The dynamic epsilon-equation (Source File: dissipationeq.F90)

*INTERFACE:*

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

The - model in its form suggested by Rodi (1987) has been implemented in GOTM. In this model, the rate of dissipation is balanced according to

where denotes the material derivative of . The production terms and follow from (152) and represents the sum of the viscous and turbulent transport terms.

For horizontally homogeneous flows, the transport term appearing in (163) is presently expressed by a simple gradient formulation,

where is the constant Schmidt-number for .

It should be pointed out that not all authors retain the buoyancy term
in (163), see e.g. Gibson and Launder (1976). Similar to the
model of Mellor and Yamada (1982), Craft et al. (1996) set
.
However, in both cases, the - model cannot
predict a proper state of full equilibrium in stratified flows at a
predefined value of the Richardson number (see
Umlauf et al. (2003) and discussion around (114)). Model constants are
summarised in table 7.

At the end of this routine the length-scale can be constrained according to a
suggestion of Galperin et al. (1988). This feature is optional and can be activated
by setting `length_lim = .true.` in `gotmturb.nml`.

*USES:*

use turbulence, only: P,B,num use turbulence, only: tke,tkeo,k_min,eps,eps_min,L use turbulence, only: ce1,ce2,ce3plus,ce3minus use turbulence, only: cm0,cde,galp,length_lim use turbulence, only: epsilon_bc, psi_ubc, psi_lbc, ubc_type, lbc_type use turbulence, only: sig_e,sig_e0,sig_peps 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: dissipationeq.F90,v $ Revision 1.10 2007-01-06 11:49:15 kbk namelist file extension changed .inp --> .nml 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 13:43:42 lars double definitions removed - to conform with DEC compiler Revision 1.3 2003/03/10 09:02:04 gotm Added new Generic Turbulence Model + improved documentation and cleaned up code

Karsten Bolding 2012-01-24