[3] | 1 | MODULE dynldf_bilap |
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| 2 | !!====================================================================== |
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| 3 | !! *** MODULE dynldf_bilap *** |
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| 4 | !! Ocean dynamics: lateral viscosity trend |
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| 5 | !!====================================================================== |
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[2715] | 6 | !! History : OPA ! 1990-09 (G. Madec) Original code |
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| 7 | !! 4.0 ! 1993-03 (M. Guyon) symetrical conditions (M. Guyon) |
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| 8 | !! 6.0 ! 1996-01 (G. Madec) statement function for e3 |
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| 9 | !! 8.0 ! 1997-07 (G. Madec) lbc calls |
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| 10 | !! NEMO 1.0 ! 2002-08 (G. Madec) F90: Free form and module |
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| 11 | !! 2.0 ! 2004-08 (C. Talandier) New trends organization |
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| 12 | !!---------------------------------------------------------------------- |
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[3] | 13 | |
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| 14 | !!---------------------------------------------------------------------- |
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| 15 | !! dyn_ldf_bilap : update the momentum trend with the lateral diffusion |
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| 16 | !! using an iso-level bilaplacian operator |
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| 17 | !!---------------------------------------------------------------------- |
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| 18 | USE oce ! ocean dynamics and tracers |
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| 19 | USE dom_oce ! ocean space and time domain |
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[10115] | 20 | USE phycst ! physical constants |
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[3] | 21 | USE ldfdyn_oce ! ocean dynamics: lateral physics |
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[4990] | 22 | ! |
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[3] | 23 | USE in_out_manager ! I/O manager |
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[10115] | 24 | USE iom ! I/O library |
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[3] | 25 | USE lbclnk ! ocean lateral boundary conditions (or mpp link) |
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[3294] | 26 | USE wrk_nemo ! Memory Allocation |
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| 27 | USE timing ! Timing |
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[3] | 28 | |
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| 29 | IMPLICIT NONE |
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| 30 | PRIVATE |
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| 31 | |
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[2715] | 32 | PUBLIC dyn_ldf_bilap ! called by step.F90 |
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[3] | 33 | |
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| 34 | !! * Substitutions |
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| 35 | # include "domzgr_substitute.h90" |
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| 36 | # include "ldfdyn_substitute.h90" |
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| 37 | # include "vectopt_loop_substitute.h90" |
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| 38 | !!---------------------------------------------------------------------- |
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[2528] | 39 | !! NEMO/OPA 3.3 , NEMO Consortium (2010) |
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[1152] | 40 | !! $Id$ |
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[2715] | 41 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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[3] | 42 | !!---------------------------------------------------------------------- |
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| 43 | CONTAINS |
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| 44 | |
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| 45 | SUBROUTINE dyn_ldf_bilap( kt ) |
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| 46 | !!---------------------------------------------------------------------- |
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| 47 | !! *** ROUTINE dyn_ldf_bilap *** |
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| 48 | !! |
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| 49 | !! ** Purpose : Compute the before trend of the lateral momentum |
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| 50 | !! diffusion and add it to the general trend of momentum equation. |
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| 51 | !! |
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| 52 | !! ** Method : The before horizontal momentum diffusion trend is a |
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| 53 | !! bi-harmonic operator (bilaplacian type) which separates the |
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| 54 | !! divergent and rotational parts of the flow. |
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| 55 | !! Its horizontal components are computed as follow: |
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| 56 | !! laplacian: |
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| 57 | !! zlu = 1/e1u di[ hdivb ] - 1/(e2u*e3u) dj-1[ e3f rotb ] |
