1 | MODULE dynvor |
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2 | !!====================================================================== |
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3 | !! *** MODULE dynvor *** |
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4 | !! Ocean dynamics: Update the momentum trend with the relative and |
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5 | !! planetary vorticity trends |
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6 | !!====================================================================== |
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7 | !! History : OPA ! 1989-12 (P. Andrich) vor_ens: Original code |
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8 | !! 5.0 ! 1991-11 (G. Madec) vor_ene, vor_mix: Original code |
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9 | !! 6.0 ! 1996-01 (G. Madec) s-coord, suppress work arrays |
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10 | !! NEMO 0.5 ! 2002-08 (G. Madec) F90: Free form and module |
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11 | !! 1.0 ! 2004-02 (G. Madec) vor_een: Original code |
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12 | !! - ! 2003-08 (G. Madec) add vor_ctl |
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13 | !! - ! 2005-11 (G. Madec) add dyn_vor (new step architecture) |
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14 | !! 2.0 ! 2006-11 (G. Madec) flux form advection: add metric term |
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15 | !! 3.2 ! 2009-04 (R. Benshila) vvl: correction of een scheme |
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16 | !! 3.3 ! 2010-10 (C. Ethe, G. Madec) reorganisation of initialisation phase |
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17 | !! 3.7 ! 2014-04 (G. Madec) trend simplification: suppress jpdyn_trd_dat vorticity |
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18 | !! - ! 2014-06 (G. Madec) suppression of velocity curl from in-core memory |
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19 | !! - ! 2016-12 (G. Madec, E. Clementi) add Stokes-Coriolis trends (ln_stcor=T) |
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20 | !! 4.0 ! 2017-07 (G. Madec) linear dynamics + trends diag. with Stokes-Coriolis |
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21 | !! - ! 2018-03 (G. Madec) add two new schemes (ln_dynvor_enT and ln_dynvor_eet) |
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22 | !! - ! 2018-04 (G. Madec) add pre-computed gradient for metric term calculation |
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23 | !!---------------------------------------------------------------------- |
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24 | |
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25 | !!---------------------------------------------------------------------- |
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26 | !! dyn_vor : Update the momentum trend with the vorticity trend |
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27 | !! vor_ens : enstrophy conserving scheme (ln_dynvor_ens=T) |
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28 | !! vor_ene : energy conserving scheme (ln_dynvor_ene=T) |
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29 | !! vor_een : energy and enstrophy conserving (ln_dynvor_een=T) |
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30 | !! dyn_vor_init : set and control of the different vorticity option |
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31 | !!---------------------------------------------------------------------- |
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32 | USE oce ! ocean dynamics and tracers |
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33 | USE dom_oce ! ocean space and time domain |
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34 | USE dommsk ! ocean mask |
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35 | USE dynadv ! momentum advection |
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36 | USE trd_oce ! trends: ocean variables |
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37 | USE trddyn ! trend manager: dynamics |
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38 | USE sbcwave ! Surface Waves (add Stokes-Coriolis force) |
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39 | USE sbc_oce , ONLY : ln_stcor ! use Stoke-Coriolis force |
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40 | ! |
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41 | USE lbclnk ! ocean lateral boundary conditions (or mpp link) |
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42 | USE prtctl ! Print control |
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43 | USE in_out_manager ! I/O manager |
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44 | USE lib_mpp ! MPP library |
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45 | USE timing ! Timing |
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46 | |
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47 | IMPLICIT NONE |
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48 | PRIVATE |
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49 | |
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50 | PUBLIC dyn_vor ! routine called by step.F90 |
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51 | PUBLIC dyn_vor_init ! routine called by nemogcm.F90 |
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52 | |
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53 | ! !!* Namelist namdyn_vor: vorticity term |
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54 | LOGICAL, PUBLIC :: ln_dynvor_ens !: enstrophy conserving scheme (ENS) |
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55 | LOGICAL, PUBLIC :: ln_dynvor_ene !: f-point energy conserving scheme (ENE) |
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56 | LOGICAL, PUBLIC :: ln_dynvor_enT !: t-point energy conserving scheme (ENT) |
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57 | LOGICAL, PUBLIC :: ln_dynvor_eeT !: t-point energy conserving scheme (EET) |
