726 



[chat. 21 



therefore, capable of completely destroying ripples. Observations of the slopes 

 of the water surface (Keulegan, 1951 ; Van Dorn, 1953 ; Cox and Munk, 1954) 

 show that even in the presence of wind, ripples are inhibited. The visibility of 

 slicks is mainly due to the absence of ripples (Cox and Munk, 1956). 



By maintaining a slick over moderately large water surfaces exposed to wind, 

 Keulegan (1951) and Van Dorn (1953) have found that the growth of gravity 

 waves can be inhibited. This observation strongly suggests that the roughness 

 produced by ripples and short gravity waves is required before wind can get a 

 grip on the water surface to raise longer waves, 



3. Shape of a Rippled Water Surface 



Scott Russell (1844) and Munk (1955a) have called attention to the observa- 

 tion that ripples are sometimes found concentrated just in front of the crest of 

 short gravity waves (Fig. 4). This effect is particularly noticeable where a 

 sharply peaked spectrum of short gravity waves has formed, as in a laboratory 



Fig. 4. Profile of a short gravity wave with ripples concentrated just in front of the crest. 



wind channel or at a fetch of a few meters on natural bodies of water (Roll, 

 1951). In the language of waves of small amplitude we may understand the 

 reason for the concentration of ripples as follows : the zone just in front of a 

 crest is a zone of convergence due to orbital currents of the gravity wave. The 

 energy of ripples having a group velocity slightly less than the phase velocity of 

 the gravity waves will then drop back until a combination of group velocity 

 plus gravity-wave orbital velocity equals the phase velocity of the gravity 

 waves. Ripples with a slightly greater group velocity will ride forward until the 

 opposing orbital velocity near the trough holds their energy back to the speed 

 of the gravity wave. The ripples tend, therefore, to be dispersed with the 

 longer wavelengths (slower group velocity) trailing. 



At long fetches, where a wide spectrum of gravity waves has developed, one 

 cannot expect this process to be operative because the gravity-wave crests are 

 no longer conservative. But the convergence forward of gravity-wave crests will 

 still act intermittently to concentrate ripple energy by steepening ripples. This 

 non-linear property of waves results in a non-random relation between the 

 positions of ripples and the phase of gravity waves (Fig, 5), 



The theory of ripples of finite amplitude and constant form in the absence of 

 wind forces has been attacked by Wilton (1915) and Sekerzh-Zenkovich (1956), 

 and an exact solution neglecting gravity has been found by Crapper (1957), 



