The values of s, and 9-^ are equal to s 2 and 9 2 in single peak spectra and are dif- 

 ferent in bi-modal spectra. Large values of s tend to narrow the directional 

 distribution. The values of s have been correlated to local wind and wave fre- 

 quency by Mitsuyasu et al. and Hasselmann et al. 



Other Spreading Functions 



For a fully developed sea, Pierson and his colleagues 2 ^ proposed the spreading 

 function 



H U (6) =1 cos 2 (6 - 9) (19) 



Furthermore, the spreading function has been modified and applied in the Spectral 

 Ocean Wave Model (SOWM) of Fleet Numerical Oceanography Center (FN0C).9' 2 ° The 

 spreading function is related to the mean wind direction, 9*, as 



H (f,9) = - {1 + [0.5 + 0.82 e _1/2f ]cos 2(9 - 9*) 



+ 0.32 e" 1 ^ cos U(8 - 9*) } (20) 



for - — <( 9 - 9*)< — and zero otherwise, and where f is the dimensionless fre- 

 2 2 



quency, defined by 



f = J*i ( 21 ) 



g 



where oj is radian wave frequency and u is local wind speed. For small values of u, 

 Hr becomes 



(22; 



H 5 (0,e) = -[l + 1-32 cos2( 9 - 9*) + 0.32 cosU( 9 - 9*) ] 



Equation (22) can also be approximated for low frequencies as 



H<-(0,9) «— cos 1+ ( 9 - 9*) 

 5 3tt 



JL [l + 1 cos2( 9 - 9*) + i cosU( 9 - 9*) ] (23) 



3tt 3 3 



