TM No. 377 



— CO 



having units of cm^ sec (L^T; where L = length, and T = time). 

 On an entirely dimensional basis: 



(V-23) 



5 ? ^ Q<3 A f B = L>T 



(V-2U) 



v;here Q, as in equation ( 11-26), is a dimensionless constant, 

 Equating (V-23) to (V-2k) and solving for A and B: 



^ = Q 3 1 " 4 



-s 



(v-25) 



Equation (V-25) can be assumed to hold for waves whose frequencies are 

 somewhat lower than those of waves in which surface tension (in lieu of gravity) 

 is the important restoring force (i.e., capillary waves). If O is the density, 

 c the phase speed, T s the surface tension, and k the wave number, then, for 

 large k values (small wave lengths): 



i ■<« **r 



Since for deep water waves the phase speed is c(k) = fS/hj 

 upper limit of the equilibrium range: ^— " 



(V-26) 



then for the 



tu 



Hi 



■aT'a. 



(V-27) 



The lower limit is indicated by the fact that, although the functional 

 variation with f in equation (V-25) is monotonic (i.e., ever-increasing for 

 larger values of f), there is in the real waves at any instant a maximum of the 

 spectral energy. Thus, equation (V-25) must obviously fail where spectral 

 maxima occur. 



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