| 1 | MODULE divcur |
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| 2 | !!============================================================================== |
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| 3 | !! *** MODULE divcur *** |
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| 4 | !! Ocean diagnostic variable : horizontal divergence and relative vorticity |
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| 5 | !!============================================================================== |
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| 6 | |
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| 7 | !!---------------------------------------------------------------------- |
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| 8 | !! div_cur : Compute the horizontal divergence and relative |
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| 9 | !! vorticity fields |
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| 10 | !!---------------------------------------------------------------------- |
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| 11 | !! * Modules used |
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| 12 | USE oce ! ocean dynamics and tracers |
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| 13 | USE dom_oce ! ocean space and time domain |
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| 14 | USE in_out_manager ! I/O manager |
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| 15 | USE obc_oce ! ocean lateral open boundary condition |
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| 16 | USE lbclnk ! ocean lateral boundary conditions (or mpp link) |
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| 17 | |
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| 18 | IMPLICIT NONE |
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| 19 | PRIVATE |
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| 20 | |
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| 21 | !! * Accessibility |
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| 22 | PUBLIC div_cur ! routine called by step.F90 and istate.F90 |
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| 23 | |
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| 24 | !! * Substitutions |
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| 25 | # include "domzgr_substitute.h90" |
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| 26 | # include "vectopt_loop_substitute.h90" |
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| 27 | !!---------------------------------------------------------------------- |
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| 28 | !! OPA 9.0 , LOCEAN-IPSL (2005) |
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| 29 | !! $Header$ |
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| 30 | !! This software is governed by the CeCILL licence see modipsl/doc/NEMO_CeCILL.txt |
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| 31 | !!---------------------------------------------------------------------- |
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| 32 | |
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| 33 | CONTAINS |
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| 34 | |
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| 35 | #if defined key_noslip_accurate |
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| 36 | !!---------------------------------------------------------------------- |
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| 37 | !! 'key_noslip_accurate' 2nd order centered scheme |
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| 38 | !! 4th order at the coast |
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| 39 | !!---------------------------------------------------------------------- |
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| 40 | |
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| 41 | SUBROUTINE div_cur( kt ) |
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| 42 | !!---------------------------------------------------------------------- |
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| 43 | !! *** ROUTINE div_cur *** |
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| 44 | !! |
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| 45 | !! ** Purpose : compute the horizontal divergence and the relative |
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| 46 | !! vorticity at before and now time-step |
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| 47 | !! |
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| 48 | !! ** Method : |
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| 49 | !! I. divergence : |
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| 50 | !! - save the divergence computed at the previous time-step |
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| 51 | !! (note that the Asselin filter has not been applied on hdivb) |
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| 52 | !! - compute the now divergence given by : |
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| 53 | !! * s-coordinate ('key_s_coord' defined) |
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| 54 | !! hdivn = 1/(e1t*e2t*e3t) ( di[e2u*e3u un] + dj[e1v*e3v vn] ) |
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| 55 | !! * z-coordinate (default key) |
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| 56 | !! hdivn = 1/(e1t*e2t) [ di(e2u un) + dj(e1v vn) ] |
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| 57 | !! - apply lateral boundary conditions on hdivn |
