[5777] | 1 | MODULE dynldf_lap_blp |
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[3] | 2 | !!====================================================================== |
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[5777] | 3 | !! *** MODULE dynldf_lap_blp *** |
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| 4 | !! Ocean dynamics: lateral viscosity trend (laplacian and bilaplacian) |
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[3] | 5 | !!====================================================================== |
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[6140] | 6 | !! History : 3.7 ! 2014-01 (G. Madec, S. Masson) Original code, re-entrant laplacian |
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[12535] | 7 | !! 4.0 ! 2020-02 (C. Wilson, ...) add bhm coefficient for bi-Laplacian GM implementation via momentum |
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[2715] | 8 | !!---------------------------------------------------------------------- |
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[3] | 9 | |
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| 10 | !!---------------------------------------------------------------------- |
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[5777] | 11 | !! dyn_ldf_lap : update the momentum trend with the lateral viscosity using an iso-level laplacian operator |
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| 12 | !! dyn_ldf_blp : update the momentum trend with the lateral viscosity using an iso-level bilaplacian operator |
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[3] | 13 | !!---------------------------------------------------------------------- |
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[5777] | 14 | USE oce ! ocean dynamics and tracers |
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| 15 | USE dom_oce ! ocean space and time domain |
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| 16 | USE ldfdyn ! lateral diffusion: eddy viscosity coef. |
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| 17 | USE ldfslp ! iso-neutral slopes |
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| 18 | USE zdf_oce ! ocean vertical physics |
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[4990] | 19 | ! |
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[5777] | 20 | USE in_out_manager ! I/O manager |
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| 21 | USE lbclnk ! ocean lateral boundary conditions (or mpp link) |
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[3] | 22 | |
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| 23 | IMPLICIT NONE |
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| 24 | PRIVATE |
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| 25 | |
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[5777] | 26 | PUBLIC dyn_ldf_lap ! called by dynldf.F90 |
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| 27 | PUBLIC dyn_ldf_blp ! called by dynldf.F90 |
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[12535] | 28 | PUBLIC dyn_ldf_bgm ! called by dynldf.F90 |
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| 29 | PRIVATE dyn_ldf_lap_no_ahm !needed by dyn_ldf_bgm |
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[3] | 30 | |
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| 31 | !! * Substitutions |
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| 32 | # include "vectopt_loop_substitute.h90" |
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| 33 | !!---------------------------------------------------------------------- |
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[9598] | 34 | !! NEMO/OCE 4.0 , NEMO Consortium (2018) |
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[12535] | 35 | !! $Id: dynldf_lap_blp.F90 10425 2018-12-19 21:54:16Z smasson $ |
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[10068] | 36 | !! Software governed by the CeCILL license (see ./LICENSE) |
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[3] | 37 | !!---------------------------------------------------------------------- |
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| 38 | CONTAINS |
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| 39 | |
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[5777] | 40 | SUBROUTINE dyn_ldf_lap( kt, pub, pvb, pua, pva, kpass ) |
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[3] | 41 | !!---------------------------------------------------------------------- |
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| 42 | !! *** ROUTINE dyn_ldf_lap *** |
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| 43 | !! |
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[5777] | 44 | !! ** Purpose : Compute the before horizontal momentum diffusive |
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| 45 | !! trend and add it to the general trend of momentum equation. |
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[3] | 46 | !! |
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[5777] | 47 | !! ** Method : The Laplacian operator apply on horizontal velocity is |
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| 48 | !! writen as : grad_h( ahmt div_h(U )) - curl_h( ahmf curl_z(U) ) |
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[3] | 49 | !! |
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[5777] | 50 | !! ** Action : - pua, pva increased by the harmonic operator applied on pub, pvb. |
