Kitaigorodskii, Krasitskii, and Zaslavskii (1975), using Phillips' (1958) 

 expression for the steepness limited form of a wave spectrum, F, in terms of 

 the wave number modulus, 



F(k) = k-3 (3) 



solved the transformation of equation (3) to a frequency spectrum in finite- 

 depth water. The finite-depth form, E (f,h), was shown to be equal to the 

 deepwater form (eq. 2) times a dimensionless function, $(w, ), 



E (f,h) = ^f^r^ $(co, ) (4) 



m \2'n)'* h 



Kitaigorodskii, Krasitskii, and Zaslavskii suggested a value of 0.0081 for a. 



The function $ requires an iterative procedure for solution and is 

 defined as 



Kcoh) = R~2 (oj^) 



20)2 r(m ) "i_i 



1 - ^ / (5) 



Sinh (2a)2)R(a) ) 



with 



oj^ = a)(h/g)l/2 (6) 



where w = Zirf and R(w^) is obtained from the solution of 



R(a3^) tanh/to2 R(a)^) ) = 1 (7) 



The dimensionless parameter o), related the frequency and depth to the devia- 

 tion from the deepwater form. Wheji w is greater than 2.5, $ is approxi- 

 mately 1, when 0) is zero $ is zero. When w, is less than 1 

 n h 



$(to, ) ^ aj2/2 (8) 



n n 



For w less than 1, a combination of equations (8) and (4) leads to the 

 expression 



E (f,h) = aghf"3/(2(2Tr)2) (9) 



Thus in the shallow-water limit, the bound on energy density in the 

 spectrum is proportional to f~^ compared to f~^ in deep water. 



the wave 



and depth 

 is included linearly. 



Resio and Tracy (U.S. Army Engineer Waterways Experiment Station, personal 

 communication, 1981) have analyzed the resonant interactions and derived 

 equivalent expressions to equations (3) and (4) on the basis of similarity 

 theory. The conclusion of their theoretical study is that the role of the 

 wave-wave interactions in both deep and shallow water is to force the spectrum 

 to evolve to the form of equation (4). Their theory may be distinguished from 



