[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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| 20 | USE ldfdyn_oce ! ocean dynamics: lateral physics |
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| 21 | USE in_out_manager ! I/O manager |
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[216] | 22 | USE trdmod ! ocean dynamics trends |
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| 23 | USE trdmod_oce ! ocean variables trends |
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[3] | 24 | USE lbclnk ! ocean lateral boundary conditions (or mpp link) |
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[3294] | 25 | USE wrk_nemo ! Memory Allocation |
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| 26 | USE timing ! Timing |
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[3] | 27 | |
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| 28 | IMPLICIT NONE |
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| 29 | PRIVATE |
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| 30 | |
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[2715] | 31 | PUBLIC dyn_ldf_bilap ! called by step.F90 |
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[3] | 32 | |
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| 33 | !! * Substitutions |
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| 34 | # include "domzgr_substitute.h90" |
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| 35 | # include "ldfdyn_substitute.h90" |
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| 36 | # include "vectopt_loop_substitute.h90" |
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| 37 | !!---------------------------------------------------------------------- |
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[2528] | 38 | !! NEMO/OPA 3.3 , NEMO Consortium (2010) |
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[1152] | 39 | !! $Id$ |
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[2715] | 40 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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[3] | 41 | !!---------------------------------------------------------------------- |
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| 42 | CONTAINS |
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| 43 | |
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| 44 | SUBROUTINE dyn_ldf_bilap( kt ) |
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| 45 | !!---------------------------------------------------------------------- |
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| 46 | !! *** ROUTINE dyn_ldf_bilap *** |
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| 47 | !! |
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| 48 | !! ** Purpose : Compute the before trend of the lateral momentum |
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| 49 | !! diffusion and add it to the general trend of momentum equation. |
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| 50 | !! |
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| 51 | !! ** Method : The before horizontal momentum diffusion trend is a |
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| 52 | !! bi-harmonic operator (bilaplacian type) which separates the |
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| 53 | !! divergent and rotational parts of the flow. |
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| 54 | !! Its horizontal components are computed as follow: |
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| 55 | !! laplacian: |
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| 56 | !! zlu = 1/e1u di[ hdivb ] - 1/(e2u*e3u) dj-1[ e3f rotb ] |
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| 57 | !! zlv = 1/e2v dj[ hdivb ] + 1/(e1v*e3v) di-1[ e3f rotb ] |
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| 58 | !! third derivative: |
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| 59 | !! * multiply by the eddy viscosity coef. at u-, v-point, resp. |
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| 60 | !! zlu = ahmu * zlu |
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| 61 | !! zlv = ahmv * zlv |
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| 62 | !! * curl and divergence of the laplacian |
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| 63 | !! zuf = 1/(e1f*e2f) ( di[e2v zlv] - dj[e1u zlu] ) |
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| 64 | !! zut = 1/(e1t*e2t*e3t) ( di[e2u*e3u zlu] + dj[e1v*e3v zlv] ) |
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| 65 | !! bilaplacian: |
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| 66 | !! diffu = 1/e1u di[ zut ] - 1/(e2u*e3u) dj-1[ e3f zuf ] |
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| 67 | !! diffv = 1/e2v dj[ zut ] + 1/(e1v*e3v) di-1[ e3f zuf ] |
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[455] | 68 | !! If ln_sco=F and ln_zps=F, the vertical scale factors in the |
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[3] | 69 | !! rotational part of the diffusion are simplified |
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| 70 | !! Add this before trend to the general trend (ua,va): |
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| 71 | !! (ua,va) = (ua,va) + (diffu,diffv) |
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| 72 | !! 'key_trddyn' defined: the two components of the horizontal |
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| 73 | !! diffusion trend are saved. |
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| 74 | !! |
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| 75 | !! ** Action : - Update (ua,va) with the before iso-level biharmonic |
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| 76 | !! mixing trend. |
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| 77 | !!---------------------------------------------------------------------- |
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[2715] | 78 | ! |
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| 79 | INTEGER, INTENT(in) :: kt ! ocean time-step index |
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| 80 | ! |
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| 81 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 82 | REAL(wp) :: zua, zva, zbt, ze2u, ze2v ! temporary scalar |