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| 58 | !! II. vorticity : |
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| 59 | !! - save the curl computed at the previous time-step |
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| 60 | !! rotb = rotn |
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| 61 | !! (note that the Asselin time filter has not been applied to rotb) |
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| 62 | !! - compute the now curl in tensorial formalism: |
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| 63 | !! rotn = 1/(e1f*e2f) ( di[e2v vn] - dj[e1u un] ) |
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| 64 | !! - apply lateral boundary conditions on rotn through a call |
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| 65 | !! of lbc_lnk routine. |
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| 66 | !! - Coastal boundary condition: 'key_noslip_accurate' defined, |
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| 67 | !! the no-slip boundary condition is computed using Schchepetkin |
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| 68 | !! and O'Brien (1996) scheme (i.e. 4th order at the coast). |
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| 69 | !! For example, along east coast, the one-sided finite difference |
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| 70 | !! approximation used for di[v] is: |
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| 71 | !! di[e2v vn] = 1/(e1f*e2f) |
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| 72 | !! * ( (e2v vn)(i) + (e2v vn)(i-1) + (e2v vn)(i-2) ) |
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| 73 | !! |
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| 74 | !! ** Action : - update hdivb, hdivn, the before & now hor. divergence |
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| 75 | !! - update rotb , rotn , the before & now rel. vorticity |
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| 76 | !! |
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| 77 | !! History : |
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| 78 | !! 8.2 ! 00-03 (G. Madec) no slip accurate |
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| 79 | !! 9.0 ! 03-08 (G. Madec) merged of cur and div, free form, F90 |
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| 80 | !!---------------------------------------------------------------------- |
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| 81 | !! * Arguments |
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| 82 | INTEGER, INTENT( in ) :: kt ! ocean time-step index |
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| 83 | |
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| 84 | !! * Local declarations |
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| 85 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 86 | INTEGER :: ii, ij, jl ! temporary integer |
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| 87 | INTEGER :: ijt, iju ! temporary integer |
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| 88 | REAL(wp) :: zdiv, zdju |
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| 89 | REAL(wp), DIMENSION( jpi ,1:jpj+2) :: zwu ! workspace |
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| 90 | REAL(wp), DIMENSION(-1:jpi+2, jpj ) :: zwv ! workspace |
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| 91 | !!---------------------------------------------------------------------- |
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| 92 | |
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| 93 | IF( kt == nit000 ) THEN |
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| 94 | IF(lwp) WRITE(numout,*) |
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| 95 | IF(lwp) WRITE(numout,*) 'div_cur : horizontal velocity divergence and relative vorticity' |
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| 96 | IF(lwp) WRITE(numout,*) '~~~~~~~ NOT optimal for auto-tasking case' |
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| 97 | ENDIF |
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| 98 | |
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| 99 | ! ! =============== |
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| 100 | DO jk = 1, jpkm1 ! Horizontal slab |
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| 101 | ! ! =============== |
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| 102 | |
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| 103 | hdivb(:,:,jk) = hdivn(:,:,jk) ! time swap of div arrays |
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| 104 | rotb (:,:,jk) = rotn (:,:,jk) ! time swap of rot arrays |
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| 105 | |
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| 106 | ! ! -------- |
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| 107 | ! Horizontal divergence ! div |
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| 108 | ! ! -------- |
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| 109 | DO jj = 2, jpjm1 |
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| 110 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 111 | #if defined key_s_coord || defined key_partial_steps |
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| 112 | hdivn(ji,jj,jk) = & |
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| 113 | ( e2u(ji,jj)*fse3u(ji,jj,jk) * un(ji,jj,jk) - e2u(ji-1,jj )*fse3u(ji-1,jj ,jk) * un(ji-1,jj ,jk) & |
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| 114 | + e1v(ji,jj)*fse3v(ji,jj,jk) * vn(ji,jj,jk) - e1v(ji ,jj-1)*fse3v(ji ,jj-1,jk) * vn(ji ,jj-1,jk) ) & |
