MODULE dynadv_cen2 !!====================================================================== !! *** MODULE dynadv *** !! Ocean dynamics: Update the momentum trend with the flux form advection !! using a 2nd order centred scheme !!====================================================================== !! History : 9.0 ! 06-08 (G. Madec, S. Theetten) Original code !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- !! dyn_adv_cen2 : flux form momentum advection (ln_dynadv_cen2=T) !! trends using a 2nd order centred scheme !!---------------------------------------------------------------------- USE oce ! ocean dynamics and tracers USE dom_oce ! ocean space and time domain USE dynspg_oce ! surface pressure gradient USE in_out_manager ! I/O manager USE dynspg_rl ! I/O manager IMPLICIT NONE PRIVATE !! * Routine accessibility PUBLIC dyn_adv_cen2 ! routine called by step.F90 !! * Substitutions # include "domzgr_substitute.h90" # include "vectopt_loop_substitute.h90" !!---------------------------------------------------------------------- !! OPA 9.0 , LODYC-IPSL (2006) !! $Id$ !! Software governed by the CeCILL licence (modipsl/doc/NEMO_CeCILL.txt) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE dyn_adv_cen2( kt ) !!---------------------------------------------------------------------- !! *** ROUTINE dyn_adv_cen2 *** !! !! ** Purpose : Compute the now momentum advection trend in flux form !! and the general trend of the momentum equation. !! !! ** Method : Trend evaluated using now fields (centered in time) !! !! ** Action : - Update (ua,va) with the now vorticity term trend !! - save the trends in (utrd,vtrd) in 2 parts (relative !! and planetary vorticity trends) ('key_trddyn') !!---------------------------------------------------------------------- USE oce, ONLY: zfu => ta, & ! use ta as 3D workspace zfv => sa ! use sa as 3D workspace INTEGER, INTENT( in ) :: kt ! ocean time-step index INTEGER :: ji, jj, jk ! dummy loop indices REAL(wp) :: zua, zva, zbu, zbv ! temporary scalars REAL(wp), DIMENSION(jpi,jpj,jpk) :: zfu_t, zfu_f, zfu_uw ! 3D workspace REAL(wp), DIMENSION(jpi,jpj,jpk) :: zfv_t, zfv_f, zfv_vw ! " " REAL(wp), DIMENSION(jpi,jpj,jpk) :: zfw ! " " !!---------------------------------------------------------------------- IF( kt == nit000 ) THEN IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) 'dyn_adv_cen2 : 2nd order flux form momentum advection' IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~' ENDIF ! I. Horizontal advection ! ----------------------- ! ! =============== DO jk = 1, jpkm1 ! Horizontal slab ! ! =============== ! horizontal volume fluxes zfu(:,:,jk) = 0.25 * e2u(:,:) * fse3u(:,:,jk) * un(:,:,jk) zfv(:,:,jk) = 0.25 * e1v(:,:) * fse3v(:,:,jk) * vn(:,:,jk) ! horizontal momentum fluxes at T- and F-point DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. zfu_t(ji+1,jj ,jk) = ( zfu(ji,jj,jk) + zfu(ji+1,jj ,jk) ) * ( un(ji,jj,jk) + un(ji+1,jj ,jk) ) zfv_f(ji ,jj ,jk) = ( zfv(ji,jj,jk) + zfv(ji+1,jj ,jk) ) * ( un(ji,jj,jk) + un(ji ,jj+1,jk) ) zfu_f(ji ,jj ,jk) = ( zfu(ji,jj,jk) + zfu(ji ,jj+1,jk) ) * ( vn(ji,jj,jk) + vn(ji+1,jj ,jk) ) zfv_t(ji ,jj+1,jk) = ( zfv(ji,jj,jk) + zfv(ji ,jj+1,jk) ) * ( vn(ji,jj,jk) + vn(ji ,jj+1,jk) ) END DO END DO ! divergence of horizontal momentum fluxes DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zbu = e1u(ji,jj) * e2u(ji,jj) * fse3u(ji,jj,jk) zbv = e1v(ji,jj) * e2v(ji,jj) * fse3v(ji,jj,jk) ! horizontal advective trends zua = - ( zfu_t(ji+1,jj ,jk) - zfu_t(ji ,jj ,jk) & & + zfv_f(ji ,jj ,jk) - zfv_f(ji ,jj-1,jk) ) / zbu zva = - ( zfu_f(ji ,jj ,jk) - zfu_f(ji-1,jj ,jk) & & + zfv_t(ji ,jj+1,jk) - zfv_t(ji ,jj ,jk) ) / zbv ! add it to the general tracer trends ua(ji,jj,jk) = ua(ji,jj,jk) + zua va(ji,jj,jk) = va(ji,jj,jk) + zva #if defined key_trddyn utrd(ji,jj,jk,1) = zua ! save the horizontal advective trend of momentum vtrd(ji,jj,jk,1) = zva #endif END DO END DO ! ! =============== END DO ! End of slab ! ! =============== ! II. Vertical advection ! ---------------------- ! Second order centered tracer flux at w-point DO jk = 1, jpkm1 ! Vertical volume fluxes zfw(:,:,jk) = 0.25 * e1t(:,:) * e2t(:,:) * wn(:,:,jk) ! Vertical advective fluxes IF( jk == 1 ) THEN zfu_uw(:,:,jpk) = 0.e0 ! Bottom value : flux set to zero zfv_vw(:,:,jpk) = 0.e0 ! ! Surface value IF( lk_dynspg_rl ) THEN ! rigid lid : flux set to zero zfu_uw(:,:, 1 ) = 0.e0 zfv_vw(:,:, 1 ) = 0.e0 ELSE ! free surface-constant volume DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 zfu_uw(ji,jj, 1 ) = 2.e0 * ( zfw(ji,jj,1) + zfw(ji+1,jj ,1) ) * un(ji,jj,1) zfv_vw(ji,jj, 1 ) = 2.e0 * ( zfw(ji,jj,1) + zfw(ji ,jj+1,1) ) * vn(ji,jj,1) END DO END DO ENDIF ELSE ! ! interior fluxes DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zfu_uw(ji,jj,jk) = ( zfw(ji,jj,jk)+ zfw(ji+1,jj ,jk) ) * ( un(ji,jj,jk) + un(ji,jj,jk-1) ) zfv_vw(ji,jj,jk) = ( zfw(ji,jj,jk)+ zfw(ji ,jj+1,jk) ) * ( vn(ji,jj,jk) + vn(ji,jj,jk-1) ) END DO END DO ENDIF END DO ! momentum flux divergence at u-, v-points added to the general trend DO jk = 1, jpkm1 DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zua = - ( zfu_uw(ji,jj,jk) - zfu_uw(ji,jj,jk+1) ) & & / ( e1u(ji,jj) * e2u(ji,jj) * fse3u(ji,jj,jk) ) zva = - ( zfv_vw(ji,jj,jk) - zfv_vw(ji,jj,jk+1) ) & & / ( e1v(ji,jj) * e2v(ji,jj) * fse3v(ji,jj,jk) ) ! add it to the general tracer 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 SUBROUTINE dyn_adv_cen2 !!============================================================================== END MODULE dynadv_cen2