MODULE dynldf_bilap !!====================================================================== !! *** MODULE dynldf_bilap *** !! Ocean dynamics: lateral viscosity trend !!====================================================================== !!---------------------------------------------------------------------- !! dyn_ldf_bilap : update the momentum trend with the lateral diffusion !! using an iso-level bilaplacian operator !!---------------------------------------------------------------------- !! * Modules used 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 trdmod ! ocean dynamics trends USE trdmod_oce ! ocean variables trends USE lbclnk ! ocean lateral boundary conditions (or mpp link) USE prtctl ! Print control IMPLICIT NONE PRIVATE !! * Routine accessibility PUBLIC dyn_ldf_bilap ! called by step.F90 !! * Substitutions # include "domzgr_substitute.h90" # include "ldfdyn_substitute.h90" # include "vectopt_loop_substitute.h90" !!---------------------------------------------------------------------- !! OPA 9.0 , LOCEAN-IPSL (2005) !! $Header$ !! This software is governed by the CeCILL licence see modipsl/doc/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 lk_sco=F and lk_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) !! 'key_trddyn' defined: the two components of the horizontal !! diffusion trend are saved. !! !! ** Action : - Update (ua,va) with the before iso-level biharmonic !! mixing trend. !! - Save in (ztdua,ztdva) the trends ('key_trddyn') !! !! History : !! ! 90-09 (G. Madec) Original code !! ! 91-11 (G. Madec) !! ! 93-03 (M. Guyon) symetrical conditions (M. Guyon) !! ! 96-01 (G. Madec) statement function for e3 !! ! 97-07 (G. Madec) lbc calls !! 8.5 ! 02-08 (G. Madec) F90: Free form and module !! 9.0 ! 04-08 (C. Talandier) New trends organization !!---------------------------------------------------------------------- !! * Modules used USE oce, ONLY : ztdua => ta, & ! use ta as 3D workspace ztdva => sa ! use sa as 3D workspace !! * Arguments INTEGER, INTENT( in ) :: kt ! ocean time-step index !! * Local declarations INTEGER :: ji, jj, jk ! dummy loop indices REAL(wp) :: zua, zva, zbt, ze2u, ze2v ! temporary scalar REAL(wp), DIMENSION(jpi,jpj) :: & zuf, zut, zlu, zlv, zcu, zcv ! temporary workspace !!---------------------------------------------------------------------- !! OPA 8.5, LODYC-IPSL (2002) !!---------------------------------------------------------------------- IF( kt == nit000 ) THEN IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) 'dyn_ldf_bilap : iso-level bilaplacian operator' IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~~' ENDIF zuf(:,:) = 0.e0 zut(:,:) = 0.e0 zlu(:,:) = 0.e0 zlv(:,:) = 0.e0 ! Save ua and va trends IF( l_trddyn ) THEN ztdua(:,:,:) = ua(:,:,:) ztdva(:,:,:) = va(:,:,:) ENDIF ! ! =============== DO jk = 1, jpkm1 ! Horizontal slab ! ! =============== ! Laplacian ! --------- IF( lk_sco .OR. lk_zps ) THEN ! s-coordinate or z-coordinate with partial steps zuf(:,:) = rotb(:,:,jk) * fse3f(:,:,jk) DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zlu(ji,jj) = - ( zuf(ji,jj) - zuf(ji,jj-1) ) / ( e2u(ji,jj) * fse3u(ji,jj,jk) ) & & + ( hdivb(ji+1,jj,jk) - hdivb(ji,jj,jk) ) / e1u(ji,jj) zlv(ji,jj) = + ( zuf(ji,jj) - zuf(ji-1,jj) ) / ( 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 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zlu(ji,jj) = - ( 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) = + ( 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 ! Boundary conditions on the laplacian (zlu,zlv) CALL lbc_lnk( zlu, 'U', -1. ) CALL lbc_lnk( zlv, 'V', -1. ) ! Third derivative ! ---------------- ! Multiply by the eddy viscosity coef. (at u- and v-points) zlu(:,:) = zlu(:,:) * fsahmu(:,:,jk) zlv(:,:) = zlv(:,:) * fsahmv(:,:,jk) ! Contravariant "laplacian" zcu(:,:) = e1u(:,:) * zlu(:,:) zcv(:,:) = e2v(:,:) * zlv(:,:) ! 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) = fmask(ji,jj,jk) * ( zcv(ji+1,jj ) - zcv(ji,jj) & & - zcu(ji ,jj+1) + zcu(ji,jj) ) & #if defined key_s_coord || defined key_partial_steps & * fse3f(ji,jj,jk) / ( e1f(ji,jj)*e2f(ji,jj) ) #else & / ( e1f(ji,jj)*e2f(ji,jj) ) #endif END DO END DO ! Laplacian Horizontal fluxes DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. #if defined key_s_coord || defined key_partial_steps zlu(ji,jj) = e2u(ji,jj) * fse3u(ji,jj,jk) * zlu(ji,jj) zlv(ji,jj) = e1v(ji,jj) * fse3v(ji,jj,jk) * zlv(ji,jj) #else zlu(ji,jj) = e2u(ji,jj) * zlu(ji,jj) zlv(ji,jj) = e1v(ji,jj) * zlv(ji,jj) #endif END DO END DO ! Laplacian divergence DO jj = 2, jpj DO ji = fs_2, jpi ! vector opt. #if defined key_s_coord || defined key_partial_steps zbt = e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) #else zbt = e1t(ji,jj) * e2t(ji,jj) #endif zut(ji,jj) = ( zlu(ji,jj) - zlu(ji-1,jj ) & & + zlv(ji,jj) - zlv(ji ,jj-1) ) / zbt END DO END DO ! boundary conditions on the laplacian curl and div (zuf,zut) CALL lbc_lnk( zuf, 'F', 1. ) CALL lbc_lnk( zut, 'T', 1. ) ! Bilaplacian ! ----------- DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. #if defined key_s_coord || defined key_partial_steps ze2u = e2u(ji,jj) * fse3u(ji,jj,jk) ze2v = e1v(ji,jj) * fse3v(ji,jj,jk) #else ze2u = e2u(ji,jj) ze2v = e1v(ji,jj) #endif ! horizontal biharmonic diffusive trends zua = - ( zuf(ji ,jj) - zuf(ji,jj-1) ) / ze2u & & + ( zut(ji+1,jj) - zut(ji,jj ) ) / e1u(ji,jj) zva = + ( zuf(ji,jj ) - zuf(ji-1,jj) ) / ze2v & & + ( zut(ji,jj+1) - zut(ji ,jj) ) / e2v(ji,jj) ! add it to the general momentum trends ua(ji,jj,jk) = ua(ji,jj,jk) + zua va(ji,jj,jk) = va(ji,jj,jk) + zva END DO END DO ! ! =============== END DO ! End of slab ! ! =============== ! save the lateral diffusion trends for diagnostic ! momentum trends IF( l_trddyn ) THEN ztdua(:,:,:) = ua(:,:,:) - ztdua(:,:,:) ztdva(:,:,:) = va(:,:,:) - ztdva(:,:,:) CALL trd_mod(ztdua, ztdva, jpdtdldf, 'DYN', kt) ENDIF IF(ln_ctl) THEN ! print sum trends (used for debugging) CALL prt_ctl(tab3d_1=ua, clinfo1=' ldf - Ua: ', mask1=umask, & & tab3d_2=va, clinfo2=' Va: ', mask2=vmask, clinfo3='dyn') ENDIF END SUBROUTINE dyn_ldf_bilap !!====================================================================== END MODULE dynldf_bilap