All-101 ^0 



Uox -^ V = ^^^^ 



and the boundary conditions 



Uq = Vq = on X = 0, X = r. (l8) 



V/ith the particular wind distribution prescribed we will 

 also be able to satisfy the additional boundary conditions 



au 



Vq = -g^ = on y - 0,1. (l8.a) 



Me shall proceed to solve equations (16), (17) together 

 with the boundary conditions (l8), (l3. a) for the velocities 

 Uo and V^. 



Define a stream function 



V = 9i, u = - ^ (19) 



ax' o Qy ^^^ 



so that (17) is satisfied identically. Then (l6) can be written 



eMil) -4)^ = (1 + a sin T:)sin nsy (20) 



where AA( ) is the biharmonic operator .2^^-x-J- + 2 — T~h^ "^ 

 h. Qx^ ax^ay^ 



9^( ) 



dy 'to 



Equation ("3:0) is similar to the one solved by Munk [ 5J 



and Munk and Carrier [6]. In the present case, however, the 



non-dimensional time, t , appears as a parameter, so that our 



problem corresponds to a quasi-steady problem. 



Equation (20) together with the boundary conditions 