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| 115 | / ( e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) ) |
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| 116 | #else |
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| 117 | hdivn(ji,jj,jk) = ( e2u(ji,jj) * un(ji,jj,jk) - e2u(ji-1,jj ) * un(ji-1,jj ,jk) & |
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| 118 | & + e1v(ji,jj) * vn(ji,jj,jk) - e1v(ji ,jj-1) * vn(ji ,jj-1,jk) ) & |
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| 119 | & / ( e1t(ji,jj) * e2t(ji,jj) ) |
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| 120 | #endif |
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| 121 | END DO |
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| 122 | END DO |
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| 123 | |
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| 124 | #if defined key_obc |
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| 125 | ! open boundaries (div must be zero behind the open boundary) |
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| 126 | ! mpp remark: The zeroing of hdivn can probably be extended to 1->jpi/jpj for the correct row/column |
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| 127 | IF( lp_obc_east ) hdivn(nie0p1:nie1p1,nje0 :nje1 ,jk) = 0.e0 ! east |
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| 128 | IF( lp_obc_west ) hdivn(niw0 :niw1 ,njw0 :njw1 ,jk) = 0.e0 ! west |
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| 129 | IF( lp_obc_north ) hdivn(nin0 :nin1 ,njn0p1:njn1p1,jk) = 0.e0 ! north |
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| 130 | IF( lp_obc_south ) hdivn(nis0 :nis1 ,njs0 :njs1 ,jk) = 0.e0 ! south |
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| 131 | #endif |
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| 132 | |
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| 133 | ! ! -------- |
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| 134 | ! relative vorticity ! rot |
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| 135 | ! ! -------- |
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| 136 | ! contravariant velocity (extended for lateral b.c.) |
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| 137 | ! inside the model domain |
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| 138 | DO jj = 1, jpj |
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| 139 | DO ji = 1, jpi |
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| 140 | zwu(ji,jj) = e1u(ji,jj) * un(ji,jj,jk) |
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| 141 | zwv(ji,jj) = e2v(ji,jj) * vn(ji,jj,jk) |
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| 142 | END DO |
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| 143 | END DO |
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| 144 | |
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| 145 | ! East-West boundary conditions |
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| 146 | IF( nperio == 1 .OR. nperio == 4 .OR. nperio == 6) THEN |
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| 147 | zwv( 0 ,:) = zwv(jpi-2,:) |
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| 148 | zwv( -1 ,:) = zwv(jpi-3,:) |
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| 149 | zwv(jpi+1,:) = zwv( 3 ,:) |
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| 150 | zwv(jpi+2,:) = zwv( 4 ,:) |
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| 151 | ELSE |
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| 152 | zwv( 0 ,:) = 0.e0 |
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| 153 | zwv( -1 ,:) = 0.e0 |
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| 154 | zwv(jpi+1,:) = 0.e0 |
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| 155 | zwv(jpi+2,:) = 0.e0 |
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| 156 | ENDIF |
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| 157 | |
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| 158 | ! North-South boundary conditions |
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| 159 | IF( nperio == 3 .OR. nperio == 4 ) THEN |
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| 160 | ! north fold ( Grid defined with a T-point pivot) ORCA 2 degre |
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| 161 | zwu(jpi,jpj+1) = 0.e0 |
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| 162 | zwu(jpi,jpj+2) = 0.e0 |
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| 163 | DO ji = 1, jpi-1 |
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| 164 | iju = jpi - ji + 1 |
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| 165 | zwu(ji,jpj+1) = - zwu(iju,jpj-3) |
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| 166 | zwu(ji,jpj+2) = - zwu(iju,jpj-4) |
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| 167 | END DO |
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| 168 | ELSEIF( nperio == 5 .OR. nperio == 6 ) THEN |
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| 169 | ! north fold ( Grid defined with a F-point pivot) ORCA 0.5 degre\ |
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| 170 | zwu(jpi,jpj+1) = 0.e0 |
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| 171 | zwu(jpi,jpj+2) = 0.e0 |
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| 172 | DO ji = 1, jpi-1 |
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| 173 | iju = jpi - ji |
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| 174 | zwu(ji,jpj ) = - zwu(iju,jpj-1) |
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| 175 | zwu(ji,jpj+1) = - zwu(iju,jpj-2) |
