The algebraic k-equation


INTERFACE:

   subroutine tkealgebraic(nlev,u_taus,u_taub,NN,SS)
DESCRIPTION:

This subroutine computes the turbulent kinetic energy based on (152), but using the local equilibrium assumption

$\displaystyle P+G-\epsilon=0 \quad .$ (171)

This statement can be re-expressed in the form

$\displaystyle k= (c_\mu^0)^{-3}   l^2 ( c_\mu M^2 - c'_\mu N^2 ) \; , \quad$ (172)

were we used the expressions in (154) together with (45) and (46). The rate of dissipaton, $ \epsilon$, has been expressed in terms of $ l$ via (155). This equation has been implemented to update $ k$ in a diagnostic way. It is possible to compute the value of $ k$ as the weighted average of (172) and the value of $ k$ at the old timestep. The weighting factor is defined by the parameter c_filt. It is recommended to take this factor small (e.g. c_filt = 0.2) in order to reduce the strong oscillations associated with this scheme, and to couple it with an algebraically prescribed length scale with the length scale limitation active (length_lim=.true. in gotmturb.nml, see Galperin et al. (1988)).


USES:

   use turbulence,   only: tke,tkeo,L,k_min
   use turbulence,   only: cmue2,cde,cmue1,cm0
 
   IMPLICIT NONE
INPUT PARAMETERS:
 
   number of vertical layers
   integer,  intent(in)                :: nlev
 
   surface and bottom
   friction velocity (m/s)
   REALTYPE, intent(in)                :: u_taus,u_taub
 
   square of shear and buoyancy
   frequency (1/s^2)
   REALTYPE, intent(in)                :: NN(0:nlev),SS(0:nlev)
DEFINED PARAMETERS:
   REALTYPE , parameter                :: c_filt=1.0
REVISION HISTORY:
   Original author(s): Hans Burchard & Karsten Bolding

Karsten Bolding 2012-12-28