## The dynamic q2/2-equation

INTERFACE:

   subroutine q2over2eq(nlev,dt,u_taus,u_taub,z0s,z0b,h,NN,SS)

DESCRIPTION:

The transport equation for the TKE can be written as

 (156)

where denotes the material derivative of . With and following from (154), evidently, this equation is formally identical to (152). The only reason why it is discretized seperately here, is the slightly different down-gradient model for the transport term,

 (157)

where is a model constant. The notation has been chosen according to that introduced by Mellor and Yamada (1982). Using their notation, also (155) can be expressed in mathematically identical form as

 (158)

where is a constant of the model. Note, that the equivalence of (155) and (158) requires that

 (159)

USES:

   use turbulence,   only: P,B
use turbulence,   only: tke,tkeo,k_min,eps,L
use turbulence,   only: q2over2_bc, k_ubc, k_lbc, ubc_type, lbc_type
use turbulence,   only: sq
use util,         only: Dirichlet,Neumann

IMPLICIT NONE

INPUT PARAMETERS:

number of vertical layers
integer,  intent(in)                :: nlev

time step (s)
REALTYPE, intent(in)                :: dt

surface and bottom
friction velocity (m/s)
REALTYPE, intent(in)                :: u_taus,u_taub

surface and bottom
roughness length (m)
REALTYPE, intent(in)                :: z0s,z0b

layer thickness (m)
REALTYPE, intent(in)                :: h(0:nlev)

square of shear and buoyancy
frequency (1/s^2)
REALTYPE, intent(in)                :: NN(0:nlev),SS(0:nlev)

REVISION HISTORY:
   Original author(s): Lars Umlauf


Karsten Bolding 2012-12-28