The quasi-equilibrium stability functions (Source File: cmue_d.F90)

INTERFACE:

    subroutine cmue_d(nlev)

DESCRIPTION:

This subroutine updates the explicit solution of (70) and (71) under the same assumptions as those discussed in section 4.7.39. Now, however, an additional equilibrium assumption is invoked. With the help of (78), one can write the equilibrium condition for the TKE as

$$\dfrac{P+G}{\epsilon} = \hat{c}_\mu(\alpha_M,\alpha_N) \alpha_M - \hat{c}'_\mu(\alpha_M,\alpha_N) \alpha_N = 1 \; , \quad$$ (195)

where (149) has been used. This is an implicit relation to determine $\alpha_M$ as a function of $\alpha_N$. With the definitions given in section 4.7.39, 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 4.7.39. 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
    $Log: cmue_d.F90,v $
    Revision 1.1  2005-06-27 10:54:33  kbk
    new files needed