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[3294] | 83 | REAL(wp), POINTER, DIMENSION(:,: ) :: zcu, zcv |
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| 84 | REAL(wp), POINTER, DIMENSION(:,:,:) :: zuf, zut, zlu, zlv |
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[3] | 85 | !!---------------------------------------------------------------------- |
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[3294] | 86 | ! |
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| 87 | IF( nn_timing == 1 ) CALL timing_start('dyn_ldf_bilap') |
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| 88 | ! |
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| 89 | CALL wrk_alloc( jpi, jpj, zcu, zcv ) |
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| 90 | CALL wrk_alloc( jpi, jpj, jpk, zuf, zut, zlu, zlv ) |
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| 91 | ! |
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[2715] | 92 | IF( kt == nit000 .AND. lwp ) THEN |
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| 93 | WRITE(numout,*) |
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| 94 | WRITE(numout,*) 'dyn_ldf_bilap : iso-level bilaplacian operator' |
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| 95 | WRITE(numout,*) '~~~~~~~~~~~~~' |
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| 96 | ENDIF |
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| 97 | |
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[474] | 98 | !!bug gm this should be enough |
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| 99 | !!$ zuf(:,:,jpk) = 0.e0 |
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| 100 | !!$ zut(:,:,jpk) = 0.e0 |
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| 101 | !!$ zlu(:,:,jpk) = 0.e0 |
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| 102 | !!$ zlv(:,:,jpk) = 0.e0 |
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[2715] | 103 | zuf(:,:,:) = 0._wp |
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| 104 | zut(:,:,:) = 0._wp |
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| 105 | zlu(:,:,:) = 0._wp |
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| 106 | zlv(:,:,:) = 0._wp |
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[474] | 107 | |
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[3] | 108 | ! ! =============== |
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| 109 | DO jk = 1, jpkm1 ! Horizontal slab |
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| 110 | ! ! =============== |
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| 111 | ! Laplacian |
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| 112 | ! --------- |
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| 113 | |
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[455] | 114 | IF( ln_sco .OR. ln_zps ) THEN ! s-coordinate or z-coordinate with partial steps |
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[474] | 115 | zuf(:,:,jk) = rotb(:,:,jk) * fse3f(:,:,jk) |
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[3] | 116 | DO jj = 2, jpjm1 |
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| 117 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[474] | 118 | zlu(ji,jj,jk) = - ( zuf(ji,jj,jk) - zuf(ji,jj-1,jk) ) / ( e2u(ji,jj) * fse3u(ji,jj,jk) ) & |
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[3] | 119 | & + ( hdivb(ji+1,jj,jk) - hdivb(ji,jj,jk) ) / e1u(ji,jj) |
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| 120 | |
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[474] | 121 | zlv(ji,jj,jk) = + ( zuf(ji,jj,jk) - zuf(ji-1,jj,jk) ) / ( e1v(ji,jj) * fse3v(ji,jj,jk) ) & |
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[3] | 122 | & + ( hdivb(ji,jj+1,jk) - hdivb(ji,jj,jk) ) / e2v(ji,jj) |
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| 123 | END DO |
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| 124 | END DO |
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[455] | 125 | ELSE ! z-coordinate - full step |
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[3] | 126 | DO jj = 2, jpjm1 |
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| 127 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[474] | 128 | zlu(ji,jj,jk) = - ( rotb (ji ,jj,jk) - rotb (ji,jj-1,jk) ) / e2u(ji,jj) & |
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[3] | 129 | & + ( hdivb(ji+1,jj,jk) - hdivb(ji,jj ,jk) ) / e1u(ji,jj) |
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| 130 | |
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[474] | 131 | zlv(ji,jj,jk) = + ( rotb (ji,jj ,jk) - rotb (ji-1,jj,jk) ) / e1v(ji,jj) & |
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[3] | 132 | & + ( hdivb(ji,jj+1,jk) - hdivb(ji ,jj,jk) ) / e2v(ji,jj) |
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| 133 | END DO |
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| 134 | END DO |
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| 135 | ENDIF |
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[2715] | 136 | END DO |
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| 137 | CALL lbc_lnk( zlu, 'U', -1. ) ; CALL lbc_lnk( zlv, 'V', -1. ) ! Boundary conditions |
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[3] | 138 | |
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| 139 | |
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[474] | 140 | DO jk = 1, jpkm1 |
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| 141 | |
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[3] | 142 | ! Third derivative |
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| 143 | ! ---------------- |
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| 144 | |
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| 145 | ! Multiply by the eddy viscosity coef. (at u- and v-points) |
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[3634] | 146 | zlu(:,:,jk) = zlu(:,:,jk) * ( fsahmu(:,:,jk) * (1-nkahm_smag) + nkahm_smag) |
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| 147 | |
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| 148 | zlv(:,:,jk) = zlv(:,:,jk) * ( fsahmv(:,:,jk) * (1-nkahm_smag) + nkahm_smag) |
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[3] | 149 | |
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| 150 | ! Contravariant "laplacian" |
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[474] | 151 | zcu(:,:) = e1u(:,:) * zlu(:,:,jk) |
