of time. A line parallel to the crests can be determined, and the direction 

 of travel of the wave will be perpendicular to this line, but the direction can 

 be either one of two directions, one the opposite of the other. 



This indeterminancy is avoided in this analysis by considering a positive 

 direction, x', to be the dominant direction of the wind and by assuming that 

 the spectral components of the waves being studied are all traveling with an 

 angle of +90° to the wind. Then [A(|j.', 8')] would be zero for tt/2< 0'<. it 

 and for -it/2 < e'< -tr, and [A(c', p')]^ would be zero for -oo<r P'< 0. (Note 

 |jl', G', a* and p' would have to be redefined with respect to the x' direction.) 

 When these assumiptions are applied to the results to be obtained the directions 

 will be completely determined. 



Consider equation (8.9) again. One can form the indicated operation 

 given by equation (8.10). 



M N 

 2/2 



(8.10) lim 



Q(x'y') cos(c*x' + p*y')dx'dy' 



M-*oo 



"2 2 



M-* oo / , 

 N-^co -— — ^ 



-M N oo .oo 



2/ 2 



/ 



= lim — 



M-^oo III 



Z 2 



/ 



i2 



[A*(a,p)]''cos(ax' + py')co8(c*x' + p*y')da dp]dx' dy' 



The term after the equals sign can also be written 



63 



