MODULE trazdf_exp !!============================================================================== !! *** MODULE trazdf_exp *** !! Ocean active tracers: vertical component of the tracer mixing trend using !! a split-explicit time-stepping !!============================================================================== !! History : OPA ! 1990-10 (B. Blanke) Original code !! 7.0 ! 1991-11 (G. Madec) !! ! 1992-06 (M. Imbard) correction on tracer trend loops !! ! 1996-01 (G. Madec) statement function for e3 !! ! 1997-05 (G. Madec) vertical component of isopycnal !! ! 1997-07 (G. Madec) geopotential diffusion in s-coord !! ! 2000-08 (G. Madec) double diffusive mixing !! NEMO 1.0 ! 2002-08 (G. Madec) F90: Free form and module !! - ! 2004-08 (C. Talandier) New trends organisation !! - ! 2005-11 (G. Madec) New organisation !! 3.0 ! 2008-04 (G. Madec) leap-frog time stepping done in trazdf !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- !! tra_zdf_exp : compute the tracer the vertical diffusion trend using a !! split-explicit time stepping and provide the after tracer !!---------------------------------------------------------------------- USE oce ! ocean dynamics and active tracers USE dom_oce ! ocean space and time domain USE domvvl ! variablevolume levels USE trdmod ! ocean active tracers trends USE trdmod_oce ! ocean variables trends USE zdf_oce ! ocean vertical physics USE zdfddm ! ocean vertical physics: double diffusion USE in_out_manager ! I/O manager USE prtctl ! Print control IMPLICIT NONE PRIVATE PUBLIC tra_zdf_exp ! routine called by step.F90 !! * Substitutions # include "domzgr_substitute.h90" # include "zdfddm_substitute.h90" # include "vectopt_loop_substitute.h90" !!---------------------------------------------------------------------- !! NEMO/OPA 3.2 , LOCEAN-IPSL (2009) !! $Id$ !! Software governed by the CeCILL licence (modipsl/doc/NEMO_CeCILL.txt) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE tra_zdf_exp( kt, p2dt ) !!---------------------------------------------------------------------- !! *** ROUTINE tra_zdf_exp *** !! !! ** Purpose : Compute the after tracer fields due to the vertical !! tracer mixing alone, and then due to the whole tracer trend. !! !! ** Method : - The after tracer fields due to the vertical diffusion !! of tracers alone is given by: !! zwx = tb + p2dt difft !! where difft = dz( avt dz(tb) ) = 1/e3t dk+1( avt/e3w dk(tb) ) !! (if lk_zdfddm=T use avs on salinity instead of avt) !! difft is evaluated with an Euler split-explit scheme using a !! no flux boundary condition at both surface and bottomi boundaries. !! (N.B. bottom condition is applied through the masked field avt). !! - the after tracer fields due to the whole trend is !! obtained in leap-frog environment by : !! ta = zwx + p2dt ta !! - in case of variable level thickness (lk_vvl=T) the !! the leap-frog is applied on thickness weighted tracer. That is: !! ta = [ tb*e3tb + e3tn*( zwx - tb + p2dt ta ) ] / e3tn !! !! ** Action : - after tracer fields (ta,sa) !!--------------------------------------------------------------------- INTEGER , INTENT(in) :: kt ! ocean time-step index REAL(wp), INTENT(in), DIMENSION(jpk) :: p2dt ! vertical profile of tracer time-step !! INTEGER :: ji, jj, jk, jl ! dummy loop indices REAL(wp) :: zlavmr, zave3r, ze3tr ! temporary scalars REAL(wp) :: zta, zsa, ze3tb ! temporary scalars REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwx, zwy, zwz, zww ! 3D workspace !!--------------------------------------------------------------------- IF( kt == nit000 ) THEN IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) 'tra_zdf_exp : explicit vertical mixing' IF(lwp) WRITE(numout,*) '~~~~~~~~~~~' ENDIF ! Initializations ! --------------- zlavmr = 1. / float( nn_zdfexp ) ! Local constant ! zwy(:,:, 1 ) = 0.e0 ; zww(:,:, 1 ) = 0.e0 ! surface boundary conditions: no flux zwy(:,:,jpk) = 0.e0 ; zww(:,:,jpk) = 0.e0 ! bottom boundary conditions: no flux ! zwx(:,:,:) = tb(:,:,:) ; zwz(:,:,:) = sb(:,:,:) ! zwx and zwz arrays set to before tracer values ! Split-explicit loop (after tracer due to the vertical diffusion alone) ! ------------------- ! DO jl = 1, nn_zdfexp ! ! first vertical derivative DO jk = 2, jpk DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zave3r = 1.e0 / fse3w_n(ji,jj,jk) zwy(ji,jj,jk) = avt(ji,jj,jk) * ( zwx(ji,jj,jk-1) - zwx(ji,jj,jk) ) * zave3r zww(ji,jj,jk) = fsavs(ji,jj,jk) * ( zwz(ji,jj,jk-1) - zwz(ji,jj,jk) ) * zave3r END DO END DO END DO ! DO jk = 1, jpkm1 ! second vertical derivative ==> tracer at kt+l*2*rdt/nn_zdfexp DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ze3tr = zlavmr / fse3t_n(ji,jj,jk) zwx(ji,jj,jk) = zwx(ji,jj,jk) + p2dt(jk) * ( zwy(ji,jj,jk) - zwy(ji,jj,jk+1) ) * ze3tr zwz(ji,jj,jk) = zwz(ji,jj,jk) + p2dt(jk) * ( zww(ji,jj,jk) - zww(ji,jj,jk+1) ) * ze3tr END DO END DO END DO ! END DO ! After tracer due to all trends ! ------------------------------ IF( lk_vvl ) THEN ! variable level thickness : leap-frog on tracer*e3t DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ze3tb = fse3t_b(ji,jj,jk) / fse3t(ji,jj,jk) ! before e3t zta = zwx(ji,jj,jk) - tb(ji,jj,jk) + p2dt(jk) * ta(ji,jj,jk) ! total trends * 2*rdt zsa = zwz(ji,jj,jk) - sb(ji,jj,jk) + p2dt(jk) * sa(ji,jj,jk) ta(ji,jj,jk) = ( ze3tb * tb(ji,jj,jk) + zta ) * tmask(ji,jj,jk) sa(ji,jj,jk) = ( ze3tb * sb(ji,jj,jk) + zsa ) * tmask(ji,jj,jk) END DO END DO END DO ELSE ! fixed level thickness : leap-frog on tracers DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ta(ji,jj,jk) = ( zwx(ji,jj,jk) + p2dt(jk) * ta(ji,jj,jk) ) * tmask(ji,jj,jk) sa(ji,jj,jk) = ( zwz(ji,jj,jk) + p2dt(jk) * sa(ji,jj,jk) ) * tmask(ji,jj,jk) END DO END DO END DO ENDIF ! END SUBROUTINE tra_zdf_exp !!============================================================================== END MODULE trazdf_exp