But r 



\ 1 1 + J^-Jl „.L JL z 1 + ^dl -1- ..x. 

 V Ap gp" D^ ^p g^ ^2 



if 



Hence 



2p 



._„-^ i X < 1. 



^P gP D^ 



gpD 

 and the pressure term can be approximated by 



■Qx 



provided the above inequality holds. It will be shown in Sec- 

 tion 5 that the values of the constants v.'hich are appropriate 

 to our problem satisfy this condition* 



Hence, the final equations take the form 



9U _ ByV = - gD ill£- + MU + T (22) 



at ^'^ ^ ax X 



^ +pyU = - gD ^ + AAV +T^ (23) 



au ^ .av ^ _ .ari£ ^ (21+) 



ax ay at 



The boundary conditions are U = V = on a land-water 

 boundary. The v/lnd -stress is prescribed to be 



T = - (W + P' sin u)t)cos ny, t =0 

 x ' y 



v;here V/ ' ^ P' represent the magnitude of the mean v/ind-^stress 

 and the amplitude of the time variation of the 

 wind-stress, respectively. 



CO 



is the frequency of the wind variation. 



n is the wave number associated with the wind dis- 

 tribution. 



