II. BACKGROUND 



Research by Kitaigorodskii, Krasitskii, and Zaslavskii (1975) 2 has pro- 

 vided an equation for the maximum energy density in a frequency component of a 

 wave spectrum in finite depth 



E„(f) = 



qg 2 2f 5 <KaJ h ) 



(2TT) 4 



(2) 



where 



= 3.1415 



f = frequency 



g = gravitational acceleration 



h = depth 

 w h 



dimensionless parameter defined as 



/h\l /2 



%= 2 * f UJ 



(3) 



$ = dimensionless function of u^ which varies monotonically from 

 to 1 



a = a function of the wave field 



Equation (2) has been shown in a number of studies to be an excellent estimate 

 of the upper bound on energy density as a function of f. 



E represents an upper bound for energy density as a function of fre- 

 quency. An estimate of an upper bound on the total variance or energy in the 

 wave field can be obtained by integrating equation (2) over the frequencies 

 containing wave energy. This estimate of total energy can be used in equation 

 (1) to obtain an estimate of H. If f denotes the lower frequency bounding 

 the energy containing frequencies, then 



H = 4 



/ E m<f) df 



1/2 



(4) 



For practical purposes the high-frequency bound for integration in equation 

 (4) is taken as 1 hertz rather than infinity, because for most cases there is 

 little energy beyond 1 hertz in comparison to that below 1 hertz. Clearly, H 

 will vary with depth, h, the lower cutoff frequency, f c , and the spectral 

 parameter, a; therefore, the notation H(f c , h, a) will be used. Table 1 

 presents values of H(f , h, a) in feet for values of f c from 0.05 to 0.34 

 hertz in steps of 0.01 hertz and for depths of 3 to 60 feet (1 to 20 meters) 

 in 3-foot (1 meter) intervals for a fixed value of a = 0.0081. (A metric 



2 KITAIG0R0DSKII, S.A. , KRASITSKII, V.P., and ZASLAVSKII, M.M. , "Phillips 

 Theory of the Equilibrium Range in the Spectra of Wind-generated Gravity 

 Waves," Journal of Physical Oceanography, Vol. 5, 1975, pp. 410-420. 



