43 - 



^ (x,y,t) = [ [ -k^ sin^ e FCa,e)e^^^^"V-V^9e 9a ^^^5) 



3y 



Information providing a partial description of the 

 directional energy spectrum S(6,Q), (equal to |F(6,B)| ), is 

 contained in the auto- and cross- spectra of the water surface 

 displacement, slope, and curvature terms. These spectra are obtained 

 through Fast Fourier Transform procedures using: 



S (a) = |F(a,e) I d6 



(4.6) 



r2lT _ 



S (a) = - ik j cose|F(a,9)l de (4^-7) 



nn. 



r2^ ,2 



S (a) = - ik sin6|FCa,e) d6 /a o) 



% Jo 



j-2Tr 2 



S (a) = k sine cose|FCo,e)l dO (4,9) 



X y 



2 f2TT 2 2 



S (a) =k cos elFCa,e).| d9 (4.10) 



XX "^0 



