MODULE traldf_bilap !!============================================================================== !! *** MODULE traldf_bilap *** !! Ocean tracers: horizontal component of the lateral tracer mixing trend !!============================================================================== !! History : ! 91-11 (G. Madec) Original code !! ! 93-03 (M. Guyon) symetrical conditions !! ! 95-11 (G. Madec) suppress volumetric scale factors !! ! 96-01 (G. Madec) statement function for e3 !! ! 96-01 (M. Imbard) mpp exchange !! ! 97-07 (G. Madec) optimization, and ahtt !! 8.5 ! 02-08 (G. Madec) F90: Free form and module !! 9.0 ! 04-08 (C. Talandier) New trends organization !! ! 05-11 (G. Madec) zps or sco as default option !! 3.3 ! 10-05 (C. Ethe, G. Madec) merge TRC-TRA !!============================================================================== !!---------------------------------------------------------------------- !! tra_ldf_bilap : update the tracer trend with the horizontal diffusion !! using a iso-level biharmonic operator !!---------------------------------------------------------------------- !! * Modules used USE oce ! ocean dynamics and active tracers USE dom_oce ! ocean space and time domain USE ldftra_oce ! ocean tracer lateral physics USE in_out_manager ! I/O manager USE ldfslp ! iso-neutral slopes USE lbclnk ! ocean lateral boundary conditions (or mpp link) USE diaptr ! poleward transport diagnostics IMPLICIT NONE PRIVATE !! * Routine accessibility PUBLIC tra_ldf_bilap ! routine called by step.F90 !! * Substitutions # include "domzgr_substitute.h90" # include "ldftra_substitute.h90" # include "ldfeiv_substitute.h90" # include "vectopt_loop_substitute.h90" !!---------------------------------------------------------------------- !! NEMO/OPA 3.3 , LOCEAN-IPSL (2010) !! $Id$ !! This software is governed by the CeCILL licence see modipsl/doc/NEMO_CeCILL.txt !!---------------------------------------------------------------------- CONTAINS SUBROUTINE tra_ldf_bilap( kt, cdtype, pgu, pgv, & & ptb, pta, kjpt ) !!---------------------------------------------------------------------- !! *** ROUTINE tra_ldf_bilap *** !! !! ** Purpose : Compute the before horizontal tracer diffusive !! trend and add it to the general trend of tracer equation. !! !! ** Method : 4th order diffusive operator along model level surfaces !! evaluated using before fields (forward time scheme). The hor. !! diffusive trends is given by: !! Laplacian of tb: !! zlt = 1/(e1t*e2t*e3t) { di-1[ e2u*e3u/e1u di(tb) ] !! + dj-1[ e1v*e3v/e2v dj(tb) ] } !! Multiply by the eddy diffusivity coef. and insure lateral bc: !! zlt = ahtt * zlt !! call to lbc_lnk !! Bilaplacian (laplacian of zlt): !! difft = 1/(e1t*e2t*e3t) { di-1[ e2u*e3u/e1u di(zlt) ] !! + dj-1[ e1v*e3v/e2v dj(zlt) ] } !! !! Add this trend to the general trend !! (pta) = (pta) + ( difft ) !! !! ** Action : - Update pta arrays with the before iso-level !! biharmonic mixing trend. !!