[643] | 1 | MODULE dynadv_ubs |
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| 2 | !!====================================================================== |
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| 3 | !! *** MODULE dynadv_ubs *** |
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| 4 | !! Ocean dynamics: Update the momentum trend with the flux form advection |
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| 5 | !! trend using a 3rd order upstream biased scheme |
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| 6 | !!====================================================================== |
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[1566] | 7 | !! History : 2.0 ! 2006-08 (R. Benshila, L. Debreu) Original code |
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| 8 | !! 3.2 ! 2009-07 (R. Benshila) Suppression of rigid-lid option |
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[643] | 9 | !!---------------------------------------------------------------------- |
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| 10 | |
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| 11 | !!---------------------------------------------------------------------- |
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| 12 | !! dyn_adv_ubs : flux form momentum advection using (ln_dynadv=T) |
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| 13 | !! an 3rd order Upstream Biased Scheme or Quick scheme |
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| 14 | !! combined with 2nd or 4th order finite differences |
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| 15 | !!---------------------------------------------------------------------- |
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| 16 | USE oce ! ocean dynamics and tracers |
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| 17 | USE dom_oce ! ocean space and time domain |
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[5062] | 18 | USE trd_oce ! trends: ocean variables |
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| 19 | USE trddyn ! trend manager: dynamics |
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| 20 | ! |
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[2715] | 21 | USE in_out_manager ! I/O manager |
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[1129] | 22 | USE prtctl ! Print control |
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[2715] | 23 | USE lbclnk ! ocean lateral boundary conditions (or mpp link) |
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| 24 | USE lib_mpp ! MPP library |
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[643] | 25 | |
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| 26 | IMPLICIT NONE |
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| 27 | PRIVATE |
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| 28 | |
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[3294] | 29 | REAL(wp), PARAMETER :: gamma1 = 1._wp/3._wp ! =1/4 quick ; =1/3 3rd order UBS |
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[4153] | 30 | REAL(wp), PARAMETER :: gamma2 = 1._wp/32._wp ! =0 2nd order ; =1/32 4th order centred |
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[643] | 31 | |
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[1566] | 32 | PUBLIC dyn_adv_ubs ! routine called by step.F90 |
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[643] | 33 | |
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| 34 | !! * Substitutions |
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| 35 | # include "vectopt_loop_substitute.h90" |
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| 36 | !!---------------------------------------------------------------------- |
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[9598] | 37 | !! NEMO/OCE 4.0 , NEMO Consortium (2018) |
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[1152] | 38 | !! $Id$ |
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[10068] | 39 | !! Software governed by the CeCILL license (see ./LICENSE) |
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[643] | 40 | !!---------------------------------------------------------------------- |
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| 41 | CONTAINS |
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| 42 | |
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[10789] | 43 | SUBROUTINE dyn_adv_ubs( kt, ktlev1, ktlev2, pu_rhs, pv_rhs ) |
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[643] | 44 | !!---------------------------------------------------------------------- |
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| 45 | !! *** ROUTINE dyn_adv_ubs *** |
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| 46 | !! |
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| 47 | !! ** Purpose : Compute the now momentum advection trend in flux form |
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[1566] | 48 | !! and the general trend of the momentum equation. |
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[643] | 49 | !! |
