Algebraic length-scale from ISPRAMIX

INTERFACE:

   subroutine ispralength(nlev,NN,h,depth)

DESCRIPTION:

This subroutine calculates the lengthscale used in the ISPRAMIX model, see Eifler and Schrimpf (1992) and Demirov et al. (1998). In both mixing regions (close to the surface and the bottom), $l$ is obtained from the formula

$$l = \frac {\kappa \tilde z} {1+\frac {\kappa \tilde z} {c_2 \cdot h_m}} (1-R_f)^e$$ (181)

where $\tilde z$ is the distance from the interface (surface or bottom). The fraction in (181) predicts an approximation to a linear behavior of $l$ near boundaries and a value proportional to the thickness of the mixed layer far from the interface, $l=c_2 h_m$, where $c_2=0.065$ is estimated from experimental data as discussed in Eifler and Schrimpf (1992). The factor $(1-R_f)$, with the flux Richardson number $R_f=-G/P$, accounts for the effect of stratification on the length-scale. The parameter $e$ is here a tuning parameter (pers. comm. Walter Eifler, JRC, Ispra, Italy) which is usually set to $e=1$.

USES:

   use turbulence, only: L,tke,k_min,eps_min,xRF,kappa,cde
 
   IMPLICIT NONE

INPUT PARAMETERS:

 
   number of vertical layers
   integer,  intent(in)                :: nlev
 
   buoyancy frequency (1/s^2)
   REALTYPE, intent(in)                :: NN(0:nlev)
 
   layer thickness (m)
   REALTYPE, intent(in)                :: h(0:nlev)
 
   local depth (m)
   REALTYPE, intent(in)                :: depth

REVISION HISTORY:

   Original author(s):  Manuel Ruiz Villarreal, Hans Burchard
   $Log: ispralength.F90,v $
   Revision 1.7  2005-11-15 11:35:02  lars
   documentation finish for print
   Revision 1.6  2005/06/27 13:44:07  kbk
   modified + removed traling blanks
   Revision 1.5  2003/03/28 09:20:35  kbk
   added new copyright to files
   Revision 1.4  2003/03/28 08:30:15  kbk
   removed tabs
   Revision 1.3  2003/03/10 09:02:05  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