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[3] | 51 | !!---------------------------------------------------------------------- |
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[5777] | 52 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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| 53 | INTEGER , INTENT(in ) :: kpass ! =1/2 first or second passage |
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| 54 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pub, pvb ! before velocity [m/s] |
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| 55 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(inout) :: pua, pva ! velocity trend [m/s2] |
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[2715] | 56 | ! |
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[5777] | 57 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 58 | REAL(wp) :: zsign ! local scalars |
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| 59 | REAL(wp) :: zua, zva ! local scalars |
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[9019] | 60 | REAL(wp), DIMENSION(jpi,jpj) :: zcur, zdiv |
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[3] | 61 | !!---------------------------------------------------------------------- |
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[2715] | 62 | ! |
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[5777] | 63 | IF( kt == nit000 .AND. lwp ) THEN |
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| 64 | WRITE(numout,*) |
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| 65 | WRITE(numout,*) 'dyn_ldf : iso-level harmonic (laplacian) operator, pass=', kpass |
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| 66 | WRITE(numout,*) '~~~~~~~ ' |
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| 67 | ENDIF |
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[3294] | 68 | ! |
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[5777] | 69 | IF( kpass == 1 ) THEN ; zsign = 1._wp ! bilaplacian operator require a minus sign |
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| 70 | ELSE ; zsign = -1._wp ! (eddy viscosity coef. >0) |
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[3] | 71 | ENDIF |
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[5777] | 72 | ! |
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[3] | 73 | ! ! =============== |
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| 74 | DO jk = 1, jpkm1 ! Horizontal slab |
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| 75 | ! ! =============== |
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[5777] | 76 | DO jj = 2, jpj |
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| 77 | DO ji = fs_2, jpi ! vector opt. |
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| 78 | ! ! ahm * e3 * curl (computed from 1 to jpim1/jpjm1) |
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[6140] | 79 | !!gm open question here : e3f at before or now ? probably now... |
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[5860] | 80 | !!gm note that ahmf has already been multiplied by fmask |
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[6140] | 81 | zcur(ji-1,jj-1) = ahmf(ji-1,jj-1,jk) * e3f_n(ji-1,jj-1,jk) * r1_e1e2f(ji-1,jj-1) & |
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[5860] | 82 | & * ( e2v(ji ,jj-1) * pvb(ji ,jj-1,jk) - e2v(ji-1,jj-1) * pvb(ji-1,jj-1,jk) & |
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[6140] | 83 | & - e1u(ji-1,jj ) * pub(ji-1,jj ,jk) + e1u(ji-1,jj-1) * pub(ji-1,jj-1,jk) ) |
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[5777] | 84 | ! ! ahm * div (computed from 2 to jpi/jpj) |
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[6140] | 85 | !!gm note that ahmt has already been multiplied by tmask |
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| 86 | zdiv(ji,jj) = ahmt(ji,jj,jk) * r1_e1e2t(ji,jj) / e3t_b(ji,jj,jk) & |
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| 87 | & * ( e2u(ji,jj)*e3u_b(ji,jj,jk) * pub(ji,jj,jk) - e2u(ji-1,jj)*e3u_b(ji-1,jj,jk) * pub(ji-1,jj,jk) & |
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| 88 | & + e1v(ji,jj)*e3v_b(ji,jj,jk) * pvb(ji,jj,jk) - e1v(ji,jj-1)*e3v_b(ji,jj-1,jk) * pvb(ji,jj-1,jk) ) |
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[5777] | 89 | END DO |
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| 90 | END DO |
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| 91 | ! |
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| 92 | DO jj = 2, jpjm1 ! - curl( curl) + grad( div ) |
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[3] | 93 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[6140] | 94 | pua(ji,jj,jk) = pua(ji,jj,jk) + zsign * ( & |
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| 95 | & - ( zcur(ji ,jj) - zcur(ji,jj-1) ) * r1_e2u(ji,jj) / e3u_n(ji,jj,jk) & |
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[5777] | 96 | & + ( zdiv(ji+1,jj) - zdiv(ji,jj ) ) * r1_e1u(ji,jj) ) |
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| 97 | ! |
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[6140] | 98 | pva(ji,jj,jk) = pva(ji,jj,jk) + zsign * ( & |
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| 99 | & ( zcur(ji,jj ) - zcur(ji-1,jj) ) * r1_e1v(ji,jj) / e3v_n(ji,jj,jk) & |
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[5777] | 100 | & + ( zdiv(ji,jj+1) - zdiv(ji ,jj) ) * r1_e2v(ji,jj) ) |