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| 58 | !! zlv = 1/e2v dj[ hdivb ] + 1/(e1v*e3v) di-1[ e3f rotb ] |
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| 59 | !! third derivative: |
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| 60 | !! * multiply by the eddy viscosity coef. at u-, v-point, resp. |
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| 61 | !! zlu = ahmu * zlu |
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| 62 | !! zlv = ahmv * zlv |
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| 63 | !! * curl and divergence of the laplacian |
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| 64 | !! zuf = 1/(e1f*e2f) ( di[e2v zlv] - dj[e1u zlu] ) |
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| 65 | !! zut = 1/(e1t*e2t*e3t) ( di[e2u*e3u zlu] + dj[e1v*e3v zlv] ) |
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| 66 | !! bilaplacian: |
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| 67 | !! diffu = 1/e1u di[ zut ] - 1/(e2u*e3u) dj-1[ e3f zuf ] |
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| 68 | !! diffv = 1/e2v dj[ zut ] + 1/(e1v*e3v) di-1[ e3f zuf ] |
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[455] | 69 | !! If ln_sco=F and ln_zps=F, the vertical scale factors in the |
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[3] | 70 | !! rotational part of the diffusion are simplified |
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| 71 | !! Add this before trend to the general trend (ua,va): |
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| 72 | !! (ua,va) = (ua,va) + (diffu,diffv) |
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| 73 | !! |
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| 74 | !! ** Action : - Update (ua,va) with the before iso-level biharmonic |
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| 75 | !! mixing trend. |
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| 76 | !!---------------------------------------------------------------------- |
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[2715] | 77 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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| 78 | ! |
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[10115] | 79 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 80 | REAL(wp) :: zua, zva, zbt, ze2u, ze2v, zzz ! local scalar |
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| 81 | REAL(wp), POINTER, DIMENSION(:,: ) :: zcu, zcv |
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| 82 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zuf, zut, zlu, zlv |
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| 83 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: z2d ! 2D workspace |
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[3] | 84 | !!---------------------------------------------------------------------- |
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[3294] | 85 | ! |
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| 86 | IF( nn_timing == 1 ) CALL timing_start('dyn_ldf_bilap') |
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| 87 | ! |
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| 88 | CALL wrk_alloc( jpi, jpj, zcu, zcv ) |
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| 89 | CALL wrk_alloc( jpi, jpj, jpk, zuf, zut, zlu, zlv ) |
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| 90 | ! |
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[2715] | 91 | IF( kt == nit000 .AND. lwp ) THEN |
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| 92 | WRITE(numout,*) |
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| 93 | WRITE(numout,*) 'dyn_ldf_bilap : iso-level bilaplacian operator' |
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| 94 | WRITE(numout,*) '~~~~~~~~~~~~~' |
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| 95 | ENDIF |
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| 96 | |
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[474] | 97 | !!bug gm this should be enough |
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| 98 | !!$ zuf(:,:,jpk) = 0.e0 |
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| 99 | !!$ zut(:,:,jpk) = 0.e0 |
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| 100 | !!$ zlu(:,:,jpk) = 0.e0 |
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| 101 | !!$ zlv(:,:,jpk) = 0.e0 |
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[2715] | 102 | zuf(:,:,:) = 0._wp |
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| 103 | zut(:,:,:) = 0._wp |
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| 104 | zlu(:,:,:) = 0._wp |
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| 105 | zlv(:,:,:) = 0._wp |
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[474] | 106 | |
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[3] | 107 | ! ! =============== |
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| 108 | DO jk = 1, jpkm1 ! Horizontal slab |
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| 109 | ! ! =============== |
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| 110 | ! Laplacian |
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| 111 | ! --------- |
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| 112 | |
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[455] | 113 | IF( ln_sco .OR. ln_zps ) THEN ! s-coordinate or z-coordinate with partial steps |
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[474] | 114 | zuf(:,:,jk) = rotb(:,:,jk) * fse3f(:,:,jk) |
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[3] | 115 | DO jj = 2, jpjm1 |
