written in the form 



Vq = Vq[1 + irS sinacCx - (Tt)] , 



where 9 = 2&/x » and v means a constant average value of the wind 

 velocity over the wave profile. Dropping terms of higher order in 

 6, we have 



and 



Vq^ = Vq^[1 + 2Tr6 sinx(x - (Tt)], 



r^ = P'ft ^o^ = P'^t ^0^1^^ "^ ^^^ sinxCx - C5-t)] (8) 



Here, P'^t v = "^^^ means a constant value of tangential stress 

 over the wave. Pig. 11 represents these simple assumptions, where 

 in the upper part the streamlines of the air over the wave are shown 

 in a schematic distribution. This distribution may or may not be 

 symmetrical to the wave profile. But in any case it is to be expected 

 that the streamlines are crowded over each crest, so that over the 

 crests a bundle of streamlines with higher velocity rushes ahead to- 

 wards the lee. An asymmetrical distribution of the air current in 

 this case may perhaps affect the wave in such a way that a flatter 

 windward slope and a steeper leeward slope of the wave profile may 

 result. In each individual case the distribution of air currents 

 may be more or less asymmetrical and complicated. It would be suffi- 

 cient to consider the effective wind force components to be composed 



of a series of harmonic terms of wave lengths A, 2A, 3A, , 



but of these terms only the one in phase with u and w does a net 

 amount of work. 



For the average rate of work done on a wave of length A and of 

 phase velocity cr , we get together with the formal expressions (7) 

 and (8) according to (3), (4a), (5) and (6) 



54 



