Parametrical Models 



Another technique for developing the spreading function is based on the 

 parameters which are determined from the measured data. Several directional 

 wave models are then proposed based on these parameters. For a wave system of 

 uni-modal directional spreading, Longuet-Higgins et al. assumed the form 



H.(f,9) = G(s) cos 2s(f) 1 (9 - 6) (12) 



J 2 



where G is a normalization factor such that Equation (2) holds and which implies 

 that 



g(s) = 2 23 " 1 ,_rU_±_il (13) 



r(2s + l) 



where r is a gamma function and where s and 9 are the exponential spreading factor 

 and mean wave approach angles, respectively. These two parameters are determined 

 from the Fourier coefficients. The mean direction, "e, is defined by 



e x = tan -1 (B 1 /A ] _) (lU) 



- 1 +n „-l 



3 2 = — tan L (B 2 /A 2 ) = 6 ] _ with an ambiguity of _+ — {15. 



r 19 



Long y showed that the values of s are determined from 



i-L = K a /(1 - Kj_j (16 



1 + 3K 2 + (Kg 2 + li*K 2 + l) 1 / 2 



2(1 - ¥^) 



IT) 



where K^ = (A-]_ + B-^ ) ' 2 and Kg = (A 2 + B 2 ) ' 2 . Another commonly used parameter 

 is the root mean square (rms) spreading angle, 6p, which is defined by 



9 p = (2 - 2K 1 )V2 (18) 



