SECT. 5] 



LONG OCEAN WAVES 



651 



then traveling seaward at a speed \/{gh). Conservation of energy flux 

 i'^a^X^igh)) would lead to a dependence of amplitude on depth according to 

 Green's law : a'^h"^*. This hypothesis is false. The new observation indicates a 

 much more rapid decrease with depth than is consistent with Green's law. 

 Furthermore, by using an array of recorders, we can now estimate the direction 

 of the surf-beat waves : it is shoreward, not seaward. 



The only safe conclusion at this time is that surf beat consists of some non- 

 linear interaction between the ordinary waves and the low-frequency waves. 

 Tucker's observation of a phase correlation between the surf beat and the 

 envelope of the ordinary wave record points in this direction. Whatever is 

 responsible for the generation of the "difference-frequencies" (Tick, 1958), the 

 important terms appear to be dependent on depth and one may assume that 

 the dimensionless number (a/^) plays the essential role. 



5. Shelf Waves 



Fig. 4 shows the low-frequency portion of the long-wave spectrum in more 

 detail. The Camp Pendleton peak to the very left of Fig. 3 now appears as a 

 broad hump of relatively high frequency as compared to other stations. 



Cycles per hour 

 4 



100 



0.01- 



1 2 



Cycles per kilosecond 



Fig. 4. Background spectra at Mar del Plata, Argentina ; Acapulco, Mexico ; Camp Pendle- 

 ton, California ; and at Lahaina Wharf, Maui, Hawaii. 



Acapulco shows a very sharp peak at 2 c/h (Munk and Cepeda, 1961). At Maui 

 the spectrum is complex (all peaks are reproducible) with the lowest frequency 

 peak at 1 c/h. At Mar del Plata (Inman et al., 1962) the spectrum is of still 

 lower frequency, with the fundamental at 0.3 c/h ; the energy density is a 

 hundred times above that at the other stations. The occurrence of high and 

 long-period "seiches" over the broad Argentinian shelf is well known. 



