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 $q^2/2=k$ can be written as

$$\dot{\overline{q^2/2}} = {\cal D}_q + P + G - \epsilon \; , \quad$$ (154)

where $\dot{\overline{q^2/2}}$ denotes the material derivative of $q^2/2$. With $P$ and $G$ following from (152), evidently, this equation is formally identical to (150). The only reason why it is discretized seperately here, is the slightly different down-gradient model for the transport term,

$${\cal D}_q = \dfrac{\partial}{\partial {z}} \left( q l S_q \dfrac{\partial {q^2/2}}{\partial {z}} \right) \; , \quad$$ (155)

where $S_q$ is a model constant. The notation has been chosen according to that introduced by Mellor and Yamada (1982). Using their notation, also (153) can be expressed in mathematically identical form as

$$\epsilon = \frac{q^3}{B_1 l} \; , \quad$$ (156)

where $B_1$ is a constant of the model. Note, that the equivalence of (153) and (156) requires that

$$(c_\mu^0)^{-2} = \frac{1}{2} B_1^\frac{2}{3} \quad .$$ (157)

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
   $Log: q2over2eq.F90,v $
   Revision 1.5  2005-12-28 09:42:33  hb
   Patankar trick reverted to older versions for stabilising 3D computations
   Revision 1.4  2005/06/27 13:44:07  kbk
   modified + removed traling blanks
   Revision 1.3  2003/03/28 09:20:35  kbk
   added new copyright to files
   Revision 1.2  2003/03/10 09:04:04  gotm
   Fixed comment char
   Revision 1.1  2003/03/10 09:00:36  gotm
   Part of new generic turbulence model