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| 116 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[10115] | 117 | zlu(ji,jj,jk) = - ( zuf(ji ,jj,jk) - zuf(ji,jj-1,jk) ) / ( e2u(ji,jj) * fse3u(ji,jj,jk) ) & |
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| 118 | & + ( hdivb(ji+1,jj,jk) - hdivb(ji,jj ,jk) ) / e1u(ji,jj) |
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[3] | 119 | |
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[10115] | 120 | zlv(ji,jj,jk) = + ( zuf(ji,jj ,jk) - zuf(ji-1,jj,jk) ) / ( e1v(ji,jj) * fse3v(ji,jj,jk) ) & |
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| 121 | & + ( hdivb(ji,jj+1,jk) - hdivb(ji ,jj,jk) ) / e2v(ji,jj) |
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[3] | 122 | END DO |
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| 123 | END DO |
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[455] | 124 | ELSE ! z-coordinate - full step |
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[3] | 125 | DO jj = 2, jpjm1 |
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| 126 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[474] | 127 | zlu(ji,jj,jk) = - ( rotb (ji ,jj,jk) - rotb (ji,jj-1,jk) ) / e2u(ji,jj) & |
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[10115] | 128 | & + ( hdivb(ji+1,jj,jk) - hdivb(ji,jj ,jk) ) / e1u(ji,jj) |
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[3] | 129 | |
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[474] | 130 | zlv(ji,jj,jk) = + ( rotb (ji,jj ,jk) - rotb (ji-1,jj,jk) ) / e1v(ji,jj) & |
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[10115] | 131 | & + ( hdivb(ji,jj+1,jk) - hdivb(ji ,jj,jk) ) / e2v(ji,jj) |
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[3] | 132 | END DO |
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| 133 | END DO |
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| 134 | ENDIF |
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[2715] | 135 | END DO |
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| 136 | CALL lbc_lnk( zlu, 'U', -1. ) ; CALL lbc_lnk( zlv, 'V', -1. ) ! Boundary conditions |
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[3] | 137 | |
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[10115] | 138 | IF( iom_use('dispkexyfo') ) THEN ! ocean kinetic energy dissipation per unit area |
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| 139 | ! ! due to xy friction (xy=lateral) |
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| 140 | ! see NEMO_book appendix C, §C.7.2 (N.B. here averaged at t-points) |
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| 141 | ! local dissipation of KE at t-point due to bilaplacian operator is given by : |
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| 142 | ! + ahmu mi( zlu**2 ) + mj( ahmv zlv**2 ) |
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| 143 | ! Note that a sign + is used as in v3.6 ahm is negative for bilaplacian viscosity |
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| 144 | ! |
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| 145 | ! NB: ahm is negative when bilaplacian is used |
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| 146 | ALLOCATE( z2d(jpi,jpj) ) |
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| 147 | z2d(:,:) = 0._wp |
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| 148 | DO jk = 1, jpkm1 |
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| 149 | DO jj = 2, jpjm1 |
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| 150 | DO ji = 2, jpim1 |
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| 151 | z2d(ji,jj) = z2d(ji,jj) & |
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| 152 | & + ( fsahmu(ji,jj,jk)*zlu(ji,jj,jk)**2 + fsahmu(ji-1,jj,jk)*zlu(ji-1,jj,jk)**2 & |
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| 153 | & + fsahmv(ji,jj,jk)*zlv(ji,jj,jk)**2 + fsahmv(ji,jj-1,jk)*zlv(ji,jj-1,jk)**2 ) * tmask(ji,jj,jk) |
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| 154 | END DO |
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| 155 | END DO |
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| 156 | END DO |
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| 157 | zzz = 0.5_wp * rau0 |
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| 158 | z2d(:,:) = zzz * z2d(:,:) |
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| 159 | CALL lbc_lnk( z2d,'T', 1. ) |
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| 160 | CALL iom_put( 'dispkexyfo', z2d ) |
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| 161 | DEALLOCATE( z2d ) |
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| 162 | ENDIF |
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| 163 | |
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| 164 | |
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| 165 | ! Third derivative |
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| 166 | ! ---------------- |
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| 167 | ! |
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[474] | 168 | DO jk = 1, jpkm1 |
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[10115] | 169 | ! |
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[3] | 170 | ! Multiply by the eddy viscosity coef. (at u- and v-points) |
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[10115] | 171 | zlu(:,:,jk) = zlu(:,:,jk) * fsahmu(:,:,jk) |
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| 172 | zlv(:,:,jk) = zlv(:,:,jk) * fsahmv(:,:,jk) |
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| 173 | ! |
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[3] | 174 | ! Contravariant "laplacian" |
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[474] | 175 | zcu(:,:) = e1u(:,:) * zlu(:,:,jk) |
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| 176 | zcv(:,:) = e2v(:,:) * zlv(:,:,jk) |