---------------------------------------------------------------------- !! USE oce , ztu => ua ! use ua as workspace USE oce , ztv => va ! use va as workspace !! INTEGER , INTENT(in ) :: kt ! ocean time-step index CHARACTER(len=3), INTENT(in ) :: cdtype ! =TRA or TRC (tracer indicator) INTEGER , INTENT(in ) :: kjpt ! number of tracers REAL(wp) , INTENT(in ), DIMENSION(jpi,jpj,kjpt ) :: pgu, pgv ! tracer gradient at pstep levels REAL(wp) , INTENT(in ), DIMENSION(jpi,jpj,jpk,kjpt) :: ptb ! before and now tracer fields REAL(wp) , INTENT(inout), DIMENSION(jpi,jpj,jpk,kjpt) :: pta ! tracer trend !! INTEGER :: ji, jj, jk, jn ! dummy loop indices INTEGER :: iku, ikv ! temporary integers REAL(wp) :: zbtr, ztra ! temporary scalars REAL(wp), DIMENSION(jpi,jpj) :: & zeeu, zeev, zlt ! 2D workspace !!---------------------------------------------------------------------- IF( kt == nit000 ) THEN IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) 'tra_ldf_bilap : iso-level biharmonic operator' IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~~' ENDIF ! ! =========== DO jn = 1, kjpt ! tracer loop ! ! =========== ! DO jk = 1, jpkm1 ! ! 0. Initialization of metric arrays (for z- or s-coordinates) ! ---------------------------------- DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. zeeu(ji,jj) = e2u(ji,jj) * fse3u(ji,jj,jk) / e1u(ji,jj) * umask(ji,jj,jk) zeev(ji,jj) = e1v(ji,jj) * fse3v(ji,jj,jk) / e2v(ji,jj) * vmask(ji,jj,jk) END DO END DO ! 1. Laplacian ! ------------ ! First derivative (gradient) DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. ztu(ji,jj,jk) = zeeu(ji,jj) * ( ptb(ji+1,jj ,jk,jn) - ptb(ji,jj,jk,jn) ) ztv(ji,jj,jk) = zeev(ji,jj) * ( ptb(ji ,jj+1,jk,jn) - ptb(ji,jj,jk,jn) ) END DO END DO IF( ln_zps ) THEN ! set gradient at partial step level DO jj = 1, jpjm1 DO ji = 1, jpim1 ! last level iku = MIN ( mbathy(ji,jj), mbathy(ji+1,jj ) ) - 1 ikv = MIN ( mbathy(ji,jj), mbathy(ji ,jj+1) ) - 1 IF( iku == jk ) ztu(ji,jj,jk) = zeeu(ji,jj) * pgu(ji,jj,jn) IF( ikv == jk ) ztv(ji,jj,jk) = zeev(ji,jj) * pgv(ji,jj,jn) END DO END DO ENDIF ! Second derivative (divergence) multiply by the eddy diffusivity coefficient DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zbtr = 1.0 / ( e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) ) zlt(ji,jj) = fsahtt(ji,jj,jk) & & * zbtr * ( ztu(ji,jj,jk) - ztu(ji-1,jj,jk) + ztv(ji,jj,jk) - ztv(ji,jj-1,jk) ) END DO END DO ! Lateral boundary conditions on the laplacian (zlt) (unchanged sgn) CALL lbc_lnk( zlt, 'T', 1. ) ! 2. Bilaplacian ! -------------- ! third derivative (gradient) DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. ztu(ji,jj,jk) = zeeu(ji,jj) * ( zlt(ji+1,jj ) - zlt(ji,jj) ) ztv(ji,jj,jk) = zeev(ji,jj) * ( zlt(ji ,jj+1) - zlt(ji,jj) ) END DO END DO ! fourth derivative (divergence) and add to the general tracer trend DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ! horizontal diffusive trends zbtr = 1.0 / ( e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) ) ztra = zbtr * ( ztu(ji,jj,jk) - ztu(ji-1,jj,jk) + ztv(ji,jj,jk) - ztv(ji,jj-1,jk) ) ! add it to the general tracer trends pta(ji,jj,jk,jn) = pta(ji,jj,jk,jn) + ztra END DO END DO ! ! =============== END DO ! Horizontal slab ! ! =============== ! "zonal" mean lateral diffusive heat and salt transport IF( cdtype == 'TRA' .AND. ln_diaptr .AND. ( MOD( kt, nf_ptr ) == 0 ) ) THEN IF( jn == jp_tem ) pht_ldf(:) = ptr_vj( ztv(:,:,:) ) IF( jn == jp_sal ) pst_ldf(:) = ptr_vj( ztv(:,:,:) ) ENDIF ! END DO END SUBROUTINE tra_ldf_bilap !!============================================================================== END MODULE traldf_bilap