The dynamic q2l-equation (Source File: lengthscaleeq.F90)

*INTERFACE:*

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

Following suggestions of Rotta (1951), Mellor and Yamada (1982) proposed an equation for the product expressed by

where denotes the material derivative of . The production terms and follow from (152), and can be computed either directly from (156), or from (153) with the help (157).

The so-called wall function, , appearing in (160) is defined by

being the von Kármán constant and some measure for the distance from the wall. Different possiblities for are implemented in GOTM, which can be activated be setting the parameter

For horizontally homogeneous flows, the transport term appearing in (160) is expressed by a simple gradient formulation,

where is a constant of the model. The values for the model constants recommended by Mellor and Yamada (1982) are displayed in table 6. They can be set in

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 use turbulence, only: tke,tkeo,k_min,eps,eps_min,L use turbulence, only: kappa,e1,e2,e3,b1 use turbulence, only: MY_length,cm0,cde,galp,length_lim use turbulence, only: q2l_bc, psi_ubc, psi_lbc, ubc_type, lbc_type use turbulence, only: sl use util, only: Dirichlet,Neumann IMPLICIT NONE

number of vertical layers integer, intent(in) :: nlev time step (s) REALTYPE, intent(in) :: dt local water depth (m) REALTYPE, intent(in) :: depth 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: lengthscaleeq.F90,v $ Revision 1.8 2007-01-06 11:49:15 kbk namelist file extension changed .inp --> .nml Revision 1.7 2005/11/15 11:35:02 lars documentation finish for print Revision 1.6 2005/11/03 20:53:37 hb Patankar trick reverted to older versions for stabilising 3D computations Revision 1.5 2005/06/27 13:44:07 kbk modified + removed traling blanks Revision 1.4 2003/03/28 09:20:35 kbk added new copyright to files Revision 1.3 2003/03/10 09:02:05 gotm Added new Generic Turbulence Model + improved documentation and cleaned up code

Karsten Bolding 2012-01-24