The non-local, exact weak-equilibrium stability function

INTERFACE:

   subroutine cmue_a(nlev)

DESCRIPTION:

The solution of (70) and (71) has the shape indicated by (74). This subroutine is used to update the quantities $c_\mu$, $c'_\mu$ and $\Gamma$, defined in (74), from which all turbulent fluxes can be computed. The non-linear terms ${\cal N}$ and ${\cal N}_b$ are updated by evaluating the right hand side of (65) at the old time step.

The numerators and the denominator appearing in (77) are polynomials of the form

$$\begin{array}{rcl} D &=& d_0 + d_1 \overline{N}^2 + d_2 \over... ...ne{N}^2 + g_2 \overline{S}^2 ) \overline{T} \quad . \end{array}$$ (185)

The coefficients of $D$ are given by

$$\begin{array}{rcl} d_0 &=& 36 {\cal N}^3 {\cal N}_b^2 \; , \q... ..._3^2 - a_2^2)(a_{b2}^2 - a_{b1}^2) {\cal N} \quad . \end{array}$$ (186)

The coefficients of the numerators $N_n$ and $N_b$ can be expressed as

$$\begin{array}{rcl} n_0 &=& 36 a_1 {\cal N}^2 {\cal N}_b^2 \; ... ...5 a_{b4} (a_2+3 a_3) {\cal N} {\cal N}_b \; , \quad \end{array}$$ (187)

$$\begin{array}{rcl} n_{b0} &=& 12 a_{b3} {\cal N}^3 {\cal N}_b... ... 4 (a_2^2-3 a_3^2) ) {\cal N} {\cal N}_b \; , \quad \end{array}$$ (188)

and the numerator of the term $\Gamma$ is

$$\begin{array}{rcl} g_0 &=& 36 a_{b4} {\cal N}^3 {\cal N}_b \;... ...{b4} ( 3 a_3^2 - a_2^2) {\cal N} {\cal N}_b \quad . \end{array}$$ (189)

USES:

   use turbulence, only: eps
   use turbulence, only: P,B,Pb,epsb
   use turbulence, only: an,as,at,r
   use turbulence, only: cmue1,cmue2,gam
   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

BUGS:

  Test stage. Do not yet use.

REVISION HISTORY:

  Original author(s): Lars Umlauf
   $Log: cmue_a.F90,v $
   Revision 1.1  2005-06-27 10:54:33  kbk
   new files needed