MODULE dynldf_bilap !!====================================================================== !! *** MODULE dynldf_bilap *** !! Ocean dynamics: lateral viscosity trend !!====================================================================== !! History : OPA ! 1990-09 (G. Madec) Original code !! 4.0 ! 1993-03 (M. Guyon) symetrical conditions (M. Guyon) !! 6.0 ! 1996-01 (G. Madec) statement function for e3 !! 8.0 ! 1997-07 (G. Madec) lbc calls !! NEMO 1.0 ! 2002-08 (G. Madec) F90: Free form and module !! 2.0 ! 2004-08 (C. Talandier) New trends organization !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- !! dyn_ldf_bilap : update the momentum trend with the lateral diffusion !! using an iso-level bilaplacian operator !!---------------------------------------------------------------------- USE oce ! ocean dynamics and tracers USE dom_oce ! ocean space and time domain USE ldfdyn_oce ! ocean dynamics: lateral physics ! USE in_out_manager ! I/O manager USE lbclnk ! ocean lateral boundary conditions (or mpp link) USE wrk_nemo ! Memory Allocation USE timing ! Timing USE yomhook, ONLY: lhook, dr_hook USE parkind1, ONLY: jprb, jpim IMPLICIT NONE PRIVATE PUBLIC dyn_ldf_bilap ! called by step.F90 !! * Substitutions # include "domzgr_substitute.h90" # include "ldfdyn_substitute.h90" # include "vectopt_loop_substitute.h90" !!---------------------------------------------------------------------- !! NEMO/OPA 3.3 , NEMO Consortium (2010) !! $Id$ !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE dyn_ldf_bilap( kt ) !!---------------------------------------------------------------------- !! *** ROUTINE dyn_ldf_bilap *** !! !! ** Purpose : Compute the before trend of the lateral momentum !! diffusion and add it to the general trend of momentum equation. !! !! ** Method : The before horizontal momentum diffusion trend is a !! bi-harmonic operator (bilaplacian type) which separates the !! divergent and rotational parts of the flow. !! Its horizontal components are computed as follow: !! laplacian: !! zlu = 1/e1u di[ hdivb ] - 1/(e2u*e3u) dj-1[ e3f rotb ] !! zlv = 1/e2v dj[ hdivb ] + 1/(e1v*e3v) di-1[ e3f rotb ] !! third derivative: !! * multiply by the eddy viscosity coef. at u-, v-point, resp. !! zlu = ahmu * zlu !! zlv = ahmv * zlv !! * curl and divergence of the laplacian !! zuf = 1/(e1f*e2f) ( di[e2v zlv] - dj[e1u zlu] ) !! zut = 1/(e1t*e2t*e3t) ( di[e2u*e3u zlu] + dj[e1v*e3v zlv] ) !! bilaplacian: !! diffu = 1/e1u di[ zut ] - 1/(e2u*e3u) dj-1[ e3f zuf ] !! diffv = 1/e2v dj[ zut ] + 1/(e1v*e3v) di-1[ e3f zuf ] !! If ln_sco=F and ln_zps=F, the vertical scale factors in the !! rotational part of the diffusion are simplified !! Add this before trend to the general trend (ua,va): !! (ua,va) = (ua,va) + (diffu,diffv) !! !! ** Action : - Update (ua,va) with the before iso-level biharmonic !! mixing trend. !!---------------------------------------------------------------------- INTEGER, INTENT(in) :: kt ! ocean time-step index ! INTEGER :: ji, jj, jk ! dummy loop indices REAL(wp) :: zua, zva, zbt, ze2u, ze2v ! temporary scalar REAL(wp), POINTER, DIMENSION(:,: ) :: zcu, zcv REAL(wp), POINTER, DIMENSION(:,:,:) :: zuf, zut, zlu, zlv INTEGER(KIND=jpim), PARAMETER :: zhook_in = 0 INTEGER(KIND=jpim), PARAMETER :: zhook_out = 1 REAL(KIND=jprb) :: zhook_handle CHARACTER(LEN=*), PARAMETER :: RoutineName='DYN_LDF_BILAP' IF (lhook) CALL dr_hook(RoutineName,zhook_in,zhook_handle) !!---------------------------------------------------------------------- ! IF( nn_timing == 1 ) CALL timing_start('dyn_ldf_bilap') ! CALL wrk_alloc( jpi, jpj, zcu, zcv ) CALL wrk_alloc( jpi, jpj, jpk, zuf, zut, zlu, zlv ) ! IF( kt == nit000 .AND. lwp ) THEN WRITE(numout,*) WRITE(numout,*) 'dyn_ldf_bilap : iso-level bilaplacian operator' WRITE(numout,*) '~~~~~~~~~~~~~' ENDIF !!bug gm this should be enough !!