 and 0.0042 hertz, corresponding to periods of 476 and 238 seconds. 

 These periods are expected to be indicative of modulation periods in the time 



series. In fact, the 476-second period is only 

 from equation (35) . 



10 percent less than 



mod 



Thus, field evidence from all three locations indicates that waves in deep 

 water sometimes tend to be organized so that high waves occur in groups (Sec. 

 I, hypothesis d) and the modulation period of wave groups is related to wave 

 period and steepness (hypothesis e) . 



61 



