MODULE dynadv_ubs !!====================================================================== !! *** MODULE dynadv_ubs *** !! Ocean dynamics: Update the momentum trend with the flux form advection !! trend using a 3rd order upstream biased scheme !!====================================================================== !! History : 2.0 ! 2006-08 (R. Benshila, L. Debreu) Original code !! 3.2 ! 2009-07 (R. Benshila) Suppression of rigid-lid option !!---------------------------------------------------------------------- !!---------------------------------------------------------------------- !! dyn_adv_ubs : flux form momentum advection using (ln_dynadv=T) !! an 3rd order Upstream Biased Scheme or Quick scheme !! combined with 2nd or 4th order finite differences !!---------------------------------------------------------------------- USE oce ! ocean dynamics and tracers USE dom_oce ! ocean space and time domain USE trd_oce ! trends: ocean variables USE trddyn ! trend manager: dynamics ! USE in_out_manager ! I/O manager USE prtctl ! Print control USE lbclnk ! ocean lateral boundary conditions (or mpp link) USE lib_mpp ! MPP library IMPLICIT NONE PRIVATE REAL(wp), PARAMETER :: gamma1 = 1._wp/3._wp ! =1/4 quick ; =1/3 3rd order UBS REAL(wp), PARAMETER :: gamma2 = 1._wp/32._wp ! =0 2nd order ; =1/32 4th order centred PUBLIC dyn_adv_ubs ! routine called by step.F90 !! * Substitutions # include "vectopt_loop_substitute.h90" !!---------------------------------------------------------------------- !! NEMO/OCE 4.0 , NEMO Consortium (2018) !! $Id$ !! Software governed by the CeCILL license (see ./LICENSE) !!---------------------------------------------------------------------- CONTAINS SUBROUTINE dyn_adv_ubs( kt ) !!---------------------------------------------------------------------- !! *** ROUTINE dyn_adv_ubs *** !! !! ** Purpose : Compute the now momentum advection trend in flux form !! and the general trend of the momentum equation. !! !! ** Method : The scheme is the one implemeted in ROMS. It depends !! on two parameter gamma1 and gamma2. The former control the !! upstream baised part of the scheme and the later the centred !! part: gamma1 = 0 pure centered (no diffusive part) !! = 1/4 Quick scheme !! = 1/3 3rd order Upstream biased scheme !! gamma2 = 0 2nd order finite differencing !! = 1/32 4th order finite differencing !! For stability reasons, the first term of the fluxes which cor- !! responds to a second order centered scheme is evaluated using !! the now velocity (centered in time) while the second term which !! is the diffusive part of the scheme, is evaluated using the !! before velocity (forward in time). !! Default value (hard coded in the begining of the module) are !! gamma1=1/3 and gamma2=1/32. !! !! ** Action : - (ua,va) updated with the 3D advective momentum trends !! !! Reference : Shchepetkin & McWilliams, 2005, Ocean Modelling. !!