X {[cosh pL cos kL (cosh p x cos kx + cosh py cos ky) 

 + sinh pL sin kL (sinh px sin kx + sinh py sin ky)] cosot 



- [cosh pL cos kL (sinh px sin kx + sinh py sin ky)] 



- sin pL sin kL (cosh px cos kx + cosh py cos ky)] sin at) 



(4.6) 



U = (2a /gh ko//p^+k2")/(cosh 2pL + cos2 kL) 



X [-(sinh px cos kx cosh pL cos kL + cosh px sin kx sinh pL sin kL) 



X cos (ot+e) 



+ (cosh px sin kx cosh pL cos kL - sinh px cos kx sinh pL sin kL) 



X sin (ot+e)] (4.7) 



where e=tan" (p/k). The expression for V is the same as Eq. (4.7) with x 

 replaced by y. The above solution was first applied to a bight with L=150 km 

 and h=10 m driven by a tide with 2a=30 cm and T=24 hrs. The bottom friction 

 coefficient was assumed to be 0.1 cm/sec. The water level at an instant of 

 time when c(x=L, y=L) = and c(j^=0. y=0) = maximum is shown in Figure 4.2. 

 Figure 4.3 shows the corresponding velocity field. 



Eqs. (4.2) through (4.4), along with the boundary condition shown by 

 Eq. (4.5), were then solved by the vertically-averaged version of our 

 numerical model discussed in the previous chapter. The numerical solutions 

 were computed with At=2 hrs and ax=15 km. The computed water level and 

 velocity field agree quite well with the analytical results at corresponding 

 times. As shown in Figure 4.2, the water levels computed by our model compare 

 very well with the analytical results over much of the bight. The numerical 

 model underestimates the water level near the lower left corner by about 10%. 

 The computed velocity field in Figure 4.3 indicates a somewhat smaller 



54 