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[3] | 101 | END DO |
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| 102 | END DO |
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| 103 | ! ! =============== |
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| 104 | END DO ! End of slab |
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| 105 | ! ! =============== |
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[5777] | 106 | ! |
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[3] | 107 | END SUBROUTINE dyn_ldf_lap |
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| 108 | |
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[12535] | 109 | !CW: new subroutine for the Laplacian of velocity, copied from dyn_ldf_lap above, but without eddy viscosity ahmf, ahmt |
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[5777] | 110 | |
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[12535] | 111 | SUBROUTINE dyn_ldf_lap_no_ahm( kt, pub, pvb, pulap, pvlap, kpass ) |
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| 112 | !!---------------------------------------------------------------------- |
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| 113 | !! *** ROUTINE dyn_ldf_lap_no_ahm *** |
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| 114 | !! |
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| 115 | !! ** Purpose : Companion subroutine to dyn_ldf_bgm to calculate |
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| 116 | !! the before horizontal momentum Laplacian |
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| 117 | !! trend and add it to the general trend of momentum equation. |
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| 118 | !! Note: mimics dyn_ldf_lap but without eddy viscosity ahmf, ahmt, |
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| 119 | !! because biharmonic GM eddy diffusivity is applied in dyn_bgm. |
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| 120 | !! |
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| 121 | !! ** Method : The Laplacian operator apply on horizontal velocity is |
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| 122 | !! writen as : grad_h( ahmt div_h(U )) - curl_h( ahmf curl_z(U) ) |
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| 123 | !! |
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| 124 | !! ** Action : - pua, pva increased by the harmonic operator applied on pub, pvb. |
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| 125 | !!---------------------------------------------------------------------- |
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| 126 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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| 127 | INTEGER , INTENT(in ) :: kpass ! =1/2 first or second passage |
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| 128 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pub, pvb ! before velocity [m/s] |
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| 129 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(out) :: pulap, pvlap ! velocity trend [m/s2] |
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| 130 | ! |
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| 131 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 132 | REAL(wp) :: zsign ! local scalars |
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| 133 | REAL(wp) :: zua, zva ! local scalars |
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| 134 | REAL(wp), DIMENSION(jpi,jpj) :: zcur, zdiv |
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| 135 | !!---------------------------------------------------------------------- |
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| 136 | ! |
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| 137 | IF( kt == nit000 .AND. lwp ) THEN |
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| 138 | WRITE(numout,*) |
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| 139 | WRITE(numout,*) 'dyn_ldf_lap_no_ahm : companion iso-level harmonic (laplacian) operator to dyn_bgm, pass=', kpass |
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| 140 | WRITE(numout,*) '~~~~~~~ ' |
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| 141 | ENDIF |
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| 142 | ! |
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| 143 | IF( kpass == 1 ) THEN ; zsign = 1._wp ! bilaplacian operator require a minus sign |
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| 144 | ELSE ; zsign = -1._wp ! (eddy viscosity coef. >0) |
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| 145 | ENDIF |
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| 146 | ! |
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| 147 | ! ! =============== |
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| 148 | DO jk = 1, jpkm1 ! Horizontal slab |
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| 149 | ! ! =============== |
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| 150 | DO jj = 2, jpj |
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| 151 | DO ji = fs_2, jpi ! vector opt. |
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| 152 | ! ! ahm * e3 * curl (computed from 1 to jpim1/jpjm1) |
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| 153 | !!gm open question here : e3f at before or now ? probably now... |
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| 154 | |