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| 50 | !! ** Method : The scheme is the one implemeted in ROMS. It depends |
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| 51 | !! on two parameter gamma1 and gamma2. The former control the |
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| 52 | !! upstream baised part of the scheme and the later the centred |
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| 53 | !! part: gamma1 = 0 pure centered (no diffusive part) |
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| 54 | !! = 1/4 Quick scheme |
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| 55 | !! = 1/3 3rd order Upstream biased scheme |
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| 56 | !! gamma2 = 0 2nd order finite differencing |
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[4153] | 57 | !! = 1/32 4th order finite differencing |
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[643] | 58 | !! For stability reasons, the first term of the fluxes which cor- |
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| 59 | !! responds to a second order centered scheme is evaluated using |
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| 60 | !! the now velocity (centered in time) while the second term which |
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| 61 | !! is the diffusive part of the scheme, is evaluated using the |
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| 62 | !! before velocity (forward in time). |
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| 63 | !! Default value (hard coded in the begining of the module) are |
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[4153] | 64 | !! gamma1=1/3 and gamma2=1/32. |
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[643] | 65 | !! |
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[10789] | 66 | !! ** Action : - (pu_rhs,pv_rhs) updated with the 3D advective momentum trends |
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[643] | 67 | !! |
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| 68 | !! Reference : Shchepetkin & McWilliams, 2005, Ocean Modelling. |
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| 69 | !!---------------------------------------------------------------------- |
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[10789] | 70 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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| 71 | INTEGER, INTENT(in) :: ktlev1, ktlev2 ! time level indices for source terms |
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| 72 | REAL(wp), INTENT(inout), DIMENSION(jpi,jpj,jpk) :: pu_rhs, pv_rhs ! momentum trends |
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[2715] | 73 | ! |
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[6140] | 74 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 75 | REAL(wp) :: zui, zvj, zfuj, zfvi, zl_u, zl_v ! local scalars |
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[9019] | 76 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zfu_t, zfu_f, zfu_uw, zfu |
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| 77 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zfv_t, zfv_f, zfv_vw, zfv, zfw |
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| 78 | REAL(wp), DIMENSION(jpi,jpj,jpk,2) :: zlu_uu, zlu_uv |
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| 79 | REAL(wp), DIMENSION(jpi,jpj,jpk,2) :: zlv_vv, zlv_vu |
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[643] | 80 | !!---------------------------------------------------------------------- |
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[3294] | 81 | ! |
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[643] | 82 | IF( kt == nit000 ) THEN |
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| 83 | IF(lwp) WRITE(numout,*) |
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| 84 | IF(lwp) WRITE(numout,*) 'dyn_adv_ubs : UBS flux form momentum advection' |
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| 85 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~' |
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| 86 | ENDIF |
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[3294] | 87 | ! |
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[2715] | 88 | zfu_t(:,:,:) = 0._wp |
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| 89 | zfv_t(:,:,:) = 0._wp |
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| 90 | zfu_f(:,:,:) = 0._wp |
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| 91 | zfv_f(:,:,:) = 0._wp |
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[1566] | 92 | ! |
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[2715] | 93 | zlu_uu(:,:,:,:) = 0._wp |
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| 94 | zlv_vv(:,:,:,:) = 0._wp |
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| 95 | zlu_uv(:,:,:,:) = 0._wp |
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| 96 | zlv_vu(:,:,:,:) = 0._wp |
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[6140] | 97 | ! |
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| 98 | IF( l_trddyn ) THEN ! trends: store the input trends |
