^.^.^ = (4.2) 



3t 3x 3y \ I 



|f=-9h|^-F,^ (4.3) 



||=-gh|i-Fj (4.4) 



where h is the depth and F^. is a friction coefficient carrying the dimension 

 of velocity. 



The water level at the open boundaries are selected such that the 

 resulting solution consists of the sum of two progressive waves propagating in 

 the positive and negative x-direction, and two progressive waves propagating 

 in the positive and negative y-direction. Thus (van de Kreeke and 

 Chiu, 1980): 



U)^=l = a cosot + [2a/(cosh 2pL + cos2kL)] 



X [(cosh yy cos ky cosh pL cos kL 



+ sinh uy sin ky sinh uL sin kL) cos at 



- (sinh uy sin ky cosh pL cos kL 



+ cosh \iy cos ky sinh pL sin kL) sin ot] (4.5) 



and c at y=L can be represented by an expression similar to Eq. (4.5) with y 

 replaced by x. In Eq. (4.5), 2a is the amplitude of the tide at (x=L, y=L), o 



1/2 2 2 2 



is the angular frequency of the tide, k^ = o/(gh) ' , k - p = k^. 

 The solution of this problem is: 



C = 2a/(cosh 2pL + cos 2kL) 



53 