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| 176 | zwu(ji,jpj+2) = - zwu(iju,jpj-3) |
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| 177 | END DO |
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| 178 | DO ji = -1, jpi+2 |
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| 179 | ijt = jpi - ji + 1 |
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| 180 | zwv(ji,jpj) = - zwv(ijt,jpj-2) |
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| 181 | END DO |
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| 182 | DO ji = jpi/2+1, jpi+2 |
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| 183 | ijt = jpi - ji + 1 |
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| 184 | zwv(ji,jpjm1) = - zwv(ijt,jpjm1) |
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| 185 | END DO |
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| 186 | ELSE |
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| 187 | ! closed |
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| 188 | zwu(:,jpj+1) = 0.e0 |
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| 189 | zwu(:,jpj+2) = 0.e0 |
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| 190 | ENDIF |
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| 191 | |
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| 192 | ! relative vorticity (vertical component of the velocity curl) |
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| 193 | DO jj = 1, jpjm1 |
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| 194 | DO ji = 1, fs_jpim1 ! vector opt. |
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| 195 | rotn(ji,jj,jk) = ( zwv(ji+1,jj ) - zwv(ji,jj) & |
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| 196 | - zwu(ji ,jj+1) + zwu(ji,jj) ) & |
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| 197 | * fmask(ji,jj,jk) / ( e1f(ji,jj)*e2f(ji,jj) ) |
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| 198 | END DO |
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| 199 | END DO |
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| 200 | |
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| 201 | ! second order accurate scheme along straight coast |
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| 202 | DO jl = 1, npcoa(1,jk) |
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| 203 | ii = nicoa(jl,1,jk) |
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| 204 | ij = njcoa(jl,1,jk) |
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| 205 | rotn(ii,ij,jk) = 1. / ( e1f(ii,ij) * e2f(ii,ij) ) & |
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| 206 | * ( + 4. * zwv(ii+1,ij) - zwv(ii+2,ij) + 0.2 * zwv(ii+3,ij) ) |
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| 207 | END DO |
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| 208 | DO jl = 1, npcoa(2,jk) |
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| 209 | ii = nicoa(jl,2,jk) |
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| 210 | ij = njcoa(jl,2,jk) |
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| 211 | rotn(ii,ij,jk) = 1./(e1f(ii,ij)*e2f(ii,ij)) & |
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| 212 | *(-4.*zwv(ii,ij)+zwv(ii-1,ij)-0.2*zwv(ii-2,ij)) |
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| 213 | END DO |
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| 214 | DO jl = 1, npcoa(3,jk) |
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| 215 | ii = nicoa(jl,3,jk) |
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| 216 | ij = njcoa(jl,3,jk) |
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| 217 | rotn(ii,ij,jk) = -1. / ( e1f(ii,ij)*e2f(ii,ij) ) & |
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| 218 | * ( +4. * zwu(ii,ij+1) - zwu(ii,ij+2) + 0.2 * zwu(ii,ij+3) ) |
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| 219 | END DO |
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| 220 | DO jl = 1, npcoa(4,jk) |
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| 221 | ii = nicoa(jl,4,jk) |
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| 222 | ij = njcoa(jl,4,jk) |
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| 223 | rotn(ii,ij,jk) = -1. / ( e1f(ii,ij)*e2f(ii,ij) ) & |
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| 224 | * ( -4. * zwu(ii,ij) + zwu(ii,ij-1) - 0.2 * zwu(ii,ij-2) ) |
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| 225 | END DO |
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| 226 | |
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| 227 | ! ! =============== |
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| 228 | END DO ! End of slab |
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| 229 | ! ! =============== |
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| 230 | |
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| 231 | ! 4. Lateral boundary conditions on hdivn and rotn |
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| 232 | ! ---------------------------------=======---====== |
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| 233 | CALL lbc_lnk( hdivn, 'T', 1. ) ! T-point, no sign change |
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| 234 | CALL lbc_lnk( rotn , 'F', 1. ) ! F-point, no sign change |
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| 235 | |
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| 236 | END SUBROUTINE div_cur |
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| 237 | |
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| 238 | #else |
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| 239 | !!---------------------------------------------------------------------- |
