The quasi-equilibrium stability functions


INTERFACE:

   subroutine cmue_d(nlev)
DESCRIPTION:

This subroutine updates the explicit solution of (72) and (73) under the same assumptions as those discussed in section 4.26. Now, however, an additional equilibrium assumption is invoked. With the help of (80), one can write the equilibrium condition for the TKE as

$\displaystyle \dfrac{P+G}{\epsilon} = \hat{c}_\mu(\alpha_M,\alpha_N) \alpha_M - \hat{c}'_\mu(\alpha_M,\alpha_N) \alpha_N = 1 \; , \quad$ (197)

where (151) has been used. This is an implicit relation to determine $ \alpha_M$ as a function of $ \alpha_N$. With the definitions given in section 4.26, it turns out that $ \alpha_M(\alpha_N)$ is a quadratic polynomial that is easily solved. The resulting value for $ \alpha_M$ is substituted into the stability functions described in section 4.26. For negative $ \alpha_N$ (convection) the shear number $ \alpha_M$ computed in this way may become negative. The value of $ \alpha_N$ is limited such that this does not happen, see Umlauf and Burchard (2005).


USES:

   use turbulence, only: an,as,at
   use turbulence, only: cmue1,cmue2
   use turbulence, only: cm0
   use turbulence, only: cc1
   use turbulence, only: ct1,ctt
   use turbulence, only: a1,a2,a3,a4,a5
   use turbulence, only: at1,at2,at3,at4,at5
 
   IMPLICIT NONE
INPUT PARAMETERS:
 
   number of vertical layers
   integer, intent(in)       :: nlev
DEFINED PARAMETERS:
   REALTYPE, parameter       :: anLimitFact = 0.5D0
   REALTYPE, parameter       :: small       = 1.0D-10
REVISION HISTORY:
   Original author(s): Lars Umlauf

Karsten Bolding 2012-12-28