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| 155 | !!CW: note that the removed ahmf had already been multiplied by fmask, so we multiply by fmask explicitly here, |
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| 156 | !! with the i,j,k of fmask aligning with those of ahmf, as defined in ldfdyn.F90. |
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| 157 | zcur(ji-1,jj-1) = fmask(ji-1,jj-1,jk) * e3f_n(ji-1,jj-1,jk) * r1_e1e2f(ji-1,jj-1) & |
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| 158 | & * ( e2v(ji ,jj-1) * pvb(ji ,jj-1,jk) - e2v(ji-1,jj-1) * pvb(ji-1,jj-1,jk) & |
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| 159 | & - e1u(ji-1,jj ) * pub(ji-1,jj ,jk) + e1u(ji-1,jj-1) * pub(ji-1,jj-1,jk) ) |
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| 160 | ! ! ahm * div (computed from 2 to jpi/jpj) |
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| 161 | !!CW: note that the removed ahmt had already been multiplied by tmask, so we multiply by tmask explicitly here, |
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| 162 | !! with the i,j,k of tmask aligning with those of ahmt, as defined in ldfdyn.F90 |
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| 163 | zdiv(ji,jj) = tmask(ji,jj,jk) * r1_e1e2t(ji,jj) / e3t_b(ji,jj,jk) & |
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| 164 | & * ( e2u(ji,jj)*e3u_b(ji,jj,jk) * pub(ji,jj,jk) - e2u(ji-1,jj)*e3u_b(ji-1,jj,jk) * pub(ji-1,jj,jk) & |
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| 165 | & + e1v(ji,jj)*e3v_b(ji,jj,jk) * pvb(ji,jj,jk) - e1v(ji,jj-1)*e3v_b(ji,jj-1,jk) * pvb(ji,jj-1,jk) ) |
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| 166 | END DO |
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| 167 | END DO |
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| 168 | ! |
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| 169 | !CW: multiply pulap, pvlap by umask, vmask |
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| 170 | DO jj = 2, jpjm1 ! - curl( curl) + grad( div ) |
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| 171 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 172 | pulap(ji,jj,jk) = umask(ji,jj,jk) * zsign * ( & |
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| 173 | & - ( zcur(ji ,jj) - zcur(ji,jj-1) ) * r1_e2u(ji,jj) / e3u_n(ji,jj,jk) & |
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| 174 | & + ( zdiv(ji+1,jj) - zdiv(ji,jj ) ) * r1_e1u(ji,jj) ) |
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| 175 | ! |
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| 176 | pvlap(ji,jj,jk) = vmask(ji,jj,jk) * zsign * ( & |
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| 177 | & ( zcur(ji,jj ) - zcur(ji-1,jj) ) * r1_e1v(ji,jj) / e3v_n(ji,jj,jk) & |
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| 178 | & + ( zdiv(ji,jj+1) - zdiv(ji ,jj) ) * r1_e2v(ji,jj) ) |
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| 179 | END DO |
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| 180 | END DO |
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| 181 | ! ! =============== |
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| 182 | END DO ! End of slab |
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| 183 | ! ! =============== |
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| 184 | ! |
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| 185 | END SUBROUTINE dyn_ldf_lap_no_ahm |
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| 186 | |
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| 187 | |
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| 188 | |
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| 189 | |
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| 190 | !CW: new subroutine for biharmonic GM, copied from SUBROUTINE dyn_ldf_blp below |
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| 191 | |
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| 192 | SUBROUTINE dyn_ldf_bgm( kt, pub, pvb, pua, pva ) |
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| 193 | !!---------------------------------------------------------------------- |
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| 194 | !! *** ROUTINE dyn_bgm *** |
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| 195 | !! |
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| 196 | !! ** Purpose : Compute the before lateral momentum trend due to the bi-Laplacian GM parameterisation |
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| 197 | !! and add it to the general trend of momentum equation. |
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| 198 | !! |
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| 199 | !! ** Method : The bi-Laplacian implementation of GM is via a -d/dz(diffusivity x d/dz(Laplacian of velocity)) |
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| 200 | !! operator applied at the 'now' time level. The existing code for the Laplacian contains the 'before' time also in zdiv. |
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| 201 | !! It is computed by a call to dyn_ldf_lap routine and vertical differentiation applied twice. |
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| 202 | !! |
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| 203 | !! ** Action : pua, pva increased with the before bi-Laplacian GM momentum trend calculated from pub, pvb. |
