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

$\displaystyle \dot{\overline{q^2/2}} = {\cal D}_q + P + G - \epsilon \; , \quad$ (156)

where $ \dot{\overline{q^2/2}}$ denotes the material derivative of $ q^2/2$. With $ P$ and $ G$ 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,

$\displaystyle {\cal D}_q = \dfrac{\partial}{\partial {z}} \left( q l S_q \dfrac{\partial {q^2/2}}{\partial {z}} \right) \; , \quad$ (157)

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 (155) can be expressed in mathematically identical form as

$\displaystyle \epsilon = \frac{q^3}{B_1 l} \; , \quad$ (158)

where $ B_1$ is a constant of the model. Note, that the equivalence of (155) and (158) requires that

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