- l^k - 



o r2Tr 

 S (o) =k sin elF(o,9) d0 (4.11) 



Vy ^0 



S (a) = ik cos e|F(a,e) p d9 (4.12) 



Vxx Jo 



o r2iT 2 



S (a) = ik sine|F(a,e)l dG (4.13) 



^v'^vv •' 



The directional spectrum at a frequency 6 is then expressed 

 as a partial Fourier series in terms of the wave direction B as : 



N N 



S(a,9) = a + y a cos n 6 + T b sin n (4.14) 



o ^, n '^ ^ n 



n=l n=l 



The Fourier coefficients are determined in the usual manner 

 as: 



1 f^'' 

 a^CcT) = ^ S(_a,e) de (4.15) 



•'o 



r2TT 



a (a) = -f^ S(a,e) cos ne dS (4.16) 



2^ io 