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[10789] | 99 | zfu_uw(:,:,:) = pu_rhs(:,:,:) |
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| 100 | zfv_vw(:,:,:) = pv_rhs(:,:,:) |
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[1129] | 101 | ENDIF |
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[1566] | 102 | ! ! =========================== ! |
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| 103 | DO jk = 1, jpkm1 ! Laplacian of the velocity ! |
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| 104 | ! ! =========================== ! |
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| 105 | ! ! horizontal volume fluxes |
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[10789] | 106 | zfu(:,:,jk) = e2u(:,:) * e3u(:,:,jk,ktlev2) * uu(:,:,jk,ktlev2) |
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| 107 | zfv(:,:,jk) = e1v(:,:) * e3v(:,:,jk,ktlev2) * vv(:,:,jk,ktlev2) |
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[1566] | 108 | ! |
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| 109 | DO jj = 2, jpjm1 ! laplacian |
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[643] | 110 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[10789] | 111 | zlu_uu(ji,jj,jk,1) = ( uu (ji+1,jj ,jk,ktlev1) - 2.*uu (ji,jj,jk,ktlev1) + uu (ji-1,jj ,jk,ktlev1) ) * umask(ji,jj,jk) |
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| 112 | zlv_vv(ji,jj,jk,1) = ( vv (ji ,jj+1,jk,ktlev1) - 2.*vv (ji,jj,jk,ktlev1) + vv (ji ,jj-1,jk,ktlev1) ) * vmask(ji,jj,jk) |
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| 113 | zlu_uv(ji,jj,jk,1) = ( uu (ji ,jj+1,jk,ktlev1) - uu (ji ,jj ,jk,ktlev1) ) * fmask(ji ,jj ,jk) & |
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| 114 | & - ( uu (ji ,jj ,jk,ktlev1) - uu (ji ,jj-1,jk,ktlev1) ) * fmask(ji ,jj-1,jk) |
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| 115 | zlv_vu(ji,jj,jk,1) = ( vv (ji+1,jj ,jk,ktlev1) - vv (ji ,jj ,jk,ktlev1) ) * fmask(ji ,jj ,jk) & |
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| 116 | & - ( vv (ji ,jj ,jk,ktlev1) - vv (ji-1,jj ,jk,ktlev1) ) * fmask(ji-1,jj ,jk) |
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[2715] | 117 | ! |
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[5069] | 118 | 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) |
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| 119 | 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) |
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| 120 | zlu_uv(ji,jj,jk,2) = ( zfu(ji ,jj+1,jk) - zfu(ji ,jj ,jk) ) * fmask(ji ,jj ,jk) & |
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| 121 | & - ( zfu(ji ,jj ,jk) - zfu(ji ,jj-1,jk) ) * fmask(ji ,jj-1,jk) |
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| 122 | zlv_vu(ji,jj,jk,2) = ( zfv(ji+1,jj ,jk) - zfv(ji ,jj ,jk) ) * fmask(ji ,jj ,jk) & |
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| 123 | & - ( zfv(ji ,jj ,jk) - zfv(ji-1,jj ,jk) ) * fmask(ji-1,jj ,jk) |
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[643] | 124 | END DO |
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| 125 | END DO |
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[1566] | 126 | END DO |
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[10425] | 127 | CALL lbc_lnk_multi( 'dynadv_ubs', zlu_uu(:,:,:,1), 'U', 1. , zlu_uv(:,:,:,1), 'U', 1., & |
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[9090] | 128 | & zlu_uu(:,:,:,2), 'U', 1. , zlu_uv(:,:,:,2), 'U', 1., & |
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| 129 | & zlv_vv(:,:,:,1), 'V', 1. , zlv_vu(:,:,:,1), 'V', 1., & |
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| 130 | & zlv_vv(:,:,:,2), 'V', 1. , zlv_vu(:,:,:,2), 'V', 1. ) |
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[6140] | 131 | ! |
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[1566] | 132 | ! ! ====================== ! |
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| 133 | ! ! Horizontal advection ! |
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| 134 | DO jk = 1, jpkm1 ! ====================== ! |
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| 135 | ! ! horizontal volume fluxes |
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[10789] | 136 | zfu(:,:,jk) = 0.25_wp * e2u(:,:) * e3u(:,:,jk,ktlev2) * uu(:,:,jk,ktlev2) |
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| 137 | zfv(:,:,jk) = 0.25_wp * e1v(:,:) * e3v(:,:,jk,ktlev2) * vv(:,:,jk,ktlev2) |
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[1566] | 138 | ! |
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| 139 | DO jj = 1, jpjm1 ! horizontal momentum fluxes at T- and F-point |
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[643] | 140 | DO ji = 1, fs_jpim1 ! vector opt. |
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[10789] | 141 | zui = ( uu(ji,jj,jk,ktlev2) + uu(ji+1,jj ,jk,ktlev2) ) |
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| 142 | zvj = ( vv(ji,jj,jk,ktlev2) + vv(ji ,jj+1,jk,ktlev2) ) |
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[1566] | 143 | ! |
