MODULE zdfric !!====================================================================== !! *** MODULE zdfric *** !! Ocean physics: vertical mixing coefficient compute from the local !! Richardson number dependent formulation !!====================================================================== #if defined key_zdfric || defined key_esopa !!---------------------------------------------------------------------- !! 'key_zdfric' Kz = f(Ri) !!---------------------------------------------------------------------- !! zdf_ric : update momentum and tracer Kz from the Richardson !! number computation !! zdf_ric_init : initialization, namelist read, & parameters control !!---------------------------------------------------------------------- USE oce ! ocean dynamics and tracers variables USE dom_oce ! ocean space and time domain variables USE zdf_oce ! ocean vertical physics USE in_out_manager ! I/O manager USE lbclnk ! ocean lateral boundary condition (or mpp link) IMPLICIT NONE PRIVATE PUBLIC zdf_ric ! called by step.F90 LOGICAL, PUBLIC, PARAMETER :: lk_zdfric = .TRUE. !: Richardson vertical mixing flag ! !!* Namelist nam_ric : Richardson number dependent Kz * INTEGER :: nn_ric = 2 ! coefficient of the parameterization REAL(wp) :: rn_avmri = 100.e-4_wp ! maximum value of the vertical eddy viscosity REAL(wp) :: rn_alp = 5._wp ! coefficient of the parameterization REAL(wp), DIMENSION(jpi,jpj,jpk) :: tmric ! coef. for the horizontal mean at t-point !! * Substitutions # include "domzgr_substitute.h90" !!---------------------------------------------------------------------- !! NEMO/OPA 3.2 , LOCEAN-IPSL (2009) !! $Id$ !! Software governed by the CeCILL licence (modipsl/doc/NEMO_CeCILL.txt) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE zdf_ric( kt ) !!---------------------------------------------------------------------- !! *** ROUTINE zdfric *** !! !! ** Purpose : Compute the before eddy viscosity and diffusivity as !! a function of the local richardson number. !! !! ** Method : Local richardson number dependent formulation of the !! vertical eddy viscosity and diffusivity coefficients. the eddy !! coefficients are given by: !! avm = avm0 + avmb !! avt = avm0 / (1 + rn_alp*ri) !! with ri = N^2 / dz(u)**2 !! = e3w**2 * rn2/[ mi( dk(ub) )+mj( dk(vb) ) ] !! avm0= rn_avmri / (1 + rn_alp*ri)**nn_ric !! Where ri is the before local Richardson number, rn_avmri the maximum !! value reaches by the vertical eddy coefficients, avmb and avtb !! the background (or minimum) values of these coefficients for !! momemtum and tracers, and rn_alp, nn_ric are adjustable parameters. !! typical values used are : avm0=1.e-2 m2/s, avmb=1.e-6 m2/s !! avtb=1.e-7 m2/s, rn_alp=5. and nn_ric=2. !! this formulation needs ri>=0 : ri is set to zero if dz(rau)<0. !! a numerical threshold is impose on the vertical shear (1.e-20) !! N.B. the mask are required for implicit scheme, and surface !! and bottom value already set in inimix.F !! !! References : !! pacanowski & philander 1981, j. phys. oceanogr., 1441-1451. !! History : !! ! 87-09 (P. Andrich) Original code !! ! 91-11 (G. Madec) !! ! 93-03 (M. Guyon) symetrical conditions !! ! 96-01 (G. Madec) complet rewriting of multitasking !! suppression of common work arrays !! ! 97-06 (G. Madec) complete rewriting of zdfmix !! 8.5 ! 02-06 (G. Madec) F90: Free form and module !!---------------------------------------------------------------------- INTEGER, INTENT( in ) :: kt ! ocean time-step indexocean time step !! INTEGER :: ji, jj, jk ! dummy loop indices REAL(wp) :: zcoef, zdku, zdkv, zri, z05alp ! temporary scalars REAL(wp), DIMENSION(jpi,jpj) :: zwx ! temporary workspace !!