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[3] | 177 | |
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| 178 | ! Laplacian curl ( * e3f if s-coordinates or z-coordinate with partial steps) |
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| 179 | DO jj = 1, jpjm1 |
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| 180 | DO ji = 1, fs_jpim1 ! vector opt. |
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[474] | 181 | zuf(ji,jj,jk) = fmask(ji,jj,jk) * ( zcv(ji+1,jj ) - zcv(ji,jj) & |
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[10115] | 182 | & - zcu(ji ,jj+1) + zcu(ji,jj) ) & |
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| 183 | & * fse3f(ji,jj,jk) * r1_e12f(ji,jj) |
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[3] | 184 | END DO |
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| 185 | END DO |
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| 186 | |
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| 187 | ! Laplacian Horizontal fluxes |
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| 188 | DO jj = 1, jpjm1 |
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| 189 | DO ji = 1, fs_jpim1 ! vector opt. |
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[474] | 190 | zlu(ji,jj,jk) = e2u(ji,jj) * fse3u(ji,jj,jk) * zlu(ji,jj,jk) |
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| 191 | zlv(ji,jj,jk) = e1v(ji,jj) * fse3v(ji,jj,jk) * zlv(ji,jj,jk) |
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[3] | 192 | END DO |
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| 193 | END DO |
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| 194 | |
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| 195 | ! Laplacian divergence |
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| 196 | DO jj = 2, jpj |
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| 197 | DO ji = fs_2, jpi ! vector opt. |
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| 198 | zbt = e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) |
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[474] | 199 | zut(ji,jj,jk) = ( zlu(ji,jj,jk) - zlu(ji-1,jj ,jk) & |
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| 200 | & + zlv(ji,jj,jk) - zlv(ji ,jj-1,jk) ) / zbt |
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[3] | 201 | END DO |
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| 202 | END DO |
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[474] | 203 | END DO |
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[3] | 204 | |
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[235] | 205 | ! boundary conditions on the laplacian curl and div (zuf,zut) |
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[474] | 206 | !!bug gm no need to do this 2 following lbc... |
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[235] | 207 | CALL lbc_lnk( zuf, 'F', 1. ) |
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| 208 | CALL lbc_lnk( zut, 'T', 1. ) |
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[3] | 209 | |
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[10115] | 210 | DO jk = 1, jpkm1 ! Bilaplacian |
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[3] | 211 | DO jj = 2, jpjm1 |
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| 212 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 213 | ze2u = e2u(ji,jj) * fse3u(ji,jj,jk) |
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| 214 | ze2v = e1v(ji,jj) * fse3v(ji,jj,jk) |
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| 215 | ! horizontal biharmonic diffusive trends |
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[474] | 216 | zua = - ( zuf(ji ,jj,jk) - zuf(ji,jj-1,jk) ) / ze2u & |
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| 217 | & + ( zut(ji+1,jj,jk) - zut(ji,jj ,jk) ) / e1u(ji,jj) |
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[3] | 218 | |
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[474] | 219 | zva = + ( zuf(ji,jj ,jk) - zuf(ji-1,jj,jk) ) / ze2v & |
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| 220 | & + ( zut(ji,jj+1,jk) - zut(ji ,jj,jk) ) / e2v(ji,jj) |
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[3] | 221 | ! add it to the general momentum trends |
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[10115] | 222 | ua(ji,jj,jk) = ua(ji,jj,jk) + zua |
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| 223 | va(ji,jj,jk) = va(ji,jj,jk) + zva |
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[3] | 224 | END DO |
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| 225 | END DO |
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| 226 | ! ! =============== |
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| 227 | END DO ! End of slab |
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| 228 | ! ! =============== |
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[3294] | 229 | CALL wrk_dealloc( jpi, jpj, zcu, zcv ) |
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| 230 | CALL wrk_dealloc( jpi, jpj, jpk, zuf, zut, zlu, zlv ) |
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[2715] | 231 | ! |
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[3294] | 232 | IF( nn_timing == 1 ) CALL timing_stop('dyn_ldf_bilap') |
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| 233 | ! |
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[3] | 234 | END SUBROUTINE dyn_ldf_bilap |
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| 235 | |
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| 236 | !!====================================================================== |
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| 237 | END MODULE dynldf_bilap |
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