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[6140] | 144 | IF( zui > 0 ) THEN ; zl_u = zlu_uu(ji ,jj,jk,1) |
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| 145 | ELSE ; zl_u = zlu_uu(ji+1,jj,jk,1) |
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[643] | 146 | ENDIF |
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[6140] | 147 | IF( zvj > 0 ) THEN ; zl_v = zlv_vv(ji,jj ,jk,1) |
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| 148 | ELSE ; zl_v = zlv_vv(ji,jj+1,jk,1) |
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[643] | 149 | ENDIF |
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[1566] | 150 | ! |
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[643] | 151 | zfu_t(ji+1,jj ,jk) = ( zfu(ji,jj,jk) + zfu(ji+1,jj ,jk) & |
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| 152 | & - gamma2 * ( zlu_uu(ji,jj,jk,2) + zlu_uu(ji+1,jj ,jk,2) ) ) & |
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| 153 | & * ( zui - gamma1 * zl_u) |
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| 154 | zfv_t(ji ,jj+1,jk) = ( zfv(ji,jj,jk) + zfv(ji ,jj+1,jk) & |
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| 155 | & - gamma2 * ( zlv_vv(ji,jj,jk,2) + zlv_vv(ji ,jj+1,jk,2) ) ) & |
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| 156 | & * ( zvj - gamma1 * zl_v) |
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[1566] | 157 | ! |
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[643] | 158 | zfuj = ( zfu(ji,jj,jk) + zfu(ji ,jj+1,jk) ) |
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| 159 | zfvi = ( zfv(ji,jj,jk) + zfv(ji+1,jj ,jk) ) |
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[6140] | 160 | IF( zfuj > 0 ) THEN ; zl_v = zlv_vu( ji ,jj ,jk,1) |
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| 161 | ELSE ; zl_v = zlv_vu( ji+1,jj,jk,1) |
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[643] | 162 | ENDIF |
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[6140] | 163 | IF( zfvi > 0 ) THEN ; zl_u = zlu_uv( ji,jj ,jk,1) |
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| 164 | ELSE ; zl_u = zlu_uv( ji,jj+1,jk,1) |
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[643] | 165 | ENDIF |
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[1566] | 166 | ! |
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[643] | 167 | zfv_f(ji ,jj ,jk) = ( zfvi - gamma2 * ( zlv_vu(ji,jj,jk,2) + zlv_vu(ji+1,jj ,jk,2) ) ) & |
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[10789] | 168 | & * ( uu(ji,jj,jk,ktlev2) + uu(ji ,jj+1,jk,ktlev2) - gamma1 * zl_u ) |
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[643] | 169 | zfu_f(ji ,jj ,jk) = ( zfuj - gamma2 * ( zlu_uv(ji,jj,jk,2) + zlu_uv(ji ,jj+1,jk,2) ) ) & |
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[10789] | 170 | & * ( vv(ji,jj,jk,ktlev2) + vv(ji+1,jj ,jk,ktlev2) - gamma1 * zl_v ) |
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[643] | 171 | END DO |
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| 172 | END DO |
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[1566] | 173 | DO jj = 2, jpjm1 ! divergence of horizontal momentum fluxes |
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[643] | 174 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[10789] | 175 | pu_rhs(ji,jj,jk) = pu_rhs(ji,jj,jk) - ( zfu_t(ji+1,jj,jk) - zfu_t(ji,jj ,jk) & |
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| 176 | & + zfv_f(ji ,jj,jk) - zfv_f(ji,jj-1,jk) ) * r1_e1e2u(ji,jj) / e3u(ji,jj,jk,ktlev2) |
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| 177 | pv_rhs(ji,jj,jk) = pv_rhs(ji,jj,jk) - ( zfu_f(ji,jj ,jk) - zfu_f(ji-1,jj,jk) & |
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| 178 | & + zfv_t(ji,jj+1,jk) - zfv_t(ji ,jj,jk) ) * r1_e1e2v(ji,jj) / e3v(ji,jj,jk,ktlev2) |
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[643] | 179 | END DO |
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| 180 | END DO |
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[1566] | 181 | END DO |
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[6140] | 182 | IF( l_trddyn ) THEN ! trends: send trends to trddyn for diagnostic |
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[10789] | 183 | zfu_uw(:,:,:) = pu_rhs(:,:,:) - zfu_uw(:,:,:) |
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| 184 | zfv_vw(:,:,:) = pv_rhs(:,:,:) - zfv_vw(:,:,:) |
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[5062] | 185 | CALL trd_dyn( zfu_uw, zfv_vw, jpdyn_keg, kt ) |
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[10789] | 186 | zfu_t(:,:,:) = pu_rhs(:,:,:) |
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| 187 | zfv_t(:,:,:) = pv_rhs(:,:,:) |
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[1129] | 188 | ENDIF |
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[1566] | 189 | ! ! ==================== ! |
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| 190 | ! ! Vertical advection ! |
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[6140] | 191 | ! ! ==================== ! |
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| 192 | DO jj = 2, jpjm1 ! surface/bottom advective fluxes set to zero |