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| 240 | !! Default option 2nd order centered schemes |
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| 241 | !!---------------------------------------------------------------------- |
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| 242 | |
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| 243 | SUBROUTINE div_cur( kt ) |
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| 244 | !!---------------------------------------------------------------------- |
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| 245 | !! *** ROUTINE div_cur *** |
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| 246 | !! |
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| 247 | !! ** Purpose : compute the horizontal divergence and the relative |
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| 248 | !! vorticity at before and now time-step |
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| 249 | !! |
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| 250 | !! ** Method : - Divergence: |
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| 251 | !! - save the divergence computed at the previous time-step |
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| 252 | !! (note that the Asselin filter has not been applied on hdivb) |
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| 253 | !! - compute the now divergence given by : |
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| 254 | !! * s-coordinate ('key_s_coord' defined) |
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| 255 | !! hdivn = 1/(e1t*e2t*e3t) ( di[e2u*e3u un] + dj[e1v*e3v vn] ) |
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| 256 | !! * z-coordinate (default key) |
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| 257 | !! hdivn = 1/(e1t*e2t) [ di(e2u un) + dj(e1v vn) ] |
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| 258 | !! - apply lateral boundary conditions on hdivn |
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| 259 | !! - Relavtive Vorticity : |
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| 260 | !! - save the curl computed at the previous time-step (rotb = rotn) |
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| 261 | !! (note that the Asselin time filter has not been applied to rotb) |
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| 262 | !! - compute the now curl in tensorial formalism: |
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| 263 | !! rotn = 1/(e1f*e2f) ( di[e2v vn] - dj[e1u un] ) |
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| 264 | !! - apply lateral boundary conditions on rotn through a call to |
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| 265 | !! routine lbc_lnk routine. |
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| 266 | !! Note: Coastal boundary condition: lateral friction set through |
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| 267 | !! the value of fmask along the coast (see dommsk.F90) and shlat |
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| 268 | !! (namelist parameter) |
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| 269 | !! |
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| 270 | !! ** Action : - update hdivb, hdivn, the before & now hor. divergence |
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| 271 | !! - update rotb , rotn , the before & now rel. vorticity |
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| 272 | !! |
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| 273 | !! History : |
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| 274 | !! 1.0 ! 87-06 (P. Andrich, D. L Hostis) Original code |
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| 275 | !! 4.0 ! 91-11 (G. Madec) |
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| 276 | !! 6.0 ! 93-03 (M. Guyon) symetrical conditions |
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| 277 | !! 7.0 ! 96-01 (G. Madec) s-coordinates |
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| 278 | !! 8.0 ! 97-06 (G. Madec) lateral boundary cond., lbc |
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| 279 | !! 8.1 ! 97-08 (J.M. Molines) Open boundaries |
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| 280 | !! 9.0 ! 02-09 (G. Madec, E. Durand) Free form, F90 |
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| 281 | !!---------------------------------------------------------------------- |
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| 282 | !! * Arguments |
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| 283 | INTEGER, INTENT( in ) :: kt ! ocean time-step index |
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| 284 | |
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| 285 | !! * Local declarations |
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| 286 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 287 | !!---------------------------------------------------------------------- |
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| 288 | |
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| 289 | IF( kt == nit000 ) THEN |
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| 290 | IF(lwp) WRITE(numout,*) |
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| 291 | IF(lwp) WRITE(numout,*) 'div_cur : horizontal velocity divergence and' |
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| 292 | IF(lwp) WRITE(numout,*) '~~~~~~~ relative vorticity' |
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| 293 | ENDIF |