---------------------------------------------------------------------- IF( kt == nit000 ) CALL zdf_ric_init ! Initialization (first time-step only) ! ! =============== DO jk = 2, jpkm1 ! Horizontal slab ! ! =============== ! Richardson number (put in zwx(ji,jj)) ! ----------------- ! minimum value set to zero DO jj = 2, jpjm1 DO ji = 2, jpim1 zcoef = 0.5 / fse3w(ji,jj,jk) ! shear of horizontal velocity zdku = zcoef * ( ub(ji-1,jj,jk-1) + ub(ji,jj,jk-1) & & -ub(ji-1,jj,jk ) - ub(ji,jj,jk ) ) zdkv = zcoef * ( vb(ji,jj-1,jk-1) + vb(ji,jj,jk-1) & & -vb(ji,jj-1,jk ) - vb(ji,jj,jk ) ) ! richardson number (minimum value set to zero) zri = rn2(ji,jj,jk) / ( zdku*zdku + zdkv*zdkv + 1.e-20 ) zwx(ji,jj) = MAX( zri, 0.e0 ) END DO END DO ! Boundary condition on zwx (sign unchanged) CALL lbc_lnk( zwx, 'W', 1. ) ! Vertical eddy viscosity and diffusivity coefficients ! ------------------------------------------------------- ! Eddy viscosity coefficients z05alp = 0.5 * rn_alp DO jj = 1, jpjm1 DO ji = 1, jpim1 avmu(ji,jj,jk) = umask(ji,jj,jk) & & * rn_avmri / ( 1. + z05alp*( zwx(ji+1,jj)+zwx(ji,jj) ) )**nn_ric avmv(ji,jj,jk) = vmask(ji,jj,jk) & & * rn_avmri / ( 1. + z05alp*( zwx(ji,jj+1)+zwx(ji,jj) ) )**nn_ric END DO END DO ! Eddy diffusivity coefficients DO jj = 2, jpjm1 DO ji = 2, jpim1 avt(ji,jj,jk) = tmric(ji,jj,jk) / ( 1. + rn_alp * zwx(ji,jj) ) & & * ( avmu(ji,jj,jk) + avmu(ji-1, jj ,jk) & & + avmv(ji,jj,jk) + avmv( ji ,jj-1,jk) ) & & + avtb(jk) * tmask(ji,jj,jk) END DO END DO ! Add the background coefficient on eddy viscosity DO jj = 2, jpjm1 DO ji = 2, jpim1 avmu(ji,jj,jk) = avmu(ji,jj,jk) + avmb(jk) * umask(ji,jj,jk) avmv(ji,jj,jk) = avmv(ji,jj,jk) + avmb(jk) * vmask(ji,jj,jk) END DO END DO ! ! =============== END DO ! End of slab ! ! =============== ! Boundary conditions on (avt,avmu,avmv) (unchanged sign) ! -----------------------=============== CALL lbc_lnk( avt , 'W', 1. ) CALL lbc_lnk( avmu, 'U', 1. ) CALL lbc_lnk( avmv, 'V', 1. ) END SUBROUTINE zdf_ric SUBROUTINE zdf_ric_init !!---------------------------------------------------------------------- !! *** ROUTINE zdfbfr_init *** !! !! ** Purpose : Initialization of the vertical eddy diffusivity and !! viscosity coef. for the Richardson number dependent formulation. !! !! ** Method : Read the namric namelist and check the parameter values !! !! ** input : Namelist namric !! !! ** Action : increase by 1 the nstop flag is setting problem encounter !! !! history : !! 8.5 ! 02-06 (G. Madec) original code !!---------------------------------------------------------------------- INTEGER :: ji, jj, jk ! dummy loop indices !! NAMELIST/nam_ric/ rn_avmri, rn_alp, nn_ric !!---------------------------------------------------------------------- REWIND ( numnam ) ! Read Namelist nam_ric : richardson number dependent Kz READ ( numnam, nam_ric ) IF(lwp) THEN ! Control print WRITE(numout,*) WRITE(numout,*) 'zdf_ric : Ri depend vertical mixing scheme' WRITE(numout,*) '~~~~~~~' WRITE(numout,*) ' Namelist namric : set Kz(Ri) parameters' WRITE(numout,*) ' maximum vertical viscosity rn_avmri = ', rn_avmri WRITE(numout,*) ' coefficient rn_alp = ', rn_alp WRITE(numout,*) ' coefficient nn_ric = ', nn_ric ENDIF ! weighting mean array tmric for 4 T-points which accounts for coastal boundary conditions. DO jk = 1, jpk DO jj = 2, jpj DO ji = 2, jpi tmric(ji,jj,jk) = tmask(ji,jj,jk) & / MAX( 1., umask(ji-1,jj ,jk) + umask(ji,jj,jk) & + vmask(ji ,jj-1,jk) + vmask(ji,jj,jk) ) END DO END DO END DO tmric(:,1,:) = 0.e0 ! Initialization of vertical eddy coef. to the background value DO jk = 1, jpk avt (:,:,jk) = avtb(jk) * tmask(:,:,jk) avmu(:,:,jk) = avmb(jk) * umask(:,:,jk) avmv(:,:,jk) = avmb(jk) * vmask(:,:,jk) END DO END SUBROUTINE zdf_ric_init #else !!---------------------------------------------------------------------- !! Dummy module : NO Richardson dependent vertical mixing !!---------------------------------------------------------------------- LOGICAL, PUBLIC, PARAMETER :: lk_zdfric = .FALSE. !: Richardson mixing flag CONTAINS SUBROUTINE zdf_ric( kt ) ! Dummy routine WRITE(*,*) 'zdf_ric: You should not have seen this print! error?', kt END SUBROUTINE zdf_ric #endif !!====================================================================== END MODULE zdfric