The dynamic k-equation (Source File: tkeeq.F90)

*INTERFACE:*

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

The transport equation for the turbulent kinetic energy, , follows immediately from the contraction of the Reynolds-stress tensor. In the case of a Boussinesq-fluid, this equation can be written as

where denotes the material derivative of . and are the production of by mean shear and buoyancy, respectively, and the rate of dissipation. represents the sum of the viscous and turbulent transport terms. For horizontally homogeneous flows, the transport term appearing in (150) is presently expressed by a simple gradient formulation,

where is the constant Schmidt-number for .

In horizontally homogeneous flows, the shear and the buoyancy production, and , can be written as

see (48). Their computation is discussed in section 4.7.21.

The rate of dissipation, , can be either obtained directly from its parameterised transport equation as discussed in section 4.7.28, or from any other model yielding an appropriate description of the dissipative length-scale, . Then, follows from the well-known cascading relation of turbulence,

where is a constant of the model.

*USES:*

use turbulence, only: P,B,num use turbulence, only: tke,tkeo,k_min,eps use turbulence, only: k_bc, k_ubc, k_lbc, ubc_type, lbc_type use turbulence, only: sig_k use util, only: Dirichlet,Neumann IMPLICIT NONE

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)

Original author(s): Lars Umlauf (re-write after first version of H. Burchard and K. Bolding) $Log: tkeeq.F90,v $ Revision 1.9 2005-11-15 11:35:02 lars documentation finish for print Revision 1.8 2005/11/03 20:53:37 hb Patankar trick reverted to older versions for stabilising 3D computations Revision 1.7 2005/08/11 13:11:50 lars Added explicit loops for diffusivities for 3-D z-level support. Thanks to Vicente Fernandez. Revision 1.6 2005/06/27 13:44:07 kbk modified + removed traling blanks Revision 1.5 2003/03/28 09:20:35 kbk added new copyright to files Revision 1.4 2003/03/10 09:02:06 gotm Added new Generic Turbulence Model + improved documentation and cleaned up code

Karsten Bolding 2012-01-24