V = J ^ d ,k-l/2 + V d + l,k-l/2 + V j,fe + l/2 + V j + l,fe + l/2) < 119 > 



The additional terms 



|^ [(h^ n *)u], |^ [(h* + n y )v], |^ [(&+ n*)*u] , 



and 



|^ [(h x + n y )*v] 



require special computational procedures for n- These are described by 

 Leendertse (1967) . 



Hwang and Divoky (1975) show the same equations in spherical coordi- 

 nates with u the velocity in the 6-direction, and v the velocity in 

 the ^-direction as defined in Figure 9. They use a different approach 

 for the computation of the terms noted above which allows more direct 

 computation. Similar equations are shown by Houston, et al. (1975b). 

 For the coordinate system in Figure 11, the equations given by Hwang and 

 Divoky (with coriolis terms added) are, at times t + At/2, t + 3At/2, 

 t + 5At/2, . . . 



Vl/2 = U n ' 2lb If (le) , „ + I At f a \ ( 12 °) 



e x 7 n+l/2 



Vi/2 = \ - 2 R e sin e tiele ^^^^ u sin 8] n+i/2 



-) 



+ 1*1* [CJTT)0 v! »' 



v = v ? &- (&\ - - At f u 



v n+l/2 n 2 R„sin 6 AA U*JL 2 c n+1/2 



with terms such as 3n/39, 3n/3<J>, u, and V computed as before. 

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



g At/3r|\ I = 



'n+l = V n+l/2 2 R sin e' A* \d$) , 2 At o u n+l/2 ^ 122 ^ 



57 



