The local, weak-equilibrium stability functions


   subroutine cmue_c(nlev)

This subroutine updates the explicit solution of (72) and (73) with shape indicated by (76). In addition to the simplifications discussed in section 4.25, $ P_b=\epsilon_b$ is assumed in (73) to eliminate the dependency on $ \overline{T}$ according to (74). As discussed in section 4.4, this implies that the last of (73) is replaced by (75). Thus, the $ \Gamma$-term in (76) drops out, and the solution is characterized by $ c_\mu$ and $ c'_\mu$ only.

As a consequence, the numerators and the denominator appearing in (79) are of somewhat different form compared to the result in section 4.24. They can be written as

\begin{displaymath}\begin{array}{rcl} D &=& d_0 + d_1 \overline{N}^2 + d_2 \over...
...{b1} \overline{N}^2 + n_{b2} \overline{S}^2 \quad . \end{array}\end{displaymath} (193)

The coefficients of $ D$ are given by

\begin{displaymath}\begin{array}{rcl} d_0 &=& 36 {\cal N}^3 {\cal N}_b^2 \; , \q...
...2 - a_2^2)(a_{b2}^2 - a_{b1}^2) {\cal N} \; , \quad \end{array}\end{displaymath} (194)

and the coefficients of the numerators are

\begin{displaymath}\begin{array}{rcl} n_0 &=& 36 a_1 {\cal N}^2 {\cal N}_b^2 \; ...
...[3mm] n_2 &=& 9 a_1 (a_{b2}^2 - a_{b1}^2){\cal N}^2 \end{array}\end{displaymath} (195)


\begin{displaymath}\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}\end{displaymath} (196)

These polynomials correspond to a slightly generalized form of the solution suggested by Canuto et al. (2001) and Cheng et al. (2002). For cases with unstable stratification, the same clipping conditions on $ \alpha_N$ is applied as described in section 4.27. For the cases of extreme shear, the limiter described in the context of (85) is active.


   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
   number of vertical layers
   integer, intent(in)       :: nlev
   REALTYPE, parameter       :: asLimitFact=1.0d0
   REALTYPE, parameter       :: anLimitFact=0.5d0
   Original author(s): Lars Umlauf

Karsten Bolding 2012-12-28