Update turbulence production

INTERFACE:

   subroutine production(nlev,NN,SS,xP)

DESCRIPTION:

This subroutine calculates the production terms of turbulent kinetic energy as defined in (152) and the production of buoayancy variance as defined in (159). The shear-production is computed according to

$$P = \nu_t (M^2 + \alpha_w N^2) + X_P \; , \quad$$ (146)

with the turbulent diffusivity of momentum, $\nu_t$, defined in (44). The shear-frequency, $M$, is discretised as described in section 3.13. The term multiplied by $\alpha_w$ traces back to a parameterisation of breaking internal waves suggested by Mellor (1989). $X_P$ is an extra production term, connected for example with turbulence production caused by sea-grass, see (339) in section 10.1. xP is an optional argument in the FORTRAN code.

Similarly, according to (78), the buoyancy production is computed from the expression

$$G=-\nu^B_t N^2 + \tilde{\Gamma}_B \; , \quad$$ (147)

with the turbulent diffusivity, $\nu^B_t$, defined in (44). The second term in (147) represents the non-local buoyancy flux. The buoyancy-frequency, $N$, is discretised as described in section 3.14.

The production of buoyancy variance by vertical meanflow gradients follows from (78) and (147)

$$P_b = -G N^2 \quad .$$ (148)

Thus, according to the definition of the potential energy (50), the buoyancy production $G$ describes the conversion between turbulent kinetic and potential energy in (150) and (158), respectively.

USES:

   use turbulence, only: P,B,Pb
   use turbulence, only: num,nuh
   use turbulence, only: alpha,iw_model
   IMPLICIT NONE

INPUT PARAMETERS:

 
   number of vertical layers
   integer,  intent(in)                :: nlev
 
   boyancy frequency squared (1/s^2)
   REALTYPE, intent(in)                :: NN(0:nlev)
 
   shear-frequency squared (1/s^2)
   REALTYPE, intent(in)                :: SS(0:nlev)
 
   TKE production due to seagrass
   friction (m^2/s^3)
   REALTYPE, intent(in), optional      :: xP(0:nlev)

REVISION HISTORY:

   Original author(s): Karsten Bolding, Hans Burchard
   $Log: production.F90,v $
   Revision 1.4  2005-08-28 09:40:03  hb
   Misspelling in documentation corrected.
   Revision 1.3  2005/08/11 13:01:49  lars
   Added explicit loops for 3-D z-level support. Thanks to Vicente Fernandez.
   Revision 1.2  2005/07/19 16:46:14  hb
   removed superfluous variables - NNT, NNS, SSU, SSV
   Revision 1.1  2005/06/27 10:54:33  kbk
   new files needed
   Revision 1.6  2003/03/28 09:20:35  kbk
   added new copyright to files
   Revision 1.5  2003/03/28 08:56:56  kbk
   removed tabs
   Revision 1.4  2003/03/10 08:50:07  gotm
   Improved documentation and cleaned up code
   Revision 1.3  2002/02/08 08:59:57  gotm
   Revision 1.2  2001/11/18 16:02:16  gotm
   Allow no_shear calculation
   Revision 1.1.1.1  2001/02/12 15:55:57  gotm
   initial import into CVS