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| 152 | zcv(:,:) = e2v(:,:) * zlv(:,:,jk) |
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[3] | 153 | |
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| 154 | ! Laplacian curl ( * e3f if s-coordinates or z-coordinate with partial steps) |
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| 155 | DO jj = 1, jpjm1 |
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| 156 | DO ji = 1, fs_jpim1 ! vector opt. |
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[474] | 157 | zuf(ji,jj,jk) = fmask(ji,jj,jk) * ( zcv(ji+1,jj ) - zcv(ji,jj) & |
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[3] | 158 | & - zcu(ji ,jj+1) + zcu(ji,jj) ) & |
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| 159 | & * fse3f(ji,jj,jk) / ( e1f(ji,jj)*e2f(ji,jj) ) |
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| 160 | END DO |
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| 161 | END DO |
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| 162 | |
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| 163 | ! Laplacian Horizontal fluxes |
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| 164 | DO jj = 1, jpjm1 |
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| 165 | DO ji = 1, fs_jpim1 ! vector opt. |
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[474] | 166 | zlu(ji,jj,jk) = e2u(ji,jj) * fse3u(ji,jj,jk) * zlu(ji,jj,jk) |
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| 167 | zlv(ji,jj,jk) = e1v(ji,jj) * fse3v(ji,jj,jk) * zlv(ji,jj,jk) |
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[3] | 168 | END DO |
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| 169 | END DO |
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| 170 | |
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| 171 | ! Laplacian divergence |
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| 172 | DO jj = 2, jpj |
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| 173 | DO ji = fs_2, jpi ! vector opt. |
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| 174 | zbt = e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) |
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[474] | 175 | zut(ji,jj,jk) = ( zlu(ji,jj,jk) - zlu(ji-1,jj ,jk) & |
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| 176 | & + zlv(ji,jj,jk) - zlv(ji ,jj-1,jk) ) / zbt |
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[3] | 177 | END DO |
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| 178 | END DO |
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[474] | 179 | END DO |
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[3] | 180 | |
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| 181 | |
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[235] | 182 | ! boundary conditions on the laplacian curl and div (zuf,zut) |
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[474] | 183 | !!bug gm no need to do this 2 following lbc... |
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[235] | 184 | CALL lbc_lnk( zuf, 'F', 1. ) |
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| 185 | CALL lbc_lnk( zut, 'T', 1. ) |
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[3] | 186 | |
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[474] | 187 | DO jk = 1, jpkm1 |
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| 188 | |
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[3] | 189 | ! Bilaplacian |
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| 190 | ! ----------- |
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| 191 | |
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| 192 | DO jj = 2, jpjm1 |
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| 193 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 194 | ze2u = e2u(ji,jj) * fse3u(ji,jj,jk) |
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| 195 | ze2v = e1v(ji,jj) * fse3v(ji,jj,jk) |
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| 196 | ! horizontal biharmonic diffusive trends |
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[474] | 197 | zua = - ( zuf(ji ,jj,jk) - zuf(ji,jj-1,jk) ) / ze2u & |
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| 198 | & + ( zut(ji+1,jj,jk) - zut(ji,jj ,jk) ) / e1u(ji,jj) |
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[3] | 199 | |
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[474] | 200 | zva = + ( zuf(ji,jj ,jk) - zuf(ji-1,jj,jk) ) / ze2v & |
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| 201 | & + ( zut(ji,jj+1,jk) - zut(ji ,jj,jk) ) / e2v(ji,jj) |
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[3] | 202 | ! add it to the general momentum trends |
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[3634] | 203 | ua(ji,jj,jk) = ua(ji,jj,jk) + zua * ( fsahmu(ji,jj,jk)*nkahm_smag +(1 -nkahm_smag )) |
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| 204 | va(ji,jj,jk) = va(ji,jj,jk) + zva * ( fsahmv(ji,jj,jk)*nkahm_smag +(1 -nkahm_smag )) |
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[3] | 205 | END DO |
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| 206 | END DO |
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| 207 | |
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| 208 | ! ! =============== |
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| 209 | END DO ! End of slab |
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| 210 | ! ! =============== |
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[3294] | 211 | CALL wrk_dealloc( jpi, jpj, zcu, zcv ) |
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| 212 | CALL wrk_dealloc( jpi, jpj, jpk, zuf, zut, zlu, zlv ) |
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[2715] | 213 | ! |
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[3294] | 214 | IF( nn_timing == 1 ) CALL timing_stop('dyn_ldf_bilap') |
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| 215 | ! |
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[3] | 216 | END SUBROUTINE dyn_ldf_bilap |
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| 217 | |
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| 218 | !!====================================================================== |
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| 219 | END MODULE dynldf_bilap |
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