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| 193 | DO ji = fs_2, fs_jpim1 |
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| 194 | zfu_uw(ji,jj,jpk) = 0._wp |
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| 195 | zfv_vw(ji,jj,jpk) = 0._wp |
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| 196 | zfu_uw(ji,jj, 1 ) = 0._wp |
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| 197 | zfv_vw(ji,jj, 1 ) = 0._wp |
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| 198 | END DO |
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| 199 | END DO |
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| 200 | IF( ln_linssh ) THEN ! constant volume : advection through the surface |
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| 201 | DO jj = 2, jpjm1 |
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| 202 | DO ji = fs_2, fs_jpim1 |
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[10789] | 203 | zfu_uw(ji,jj,1) = 0.5_wp * ( e1e2t(ji,jj) * ww(ji,jj,1) + e1e2t(ji+1,jj) * ww(ji+1,jj,1) ) * uu(ji,jj,1,ktlev2) |
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| 204 | zfv_vw(ji,jj,1) = 0.5_wp * ( e1e2t(ji,jj) * ww(ji,jj,1) + e1e2t(ji,jj+1) * ww(ji,jj+1,1) ) * vv(ji,jj,1,ktlev2) |
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[643] | 205 | END DO |
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[6140] | 206 | END DO |
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| 207 | ENDIF |
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| 208 | DO jk = 2, jpkm1 ! interior fluxes |
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[6750] | 209 | DO jj = 2, jpj |
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| 210 | DO ji = 2, jpi |
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[10789] | 211 | zfw(ji,jj,jk) = 0.25_wp * e1e2t(ji,jj) * ww(ji,jj,jk) |
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[6140] | 212 | END DO |
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| 213 | END DO |
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| 214 | DO jj = 2, jpjm1 |
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| 215 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[10789] | 216 | zfu_uw(ji,jj,jk) = ( zfw(ji,jj,jk)+ zfw(ji+1,jj,jk) ) * ( uu(ji,jj,jk,ktlev2) + uu(ji,jj,jk-1,ktlev2) ) |
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| 217 | zfv_vw(ji,jj,jk) = ( zfw(ji,jj,jk)+ zfw(ji,jj+1,jk) ) * ( vv(ji,jj,jk,ktlev2) + vv(ji,jj,jk-1,ktlev2) ) |
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[6140] | 218 | END DO |
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| 219 | END DO |
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[643] | 220 | END DO |
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[6140] | 221 | DO jk = 1, jpkm1 ! divergence of vertical momentum flux divergence |
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| 222 | DO jj = 2, jpjm1 |
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[643] | 223 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[10789] | 224 | pu_rhs(ji,jj,jk) = pu_rhs(ji,jj,jk) - ( zfu_uw(ji,jj,jk) - zfu_uw(ji,jj,jk+1) ) * r1_e1e2u(ji,jj) / e3u(ji,jj,jk,ktlev2) |
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| 225 | pv_rhs(ji,jj,jk) = pv_rhs(ji,jj,jk) - ( zfv_vw(ji,jj,jk) - zfv_vw(ji,jj,jk+1) ) * r1_e1e2v(ji,jj) / e3v(ji,jj,jk,ktlev2) |
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[643] | 226 | END DO |
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| 227 | END DO |
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| 228 | END DO |
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[1566] | 229 | ! |
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[6140] | 230 | IF( l_trddyn ) THEN ! save the vertical advection trend for diagnostic |
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[10789] | 231 | zfu_t(:,:,:) = pu_rhs(:,:,:) - zfu_t(:,:,:) |
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| 232 | zfv_t(:,:,:) = pv_rhs(:,:,:) - zfv_t(:,:,:) |
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[5062] | 233 | CALL trd_dyn( zfu_t, zfv_t, jpdyn_zad, kt ) |
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[1129] | 234 | ENDIF |
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[6140] | 235 | ! ! Control print |
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[10802] | 236 | IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' ubs2 adv - Ua: ', mask1=umask, & |
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[1129] | 237 | & tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' ) |
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[1566] | 238 | ! |
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[643] | 239 | END SUBROUTINE dyn_adv_ubs |
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| 240 | |
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| 241 | !!============================================================================== |
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| 242 | END MODULE dynadv_ubs |
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