(11.40) f(|jL,e) =^[1 +(0.50 + 0.82 e'^"^^^^^ ''^) cos 2G+ (0.32 e"^^^^^^ ^^)cos4e] 



IT 



1 r -(M.v/g)*/2 -(|J.v/g)^/2 2 



(11.41) f(iJL, 9) =-^[0.50(1 - e ^*^ '^' ' ) + (1.00 - 0.92e "^ ^ ) (cos 9) 



+ (2.56e-<l"^''g)^/2)(cos9)4] 

 A value of c^ greater than 0,33 would make the coefficient of (cos 9) in (11.41) 

 negative for small \i with the accompanying possibility of negative values for f(|jL,G). 



The curves for cj and 03 are graphed against the observed values of ci 

 and C2 in figure 11,31. The fit is fairly good for c^; and for 03 for frequencies 

 corresponding to k equal to 1 1 through 15j the fit is not too bad. The extension 

 of the curves outside of the region where data are available is quite arbitrary. 

 For the longer waves the value of (11,38) has little total effect on the spectrum 

 because the energy is very low there. For the shorter waves if Ci became less 

 than 0.50, the effect would be even greater angular spreading. Note that in 

 figure 11.30 -y, and ^2 ^-^^ close together for k equal to 11 through 14, and 

 that in a sense the vailue of C2 used above is only the in-phase part of cos 49 

 with respect to the original data when k is larger, 



A possible functional form for the directional spectrum of a wind generated 

 sea is finally given by equation (11,42) if the wind is uniform in direction and 

 speed over the area of wave generation and if the sea is fully developed. 



(11.42) [A(|X, e)]^ =^"^^^5-!^-i[l + (0-50 + 0.82e-'l'^'8) /2) cos 26 



,6 



A 



+ (0.32e-<»^^/s) /^) cos 49] 

 for -Tr/2 < 9-^ ■t/2, and zero otherwise. 



237 



