The non-local, exact weak-equilibrium stability function


   subroutine cmue_a(nlev)

The solution of (72) and (73) has the shape indicated by (76). This subroutine is used to update the quantities $ c_\mu$, $ c'_\mu$ and $ \Gamma$, defined in (76), 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 (67) at the old time step.

The numerators and the denominator appearing in (79) are polynomials of the form

\begin{displaymath}\begin{array}{rcl} D &=& d_0 + d_1 \overline{N}^2 + d_2 \over...{N}^2 + g_2 \overline{S}^2 ) \overline{T} \quad . \end{array}\end{displaymath} (187)

The coefficients of $ D$ are given by

\begin{displaymath}\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}\end{displaymath} (188)

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

\begin{displaymath}\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}\end{displaymath} (189)

\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} (190)

and the numerator of the term $ \Gamma$ is

\begin{displaymath}\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}\end{displaymath} (191)


   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
   number of vertical layers
   integer, intent(in)       :: nlev
  Test stage. Do not yet use.
   Original author(s): Lars Umlauf

Karsten Bolding 2012-12-28