The cycle of calculation is separated into two operations. 

 During the first-half cycle, at odd time steps, >// and U are computed 

 implicitly along lines of constant latitude, followed by an explicit 

 computation of the V field. For the second half-cycle, the 

 computations proceed along lines of constant longitude with \}/, V 

 updated implicitly and U computed explicitly. In each half -cycle, 

 the external mode computations are executed first and, after 

 completing the entire computing domain, are repeated for the internal 

 mode. 



The implicit formulation of the finite difference analogs of the 

 external mode momentum and mass conservation equations, respectively, 

 are, for odd time steps, 



1 n+1 ^ n+1 T n+l ■, 



--7^(1-^,3)4/^(1-^,3) + UgCJ) + 7^(1+-^,J)4;^(1^,J) 



= U^(I,J)+2Atf(J)V^(I,J) + AtFe+ x^, and (42) 



n+1 T n+1 n+1 ■, 



-v^(J)]J^(l-^,J) + i/'e(I,J)+ Djj(J)Ue(I+^,J) 



= V^(I,J) - u 6 V^(I,J) + ^i, (43) 



and for even time steps 



T n+1 T ^ n+1 T n+1 ■, ■, 



-7y(I,J-J)i//g(I,J-J)e(J-^) + Vg(I,J) + y^(l,J+^)yp^(l,J+^)e(J+^) 



= V^(I,J) - Atf(J)U^(I,J) + Xi+ AtFg, (44) 



T n+1 1 n+1 1 n+1 •■ 

 -i;y(J-^)Ve(I,J-^) + i//e(I,J) + Uy(J+^)Vg(I, j+^) 



= ^ - '^xSxUe<I'J> -^ ^i' <45) 



22 



