APPENDIX 



METHODOLOGY AND GOVERNING SPECTRAL EQUATIONS 



1. Deepwater Representation of Fetch-Limited Wave Spectrum . 



A spectrum of wind waves, generated in deep water for a long period of 

 time, is limited by the length of the fetch over which the wind is blowing. 

 The wind will generate a spectrum with a shape which ?ias been parameterized 

 by Hasselmann, et al. (1973). The parameterization, or JONSWAP spectrum, pro- 

 vides a functional relationship between energy and frequency as well as the 

 windspeed, fetch length, and width of the spectral peak: 



r . ,. . -| exp ^^~^"^^ 

 E(f) = ag2(2Tr)-'^ fS exp |- f (|-yt*J y 2a2f2 ^^_^^ 



and 



a^ for f < fn 



Ox, for f > f „ 



where 



E = energy density 



F = fetch length 



f = frequency of wave component 



fiQ = frequency of spectral peak = 3.5g/(Uio ^ / 



g = acceleration due to gravity 



Ua = adjusted 10-meter windspeed 



X = dimensionless fetch = gF/U^ 



a = Phillips equilibrium constant = 0.076 x 



-0.22 



Y = ratio of maximal spectral energy to the maximum of the corresponding 

 Pierson-Moskowitz spectrum = 3.3 



CTg = left-side width of the spectral peak =0.07 



a-. = right-side width of the spectral peak = 0.09 



This equation provides a wave spectrum as shown in curve 1 (Fig. 1), with a 

 total energy equal to the deepwater significant wave height, squared over 16. 



15 