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| 204 | !!---------------------------------------------------------------------- |
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| 205 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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| 206 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pub, pvb ! before velocity fields |
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| 207 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(inout) :: pua, pva ! momentum trend |
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| 208 | ! |
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| 209 | INTEGER :: iku, ikv ! local integers |
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| 210 | !CW |
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| 211 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 212 | ! |
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| 213 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zulap, zvlap ! laplacian at u- and v-point |
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| 214 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zulapdz, zvlapdz ! -1*bhm * d/dz(del^2 u) at u- and v-point |
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| 215 | !!---------------------------------------------------------------------- |
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| 216 | ! |
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| 217 | IF( kt == nit000 ) THEN |
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| 218 | IF(lwp) WRITE(numout,*) |
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| 219 | IF(lwp) WRITE(numout,*) 'dyn_bgm : bi-Laplacian GM operator via momentum ' |
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| 220 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~' |
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| 221 | ENDIF |
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| 222 | ! |
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| 223 | |
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| 224 | CALL dyn_ldf_lap_no_ahm( kt, pub, pvb, zulap, zvlap, 1 ) |
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| 225 | |
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| 226 | ! =============== |
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| 227 | !CW: calculate -bhm * d/dz(del^2 u) |
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[12688] | 228 | ! Use of wumask and wvmask to ensure diffusive fluxes at topography are zero. |
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[12535] | 229 | DO jk = 2, jpkm1 |
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| 230 | DO jj = 2, jpjm1 |
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| 231 | DO ji = fs_2, jpim1 ! vector opt. |
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[12688] | 232 | zulapdz(ji,jj,jk) = -0.5_wp*(bhm(ji+1,jj ,jk)+bhm(ji,jj,jk))*(zulap(ji,jj,jk-1) - zulap(ji,jj,jk)) * wumask(ji,jj,jk) / e3uw_n(ji,jj,jk) |
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| 233 | zvlapdz(ji,jj,jk) = -0.5_wp*(bhm(ji ,jj+1,jk)+bhm(ji,jj,jk))*(zvlap(ji,jj,jk-1) - zvlap(ji,jj,jk)) * wvmask(ji,jj,jk) / e3vw_n(ji,jj,jk) |
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[12535] | 234 | ENDDO |
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| 235 | ENDDO |
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| 236 | ENDDO |
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| 237 | |
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| 238 | |
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| 239 | !CW: set boundary conditions: d/dz(del^2 u) = 0 at top and bottom, so that eddy-induced velocity, w*=0 |
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| 240 | ! Surface |
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| 241 | zulapdz(:,:,1) = 0._wp ; zvlapdz(:,:,1) = 0._wp |
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| 242 | ! Flat bottom case |
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| 243 | zulapdz(:,:,jpk) = 0._wp ; zvlapdz(:,:,jpk) = 0._wp |
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| 244 | ! Variable bathymetry case, including z-partial steps, as in dynhpg.F90, subroutine hpg_zps |
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| 245 | DO jj = 2, jpjm1 |
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| 246 | DO ji = 2, jpim1 |
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| 247 | iku = mbku(ji,jj)+1 |
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| 248 | ikv = mbkv(ji,jj)+1 |
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| 249 | zulapdz(:,:,iku) = 0._wp |
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| 250 | zvlapdz(:,:,ikv) = 0._wp |
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| 251 | ENDDO |
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| 252 | ENDDO |
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| 253 | |
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| 254 | |
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| 255 | |
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| 256 | |
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| 257 | !! calculate d/dz(-bhm * d/dz(del^2 u)) |
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| 258 | ! =============== |
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| 259 | DO jk = 1, jpkm1 ! Horizontal slab |
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| 260 | ! ! =============== |