---------------------------------------------------------------------- INTEGER, INTENT(in) :: kt ! ocean time-step index ! INTEGER :: ji, jj, jk ! dummy loop indices REAL(wp) :: zui, zvj, zfuj, zfvi, zl_u, zl_v ! local scalars REAL(wp), DIMENSION(jpi,jpj,jpk) :: zfu_t, zfu_f, zfu_uw, zfu REAL(wp), DIMENSION(jpi,jpj,jpk) :: zfv_t, zfv_f, zfv_vw, zfv, zfw REAL(wp), DIMENSION(jpi,jpj,jpk,2) :: zlu_uu, zlu_uv REAL(wp), DIMENSION(jpi,jpj,jpk,2) :: zlv_vv, zlv_vu !!---------------------------------------------------------------------- ! IF( kt == nit000 ) THEN IF(lwp) WRITE(numout,*) IF(lwp) WRITE(numout,*) 'dyn_adv_ubs : UBS flux form momentum advection' IF(lwp) WRITE(numout,*) '~~~~~~~~~~~' ENDIF ! zfu_t(:,:,:) = 0._wp zfv_t(:,:,:) = 0._wp zfu_f(:,:,:) = 0._wp zfv_f(:,:,:) = 0._wp ! zlu_uu(:,:,:,:) = 0._wp zlv_vv(:,:,:,:) = 0._wp zlu_uv(:,:,:,:) = 0._wp zlv_vu(:,:,:,:) = 0._wp ! IF( l_trddyn ) THEN ! trends: store the input trends zfu_uw(:,:,:) = ua(:,:,:) zfv_vw(:,:,:) = va(:,:,:) ENDIF ! ! =========================== ! DO jk = 1, jpkm1 ! Laplacian of the velocity ! ! ! =========================== ! ! ! horizontal volume fluxes zfu(:,:,jk) = e2u(:,:) * e3u_n(:,:,jk) * un(:,:,jk) zfv(:,:,jk) = e1v(:,:) * e3v_n(:,:,jk) * vn(:,:,jk) ! DO jj = 2, jpjm1 ! laplacian DO ji = fs_2, fs_jpim1 ! vector opt. zlu_uu(ji,jj,jk,1) = ( ub (ji+1,jj ,jk) - 2.*ub (ji,jj,jk) + ub (ji-1,jj ,jk) ) * umask(ji,jj,jk) zlv_vv(ji,jj,jk,1) = ( vb (ji ,jj+1,jk) - 2.*vb (ji,jj,jk) + vb (ji ,jj-1,jk) ) * vmask(ji,jj,jk) zlu_uv(ji,jj,jk,1) = ( ub (ji ,jj+1,jk) - ub (ji ,jj ,jk) ) * fmask(ji ,jj ,jk) & & - ( ub (ji ,jj ,jk) - ub (ji ,jj-1,jk) ) * fmask(ji ,jj-1,jk) zlv_vu(ji,jj,jk,1) = ( vb (ji+1,jj ,jk) - vb (ji ,jj ,jk) ) * fmask(ji ,jj ,jk) & & - ( vb (ji ,jj ,jk) - vb (ji-1,jj ,jk) ) * fmask(ji-1,jj ,jk) ! zlu_uu(ji,jj,jk,2) = ( zfu(ji+1,jj ,jk) - 2.*zfu(ji,jj,jk) + zfu(ji-1,jj ,jk) ) * umask(ji,jj,jk) zlv_vv(ji,jj,jk,2) = ( zfv(ji ,jj+1,jk) - 2.*zfv(ji,jj,jk) + zfv(ji ,jj-1,jk) ) * vmask(ji,jj,jk) zlu_uv(ji,jj,jk,2) = ( zfu(ji ,jj+1,jk) - zfu(ji ,jj ,jk) ) * fmask(ji ,jj ,jk) & & - ( zfu(ji ,jj ,jk) - zfu(ji ,jj-1,jk) ) * fmask(ji ,jj-1,jk) zlv_vu(ji,jj,jk,2) = ( zfv(ji+1,jj ,jk) - zfv(ji ,jj ,jk) ) * fmask(ji ,jj ,jk) & & - ( zfv(ji ,jj ,jk) - zfv(ji-1,jj ,jk) ) * fmask(ji-1,jj ,jk) END DO END DO END DO CALL lbc_lnk_multi( 'dynadv_ubs', zlu_uu(:,:,:,1), 'U', 1. , zlu_uv(:,:,:,1), 'U', 1., & & zlu_uu(:,:,:,2), 'U', 1. , zlu_uv(:,:,:,2), 'U', 1., & & zlv_vv(:,:,:,1), 'V', 1. , zlv_vu(:,:,:,1), 'V', 1., & & zlv_vv(:,:,:,2), 'V', 1. , zlv_vu(:,:,:,2), 'V', 1. ) ! ! ! ====================== ! ! ! Horizontal advection ! DO jk = 1, jpkm1 ! ====================== ! ! ! horizontal volume fluxes zfu(:,:,jk) = 0.25_wp * e2u(:,:) * e3u_n(:,:,jk) * un(:,:,jk) zfv(:,:,jk) = 0.25_wp * e1v(:,:) * e3v_n(:,:,jk) * vn(:,:,jk) ! DO jj = 1, jpjm1 ! horizontal momentum fluxes at T- and F-point DO ji = 1, fs_jpim1 ! vector opt. zui = ( un(ji,jj,jk) + un(ji+1,jj ,jk) ) zvj = ( vn(ji,jj,jk) + vn(ji ,jj+1,jk) ) ! IF( zui > 0 ) THEN ; zl_u = zlu_uu(ji ,jj,jk,1) ELSE ; zl_u = zlu_uu(ji+1,jj,jk,1) ENDIF IF( zvj > 0 ) THEN ; zl_v = zlv_vv(ji,jj ,jk,1) ELSE ; zl_v = zlv_vv(ji,jj+1,jk,1) ENDIF ! zfu_t(ji+1,jj ,jk) = ( zfu(ji,jj,jk) + zfu(ji+1,jj ,jk) & & - gamma2 * ( zlu_uu(ji,jj,jk,2) + zlu_uu(ji+1,jj ,jk,2) ) ) & & * ( zui - gamma1 * zl_u) zfv_t(ji ,jj+1,jk) = ( zfv(ji,jj,jk) + zfv(ji ,jj+1,jk) & & - gamma2 * ( zlv_vv(ji,jj,jk,2) + zlv_vv(ji ,jj+1,jk,2) ) ) & & * ( zvj - gamma1 * zl_v) ! zfuj = ( zfu(ji,jj,jk) + zfu(ji ,jj+1,jk) ) zfvi = ( zfv(ji,jj,jk) + zfv(ji+1,jj ,jk) ) IF( zfuj > 0 ) THEN ; zl_v = zlv_vu( ji ,jj ,jk,1) ELSE ; zl_v = zlv_vu( ji+1,jj,jk,1) ENDIF IF( zfvi > 0 ) THEN ; zl_u = zlu_uv( ji,jj ,jk,1) ELSE ; zl_u = zlu_uv( ji,jj+1,jk,1) ENDIF ! zfv_f(ji ,jj ,jk) = ( zfvi - gamma2 * ( zlv_vu(ji,jj,jk,2) + zlv_vu(ji+1,jj ,jk,2) ) ) & & * ( un(ji,jj,jk) + un(ji ,jj+1,jk) - gamma1 * zl_u ) zfu_f(ji ,jj ,jk) = ( zfuj - gamma2 * ( zlu_uv(ji,jj,jk,2) + zlu_uv(ji ,jj+1,jk,2) ) ) & & * ( vn(ji,jj,jk) + vn(ji+1,jj ,jk) - gamma1 * zl_v ) END DO END DO DO jj = 2, jpjm1 ! divergence of horizontal momentum fluxes DO ji = fs_2, fs_jpim1 ! vector opt. ua(ji,jj,jk) = ua(ji,jj,jk) - ( zfu_t(ji+1,jj,jk) - zfu_t(ji,jj ,jk) & & + zfv_f(ji ,jj,jk) - zfv_f(ji,jj-1,jk) ) * r1_e1e2u(ji,jj) / e3u_n(ji,jj,jk) va(ji,jj,jk) = va(ji,jj,jk) - ( zfu_f(ji,jj ,jk) - zfu_f(ji-1,jj,jk) & & + zfv_t(ji,jj+1,jk) - zfv_t(ji ,jj,jk) ) * r1_e1e2v(ji,jj) / e3v_n(ji,jj,jk) END DO END DO END DO IF( l_trddyn ) THEN ! trends: send trends to trddyn for diagnostic zfu_uw(:,:,:) = ua(:,:,:) - zfu_uw(:,:,:) zfv_vw(:,:,:) = va(:,:,:) - zfv_vw(:,:,:) CALL trd_dyn( zfu_uw, zfv_vw, jpdyn_keg, kt ) zfu_t(:,:,:) = ua(:,:,:) zfv_t(:,:,:) = va(:,:,:) ENDIF ! ! ==================== ! ! ! Vertical advection ! ! ! ==================== ! DO jj = 2, jpjm1 ! surface/bottom advective fluxes set to zero DO ji = fs_2, fs_jpim1 zfu_uw(ji,jj,jpk) = 0._wp zfv_vw(ji,jj,jpk) = 0._wp zfu_uw(ji,jj, 1 ) = 0._wp zfv_vw(ji,jj, 1 ) = 0._wp END DO END DO IF( ln_linssh ) THEN ! constant volume : advection through the surface DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 zfu_uw(ji,jj,1) = 0.5_wp * ( e1e2t(ji,jj) * wn(ji,jj,1) + e1e2t(ji+1,jj) * wn(ji+1,jj,1) ) * un(ji,jj,1) zfv_vw(ji,jj,1) = 0.5_wp * ( e1e2t(ji,jj) * wn(ji,jj,1) + e1e2t(ji,jj+1) * wn(ji,jj+1,1) ) * vn(ji,jj,1) END DO END DO ENDIF DO jk = 2, jpkm1 ! interior fluxes DO jj = 2, jpj DO ji = 2, jpi zfw(ji,jj,jk) = 0.25_wp * e1e2t(ji,jj) * wn(ji,jj,jk) END DO END DO 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 END DO DO jk = 1, jpkm1 ! divergence of vertical momentum flux divergence DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. ua(ji,jj,jk) = ua(ji,jj,jk) - ( zfu_uw(ji,jj,jk) - zfu_uw(ji,jj,jk+1) ) * r1_e1e2u(ji,jj) / e3u_n(ji,jj,jk) va(ji,jj,jk) = va(ji,jj,jk) - ( zfv_vw(ji,jj,jk) - zfv_vw(ji,jj,jk+1) ) * r1_e1e2v(ji,jj) / e3v_n(ji,jj,jk) END DO END DO END DO ! IF( l_trddyn ) THEN ! save the vertical advection trend for diagnostic zfu_t(:,:,:) = ua(:,:,:) - zfu_t(:,:,:) zfv_t(:,:,:) = va(:,:,:) - zfv_t(:,:,:) CALL trd_dyn( zfu_t, zfv_t, jpdyn_zad, kt ) ENDIF ! ! Control print IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' ubs2 adv - Ua: ', mask1=umask, & & tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' ) ! END SUBROUTINE dyn_adv_ubs !!============================================================================== END MODULE dynadv_ubs