A = -^ trdo- I [t cos 5t(x - 0"t) + r' cos^xCx - <Tt)]dx 



A. = ^ p'f^ Vq^ j [irSff sin 3t(x - (Tt) + 2Tr^6^(r sln^ ae (x - <rt) + 



+ 7r^6^(3-]dx 



after the term with d^ in the expression for A. is dropped. The terms 

 with sine and cosine do not contribute to an energy transfer from wind 

 to waves, and on the average after integrating over one wave length, 

 the result is 



A„ = i ttS r ' . cr 

 n ^ n 



K = STT^p'S^f 2 .^ 



(9) 

 ^t - - H " -t ^o" "^ 



The accuracy to which A and A. can be separately evaluated is perhaps 

 not sufficient, because the effective wind force components depend 

 upon several unknown factors of the hydrodynamical character of the 

 sea surface (G. Neumann [12]). But one might see that both of the 

 components may contribute to an energy transfer, and only in the case 

 where in (8) T. = const, over the wave, does the average work of this 

 drag at the particle velocity u become zero. H. U. Sverdrup and W. 

 H, Munk [1] therefore only consider the work done by the stress 

 "C. = const, at the mass transport velocity u ' , which accompanies 

 Stokes' waves of finite amplitude. 

 Let 



^n' =±P'^n(^o -^)^ 



where "C„ ' > for (T'< v^ , and Z^„ ' < for cr > v , 

 n o ' n o' 



then . A^ = ± i TrSp'f^ (v^ _ (T )^ . O^ . 



55 



