Flux Richardson number stability function

INTERFACE:

   subroutine cmue_rf(nlev)

DESCRIPTION:

In the ISPRAMIX ocean model (see Eifler and Schrimpf (1992)), another approach is used for considering stability effects on vertical mixing. The stability functions in this model are of the form:

$$c_{\mu}= =0.5,$$ (199)

$$c'_{\mu}=c_{\mu} f(R_f)=c_{\mu} \frac{1}{P_r^0}(1-R_f)^{1/2}.$$ (200)

The neutral Prandtl number used there is $P_r^0=0.7143$. The function $f(R_f)$ is assumed to lay between the values 0.18 (corresponding to a supercritically stratified situation) and 2.0 (preventing it from growing too much under unstable conditions).

A formulation for $(1-R_f)$ can be derived from the definition of the flux Richardson number

$$R_f=\frac{c'_{\mu}}{c_{\mu}}R_i$$ (201)

and (200), see Beckers (1995):

$$(1-R_f)=[(\tilde R_i^2+1)^{1/2}-\tilde R_i]^2$$ (202)

with

$$\tilde R_i=\frac{0.5}{P_r^0} R_i$$ (203)

where $R_i$ is the gradient Richardson number.

USES:

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

INPUT PARAMETERS:

   integer, intent(in)                 :: nlev

REVISION HISTORY:

   Original author(s):  Manuel Ruiz Villarreal, Hans Burchard
   $Log: cmue_rf.F90,v $
   Revision 1.8  2005-11-15 11:35:02  lars
   documentation finish for print
   Revision 1.7  2005/06/27 13:44:07  kbk
   modified + removed traling blanks
   Revision 1.6  2004/08/18 12:53:07  lars
   updated documentation
   Revision 1.5  2003/03/28 09:20:35  kbk
   added new copyright to files
   Revision 1.4  2003/03/28 08:37:27  kbk
   removed tabs
   Revision 1.3  2003/03/10 09:02:04  gotm
   Added new Generic Turbulence Model + 
   improved documentation and cleaned up code
   Revision 1.2  2002/02/08 08:59:58  gotm
 
   Revision 1.1.1.1  2001/02/12 15:55:58  gotm
   initial import into CVS