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| 294 | |
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| 295 | ! ! =============== |
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| 296 | DO jk = 1, jpkm1 ! Horizontal slab |
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| 297 | ! ! =============== |
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| 298 | |
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| 299 | hdivb(:,:,jk) = hdivn(:,:,jk) ! time swap of div arrays |
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| 300 | rotb (:,:,jk) = rotn (:,:,jk) ! time swap of rot arrays |
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| 301 | |
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| 302 | ! ! -------- |
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| 303 | ! Horizontal divergence ! div |
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| 304 | ! ! -------- |
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| 305 | DO jj = 2, jpjm1 |
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| 306 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 307 | #if defined key_s_coord || defined key_partial_steps |
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| 308 | hdivn(ji,jj,jk) = & |
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| 309 | ( e2u(ji,jj)*fse3u(ji,jj,jk) * un(ji,jj,jk) - e2u(ji-1,jj )*fse3u(ji-1,jj ,jk) * un(ji-1,jj ,jk) & |
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| 310 | + e1v(ji,jj)*fse3v(ji,jj,jk) * vn(ji,jj,jk) - e1v(ji ,jj-1)*fse3v(ji ,jj-1,jk) * vn(ji ,jj-1,jk) ) & |
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| 311 | / ( e1t(ji,jj) * e2t(ji,jj) * fse3t(ji,jj,jk) ) |
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| 312 | #else |
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| 313 | hdivn(ji,jj,jk) = ( e2u(ji,jj) * un(ji,jj,jk) - e2u(ji-1,jj ) * un(ji-1,jj ,jk) & |
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| 314 | & + e1v(ji,jj) * vn(ji,jj,jk) - e1v(ji ,jj-1) * vn(ji ,jj-1,jk) ) & |
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| 315 | / ( e1t(ji,jj) * e2t(ji,jj) ) |
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| 316 | #endif |
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| 317 | END DO |
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| 318 | END DO |
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| 319 | |
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| 320 | #if defined key_obc |
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| 321 | ! open boundaries (div must be zero behind the open boundary) |
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| 322 | ! mpp remark: The zeroing of hdivn can probably be extended to 1->jpi/jpj for the correct row/column |
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| 323 | IF( lp_obc_east ) hdivn(nie0p1:nie1p1,nje0 :nje1 ,jk) = 0.e0 ! east |
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| 324 | IF( lp_obc_west ) hdivn(niw0 :niw1 ,njw0 :njw1 ,jk) = 0.e0 ! west |
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| 325 | IF( lp_obc_north ) hdivn(nin0 :nin1 ,njn0p1:njn1p1,jk) = 0.e0 ! north |
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| 326 | IF( lp_obc_south ) hdivn(nis0 :nis1 ,njs0 :njs1 ,jk) = 0.e0 ! south |
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| 327 | #endif |
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| 328 | ! ! -------- |
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| 329 | ! relative vorticity ! rot |
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| 330 | ! ! -------- |
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| 331 | DO jj = 1, jpjm1 |
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| 332 | DO ji = 1, fs_jpim1 ! vector opt. |
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| 333 | rotn(ji,jj,jk) = ( e2v(ji+1,jj ) * vn(ji+1,jj ,jk) - e2v(ji,jj) * vn(ji,jj,jk) & |
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| 334 | & - e1u(ji ,jj+1) * un(ji ,jj+1,jk) + e1u(ji,jj) * un(ji,jj,jk) ) & |
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| 335 | & * fmask(ji,jj,jk) / ( e1f(ji,jj) * e2f(ji,jj) ) |
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| 336 | END DO |
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| 337 | END DO |
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| 338 | ! ! =============== |
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| 339 | END DO ! End of slab |
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| 340 | ! ! =============== |
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| 341 | |
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| 342 | ! 4. Lateral boundary conditions on hdivn and rotn |
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| 343 | ! ---------------------------------=======---====== |
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| 344 | CALL lbc_lnk( hdivn, 'T', 1. ) ! T-point, no sign change |
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| 345 | CALL lbc_lnk( rotn , 'F', 1. ) ! F-point, no sign change |
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| 346 | |
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| 347 | END SUBROUTINE div_cur |
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| 348 | |
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| 349 | #endif |
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| 350 | !!====================================================================== |
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| 351 | END MODULE divcur |
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