The Schumann and Gerz (1995) stability function

INTERFACE:

   subroutine cmue_sg(nlev)

DESCRIPTION:

This subroutine computes stability functions according to

$$c_{\mu}=c_{\mu}^0,\qquad c'_{\mu}=\frac{c_{\mu}^0}{Pr_t}$$ (197)

with constant $c_{\mu}^0$. Based simulation data on stratified homogeneous shear-flows, Schumann and Gerz (1995) proposed the empirical relation for the turbulent Prandtl-number,

$$Pr_t = Pr_t^0 \exp\left(-\frac{Ri}{Pr_t^0 Ri^{\infty}}\right) -\frac{Ri}{Ri^{\infty}} \; , \quad$$ (198)

where where $Ri$ is the gradient Richardson-number and $Pr_t^0$ is the turbulent Prandtl-number for $Ri \rightarrow 0$. $Pr_t^0$ and the fixed value $c_\mu^0$ have to be set in gotmturb.nml. Schumann and Gerz (1995) suggested $Pr_t^0=0.74$ and $Ri^{\infty}=0.25$.

USES:

   use turbulence, only: Prandtl0_fix,cm0_fix
   use turbulence, only: cmue1,cmue2,as,an
   IMPLICIT NONE

INPUT PARAMETERS:

   integer, intent(in)                 :: nlev

REVISION HISTORY:

   Original author(s): Hans Burchard & Karsten Bolding
   $Log: cmue_sg.F90,v $
   Revision 1.8  2007-01-06 11:49:15  kbk
   namelist file extension changed .inp --> .nml
   Revision 1.7  2005/11/15 11:35:02  lars
   documentation finish for print
   Revision 1.6  2005/07/18 08:54:56  lars
   changed docu for html compliance
   Revision 1.5  2005/06/27 13:44:07  kbk
   modified + removed traling blanks
   Revision 1.4  2004/08/18 12:53:07  lars
   updated documentation
   Revision 1.3  2003/03/28 09:20:35  kbk
   added new copyright to files
   Revision 1.2  2003/03/10 09:02:04  gotm
   Added new Generic Turbulence Model + 
   improved documentation and cleaned up code
   Revision 1.1.1.1  2001/02/12 15:55:58  gotm
   initial import into CVS