i-l 



8 



«► 



4 



jtl ii 



k-l 



k+l 



O Woter Depth (d) 

 X Water Level (if) 

 — u Velocity in the 9- direction 

 v Velocity in the ^—direction 



Figure 11. Coordinate system, 



spherical coordinates . 



Vi = Vi/2 -Yx&re\hh [( ^^^ U5in 9] 



1 3 r rXT S 9 i \ 



77 7- (d + ll) V] ) 



g At /9n\ 1 . ,. = 



n+l/2 



'n+l 



n+l/2 



(123) 

 (124) 



Again, the bottom-friction, forc ing fu nctions, and convective inertia 

 terms are ignored. Te rms li ke (d + n) e are computed by averaging in 

 the 9 -direction, and (d + n)* by averaging in the <}> -direction. 



In addition to specifying equations of motion, boundary conditions 

 for the computational area must be established. Hwang and Divoky (1975) 

 use solid boundaries at coastlines and fictitious open boundaries at 

 edges of the computational area where it is necessary to truncate the 

 region of computation. At solid boundaries, complete reflection is 

 assumed. At open boundaries, the wave is assumed to travel without 

 change in form across the final space step, so that 



- n. 



At /gd 



As 



(125) 



with the terms defined in Figure 12 



58 