$ zuf(:,:,jpk) = 0.e0 !!$ zut(:,:,jpk) = 0.e0 !!$ zlu(:,:,jpk) = 0.e0 !!$ zlv(:,:,jpk) = 0.e0 zuf(:,:,:) = 0._wp zut(:,:,:) = 0._wp zlu(:,:,:) = 0._wp zlv(:,:,:) = 0._wp ! ! =============== DO jk = 1, jpkm1 ! Horizontal slab ! ! =============== ! Laplacian ! --------- IF( ln_sco .OR. ln_zps ) THEN ! s-coordinate or z-coordinate with partial steps zuf(:,:,jk) = rotb(:,:,jk) * fse3f(:,:,jk) DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zlu(ji,jj,jk) = - ( zuf(ji,jj,jk) - zuf(ji,jj-1,jk) ) / ( e2u(ji,jj) * fse3u(ji,jj,jk) ) & & + ( hdivb(ji+1,jj,jk) - hdivb(ji,jj,jk) ) / e1u(ji,jj) zlv(ji,jj,jk) = + ( zuf(ji,jj,jk) - zuf(ji-1,jj,jk) ) / ( e1v(ji,jj) * fse3v(ji,jj,jk) ) & & + ( hdivb(ji,jj+1,jk) - hdivb(ji,jj,jk) ) / e2v(ji,jj) END DO END DO ELSE ! z-coordinate - full step DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zlu(ji,jj,jk) = - ( rotb (ji ,jj,jk) - rotb (ji,jj-1,jk) ) / e2u(ji,jj) & & + ( hdivb(ji+1,jj,jk) - hdivb(ji,jj ,jk) ) / e1u(ji,jj) zlv(ji,jj,jk) = + ( rotb (ji,jj ,jk) - rotb (ji-1,jj,jk) ) / e1v(ji,jj) & & + ( hdivb(ji,jj+1,jk) - hdivb(ji ,jj,jk) ) / e2v(ji,jj) END DO END DO ENDIF END DO CALL lbc_lnk( zlu, 'U', -1. ) ; CALL lbc_lnk( zlv, 'V', -1. ) ! Boundary conditions DO jk = 1, jpkm1 ! Third derivative ! ---------------- ! Multiply by the eddy viscosity coef. (at u- and v-points) zlu(:,:,jk) = zlu(:,:,jk) * ( fsahmu(:,:,jk) * (1-nkahm_smag) + nkahm_smag) zlv(:,:,jk) = zlv(:,:,jk) * ( fsahmv(:,:,jk) * (1-nkahm_smag) + nkahm_smag) ! Contravariant "laplacian" zcu(:,:) = e1u(:,:) * zlu(:,:,jk) zcv(:,:) = e2v(:,:) * zlv(:,:,jk) ! Laplacian curl ( * e3f if s-coordinates or z-coordinate with partial steps) DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. zuf(ji,jj,jk) = fmask(ji,jj,jk) * ( zcv(ji+1,jj ) - zcv(ji,jj) & & - zcu(ji ,jj+1) + zcu(ji,jj) ) & & * fse3f(ji,jj,jk) / ( e1f(ji,jj)*e2f(ji,jj) ) END DO END DO ! Laplacian Horizontal fluxes DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. zlu(ji,jj,jk) = e2u(ji,jj) * fse3u(ji,jj,jk) * zlu(ji,jj,jk) zlv(ji,jj,jk) = e1v(ji,jj) * fse3v(ji,jj,jk) * zlv(ji,jj,jk) END DO END DO ! Laplacian divergence DO jj = 2, jpj DO ji = fs_2, jpi ! vector opt. zbt = e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) zut(ji,jj,jk) = ( zlu(ji,jj,jk) - zlu(ji-1,jj ,jk) & & + zlv(ji,jj,jk) - zlv(ji ,jj-1,jk) ) / zbt END DO END DO END DO ! boundary conditions on the laplacian curl and div (zuf,zut) !!bug gm no need to do this 2 following lbc... CALL lbc_lnk( zuf, 'F', 1. ) CALL lbc_lnk( zut, 'T', 1. ) DO jk = 1, jpkm1 ! Bilaplacian ! ----------- DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ze2u = e2u(ji,jj) * fse3u(ji,jj,jk) ze2v = e1v(ji,jj) * fse3v(ji,jj,jk) ! horizontal biharmonic diffusive trends zua = - ( zuf(ji ,jj,jk) - zuf(ji,jj-1,jk) ) / ze2u & & + ( zut(ji+1,jj,jk) - zut(ji,jj ,jk) ) / e1u(ji,jj) zva = + ( zuf(ji,jj ,jk) - zuf(ji-1,jj,jk) ) / ze2v & & + ( zut(ji,jj+1,jk) - zut(ji ,jj,jk) ) / e2v(ji,jj) ! add it to the general momentum trends ua(ji,jj,jk) = ua(ji,jj,jk) + zua * ( fsahmu(ji,jj,jk)*nkahm_smag +(1 -nkahm_smag )) va(ji,jj,jk) = va(ji,jj,jk) + zva * ( fsahmv(ji,jj,jk)*nkahm_smag +(1 -nkahm_smag )) END DO END DO ! ! =============== END DO ! End of slab ! ! =============== CALL wrk_dealloc( jpi, jpj, zcu, zcv ) CALL wrk_dealloc( jpi, jpj, jpk, zuf, zut, zlu, zlv ) ! IF( nn_timing == 1 ) CALL timing_stop('dyn_ldf_bilap') ! IF (lhook) CALL dr_hook(RoutineName,zhook_out,zhook_handle) END SUBROUTINE dyn_ldf_bilap !!====================================================================== END MODULE dynldf_bilap