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:

$\displaystyle c_{\mu}=$const$\displaystyle =0.5,$ (201)

$\displaystyle c'_{\mu}=c_{\mu} f(R_f)=c_{\mu} \frac{1}{P_r^0}(1-R_f)^{1/2}.$ (202)

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

$\displaystyle R_f=\frac{c'_{\mu}}{c_{\mu}}R_i$ (203)

and (202), see Beckers (1995):

$\displaystyle (1-R_f)=[(\tilde R_i^2+1)^{1/2}-\tilde R_i]^2$ (204)

with

$\displaystyle \tilde R_i=\frac{0.5}{P_r^0} R_i$ (205)

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

Karsten Bolding 2012-12-28