51
= vJ:. + 8t p~
(25)
Therefore, the minimum value, at the new time level, of the unknown lfI satisfies
(I + t:.tD~/ vi;> minvJ:.+!
k
= 8k~1/2 (~~!1 - mlnvJ:.+!) + 8 k :!12 (~:; - mlnvJ:.+!) + V;; + t:.tP;. (26)
If the minimum value of lfI is not found at a grid point adjacent to a boundary of the
computational domain, then
V;; + t:.tP~
+ t:.t D ~ / lfI~
~ O .
(27)
The scheme may be considered positive, although there exists a slight risk that the boundary
conditions be so ill-conditioned that negative values of lfImay be generated. This did not occur
in our simulations.
Obviously, discretizing the sink term in an explicit manner would have been less safe,
especially when t:.tD; » 8t P; + IJI;.
(a) PrAQOU Ir.q .. (10·· .+*J
"' r----:::::' :::";--,' :...;"=----=:,' : : . . " -
... •
• •
(c)
•• • •
!
~ .. I
~
,
. , ..
,
,
t
i l l . "
iI
"" • ,
l
• •
.... IOC:il' ~ (CD ,-I)
(b) Pr .... U' .... W (10" , -')
,';-......;,':' -..:.' ..:.' ..."......:. . ..:.' -
I I I
• •• •
• •
• •
,
,
,
,
'" . ,
• •
,.toelt7 u (m .~I)
Figure 3. Profiles of Prandtl frequency M (solid curves) and velocity (dashed curves) for f = 0
(no rotation) and t = 30 hours in the four types of numerical simulations.
Numerical experiments_ In order to investigate the supposedly harmful influence of M2 on
Su' four model runs are defined. The first, referred to as run (a), corresponds to the standard
level2.S model. The experiments (b) and (c) are similar to (a), with two noticeable exceptions.
= vJ:. + 8t p~
(25)
Therefore, the minimum value, at the new time level, of the unknown lfI satisfies
(I + t:.tD~/ vi;> minvJ:.+!
k
= 8k~1/2 (~~!1 - mlnvJ:.+!) + 8 k :!12 (~:; - mlnvJ:.+!) + V;; + t:.tP;. (26)
If the minimum value of lfI is not found at a grid point adjacent to a boundary of the
computational domain, then
V;; + t:.tP~
+ t:.t D ~ / lfI~
~ O .
(27)
The scheme may be considered positive, although there exists a slight risk that the boundary
conditions be so ill-conditioned that negative values of lfImay be generated. This did not occur
in our simulations.
Obviously, discretizing the sink term in an explicit manner would have been less safe,
especially when t:.tD; » 8t P; + IJI;.
(a) PrAQOU Ir.q .. (10·· .+*J
"' r----:::::' :::";--,' :...;"=----=:,' : : . . " -
... •
• •
(c)
•• • •
!
~ .. I
~
,
. , ..
,
,
t
i l l . "
iI
"" • ,
l
• •
.... IOC:il' ~ (CD ,-I)
(b) Pr .... U' .... W (10" , -')
,';-......;,':' -..:.' ..:.' ..."......:. . ..:.' -
I I I
• •• •
• •
• •
,
,
,
,
'" . ,
• •
,.toelt7 u (m .~I)
Figure 3. Profiles of Prandtl frequency M (solid curves) and velocity (dashed curves) for f = 0
(no rotation) and t = 30 hours in the four types of numerical simulations.
Numerical experiments_ In order to investigate the supposedly harmful influence of M2 on
Su' four model runs are defined. The first, referred to as run (a), corresponds to the standard
level2.S model. The experiments (b) and (c) are similar to (a), with two noticeable exceptions.