-4--f-h-?--h" 



— ■— 9-Hh~9 — II — 



h-l 



* Water Level (17) 



Depth (d) 



— U Velocity (u) 



1 V Velocity ( v ) 



Figure 10. Coordinate system, 



rectangular coordinates. 



and at times t + At, t + 2At, t + 3At, . . 



v , , - v 



n„ tl = n 



At f u 



I£t /3n\ 



(111) 



: '<■■■ ': 2 " u "c "n+1/2 2 As 6 (ay) +J 



(113) 



n+1 'n+1/2 



+ I At f = - — ( — \ 



U n+1 " U n+l/2 2 e V n+1 2 As g V3x/ .. 



These equations omit convective inertia terms, bottom effects, and any- 

 forcing functions. The various terms used are defined as follows: 



^ = 2 Cn j-l/ 2j k + Vl/2, P 

 ^ = I fy, fe-1/2 + ^ fe.1/2^ 



3n_ _ r _ ■> 

 8x " Ln j+l/2,fe " n j-l/2,fe J 



in 



9y 



(n j,^i/2 " ^fc-l/Z 3 



" " 4 (u j-i/2,fe + u j+i/2,fe + u j-i/2,£+i + "j+i/a.fc+i 3 



(114) 

 (115) 



(116) 



(117) 

 (118) 



56 



