When considering waves of finite amplitude, Stokes' theory con- 

 cerning irrotational waves leads to the important result that upon 

 the completion of each nearly circular orbital motion the water 

 particles have advanced a short distance in the direction of wave 



propagation. The average velocity of this forward motion at the sea 



2 2 

 surface during one wave period is u^' = a ae O" . Thus Stokes' waves 



with finite amplitude are accompanied by a horizontal mass transport 



of water. Taking this into account, the horizontal component of 



particle velocity at the water surface may be written 



2 2 

 U = u^ + u^ ' = aae<rsin9e(x - <Tt) + a sc <r - (4a) 







The average rate at which energy is transmitted to the wave by 

 normal pressure is 



and by tangential stress, considering (4a) 



d 



(6) 



Whether these forces do a net amount of work on the wave motion 

 or not depends upon the distribution of T and ^. along the wave 

 profile. In order to do a positive amount of work on the wave, the 

 wind force components have to be in phase with the components of 

 the particle velocity. Because the normal pressure on the windward 

 slope of the wave profile is on the average greater than on the lee- 

 ward slope, these pressure forces in general will do a positive amount 

 of work, as long as the phase velocity of the wave is smaller than 

 the wind velocity. In the case where the phase velocity <T exceeds 

 the wind velocity v, the wave form encounters an air resistance. 



50 



