382
7. PhysicallyInsignificant Fast Waves
0"=0
0"1 ---- -- -- - --- -- --- --- --- -- -- ---------- --1
1
<11
1{!1 , XI, T{, 4JI
<13
O"k - - - - -- - -- - - - - -- - -- --- - - -- - - -- - - - --- - -- - -
<1k_!
1{!k, x«. Tl, 4Jk
<1k+!
O"N - ----- --- - --- -- - --- --- -- ------- -- --- -- - -
0" = 1
<1 N
1
-1
1{!N,
<1N+!
4JN
FIGURE 7.6. Vertical distribution of the unknown variables on a c -coordinate grid. The
thickness of the CT layers need not be uniform . The center of each layer is at level CT = CTk
and is indicated by the dashed lines. Note that the vertical index k increases with CT and
decreases with geometric height.
The preceding is the generalization of the "averaging scheme" discussed in Sec -
tion 3.5 to the nonuniform staggered mesh shown in Fig. 7.6.
The vertical derivative of <1 in (7.115) is approximated as
(7.119)
Defining G k = '\lo . Uk + Uk . '\la (In Ps), the preceding implies that the vertically
discretized approximation to the surface-pressure-tendency equation (7.105) is
(7.120)
and that (7.106) is approximated as
(7.121)
The hydrostatic equation (7.108) is approximated as
4Jk+I - 4Jk _
- - -
R (7'
+ 7' )
InO"k+1 -lnO"k
2