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| 261 | DO jj = 2, jpjm1 |
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| 262 | DO ji = fs_2, jpim1 ! vector opt. |
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| 263 | pua(ji,jj,jk) = pua(ji,jj,jk) + (zulapdz(ji,jj,jk) - zulapdz(ji,jj,jk+1)) / e3u_n(ji,jj,jk) |
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| 264 | pva(ji,jj,jk) = pva(ji,jj,jk) + (zvlapdz(ji,jj,jk) - zvlapdz(ji,jj,jk+1)) / e3v_n(ji,jj,jk) |
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| 265 | ENDDO |
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| 266 | ENDDO |
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| 267 | ENDDO |
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| 268 | |
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| 269 | ! ----- |
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| 270 | |
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| 271 | |
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| 272 | END SUBROUTINE dyn_ldf_bgm |
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| 273 | |
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| 274 | |
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[5777] | 275 | SUBROUTINE dyn_ldf_blp( kt, pub, pvb, pua, pva ) |
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| 276 | !!---------------------------------------------------------------------- |
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| 277 | !! *** ROUTINE dyn_ldf_blp *** |
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| 278 | !! |
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| 279 | !! ** Purpose : Compute the before lateral momentum viscous trend |
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| 280 | !! and add it to the general trend of momentum equation. |
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| 281 | !! |
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| 282 | !! ** Method : The lateral viscous trends is provided by a bilaplacian |
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| 283 | !! operator applied to before field (forward in time). |
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| 284 | !! It is computed by two successive calls to dyn_ldf_lap routine |
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| 285 | !! |
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| 286 | !! ** Action : pta updated with the before rotated bilaplacian diffusion |
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| 287 | !!---------------------------------------------------------------------- |
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| 288 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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| 289 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(in ) :: pub, pvb ! before velocity fields |
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| 290 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(inout) :: pua, pva ! momentum trend |
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| 291 | ! |
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[9019] | 292 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zulap, zvlap ! laplacian at u- and v-point |
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[5777] | 293 | !!---------------------------------------------------------------------- |
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| 294 | ! |
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| 295 | IF( kt == nit000 ) THEN |
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| 296 | IF(lwp) WRITE(numout,*) |
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| 297 | IF(lwp) WRITE(numout,*) 'dyn_ldf_blp : bilaplacian operator momentum ' |
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| 298 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~~' |
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| 299 | ENDIF |
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| 300 | ! |
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[7753] | 301 | zulap(:,:,:) = 0._wp |
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| 302 | zvlap(:,:,:) = 0._wp |
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[5777] | 303 | ! |
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| 304 | CALL dyn_ldf_lap( kt, pub, pvb, zulap, zvlap, 1 ) ! rotated laplacian applied to ptb (output in zlap) |
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| 305 | ! |
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[10425] | 306 | CALL lbc_lnk_multi( 'dynldf_lap_blp', zulap, 'U', -1., zvlap, 'V', -1. ) ! Lateral boundary conditions |
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[5777] | 307 | ! |
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| 308 | CALL dyn_ldf_lap( kt, zulap, zvlap, pua, pva, 2 ) ! rotated laplacian applied to zlap (output in pta) |
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| 309 | ! |
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| 310 | END SUBROUTINE dyn_ldf_blp |
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| 311 | |
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[3] | 312 | !!====================================================================== |
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[5777] | 313 | END MODULE dynldf_lap_blp |
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