The Schumann and Gerz (1995) stability function


INTERFACE:

   subroutine cmue_sg(nlev)
DESCRIPTION:

This subroutine computes stability functions according to

$\displaystyle c_{\mu}=c_{\mu}^0,\qquad c'_{\mu}=\frac{c_{\mu}^0}{Pr_t}$ (199)

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,

$\displaystyle Pr_t = Pr_t^0 \exp\left(-\frac{Ri}{Pr_t^0 Ri^{\infty}}\right) -\frac{Ri}{Ri^{\infty}} \; , \quad$ (200)

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



Karsten Bolding 2012-12-28