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58 | LOGICAL, PUBLIC :: ln_dynvor_een !: energy & enstrophy conserving scheme (EEN) |
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59 | INTEGER, PUBLIC :: nn_een_e3f !: e3f=masked averaging of e3t divided by 4 (=0) or by the sum of mask (=1) |
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60 | LOGICAL, PUBLIC :: ln_dynvor_mix !: mixed scheme (MIX) |
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61 | LOGICAL, PUBLIC :: ln_dynvor_msk !: vorticity multiplied by fmask (=T) or not (=F) (all vorticity schemes) |
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62 | |
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63 | INTEGER, PUBLIC :: nvor_scheme !: choice of the type of advection scheme |
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64 | ! ! associated indices: |
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65 | INTEGER, PUBLIC, PARAMETER :: np_ENS = 0 ! ENS scheme |
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66 | INTEGER, PUBLIC, PARAMETER :: np_ENE = 1 ! ENE scheme |
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67 | INTEGER, PUBLIC, PARAMETER :: np_ENT = 2 ! ENT scheme (t-point vorticity) |
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68 | INTEGER, PUBLIC, PARAMETER :: np_EET = 3 ! EET scheme (EEN using e3t) |
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69 | INTEGER, PUBLIC, PARAMETER :: np_EEN = 4 ! EEN scheme |
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70 | INTEGER, PUBLIC, PARAMETER :: np_MIX = 5 ! MIX scheme |
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71 | |
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72 | INTEGER :: ncor, nrvm, ntot ! choice of calculated vorticity |
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73 | ! ! associated indices: |
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74 | INTEGER, PUBLIC, PARAMETER :: np_COR = 1 ! Coriolis (planetary) |
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75 | INTEGER, PUBLIC, PARAMETER :: np_RVO = 2 ! relative vorticity |
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76 | INTEGER, PUBLIC, PARAMETER :: np_MET = 3 ! metric term |
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77 | INTEGER, PUBLIC, PARAMETER :: np_CRV = 4 ! relative + planetary (total vorticity) |
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78 | INTEGER, PUBLIC, PARAMETER :: np_CME = 5 ! Coriolis + metric term |
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79 | |
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80 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: di_e2u_2 ! = di(e2u)/2 used in T-point metric term calculation |
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81 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: dj_e1v_2 ! = dj(e1v)/2 - - - - |
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82 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: di_e2v_2e1e2f ! = di(e2u)/(2*e1e2f) used in F-point metric term calculation |
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83 | REAL(wp), ALLOCATABLE, DIMENSION(:,:) :: dj_e1u_2e1e2f ! = dj(e1v)/(2*e1e2f) - - - - |
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84 | |
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85 | REAL(wp) :: r1_4 = 0.250_wp ! =1/4 |
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86 | REAL(wp) :: r1_8 = 0.125_wp ! =1/8 |
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87 | REAL(wp) :: r1_12 = 1._wp / 12._wp ! 1/12 |
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88 | |
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89 | !! * Substitutions |
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90 | # include "vectopt_loop_substitute.h90" |
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91 | !!---------------------------------------------------------------------- |
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92 | !! NEMO/OCE 4.0 , NEMO Consortium (2018) |
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93 | !! $Id$ |
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94 | !! Software governed by the CeCILL license (see ./LICENSE) |
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95 | !!---------------------------------------------------------------------- |
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96 | CONTAINS |
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97 | |
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98 | SUBROUTINE dyn_vor( kt ) |
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99 | !!---------------------------------------------------------------------- |
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100 | !! |
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101 | !! ** Purpose : compute the lateral ocean tracer physics. |
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102 | !! |
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103 | !! ** Action : - Update (ua,va) with the now vorticity term trend |
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104 | !! - save the trends in (ztrdu,ztrdv) in 2 parts (relative |
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105 | !! and planetary vorticity trends) and send them to trd_dyn |
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106 | !! for futher diagnostics (l_trddyn=T) |
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107 | !!---------------------------------------------------------------------- |
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108 | INTEGER, INTENT( in ) :: kt ! ocean time-step index |
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109 | ! |
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110 | REAL(wp), ALLOCATABLE, DIMENSION(:,:,:) :: ztrdu, ztrdv |
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111 | !!---------------------------------------------------------------------- |
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112 | ! |
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113 | IF( ln_timing ) CALL timing_start('dyn_vor') |
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114 | ! |
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115 | IF( l_trddyn ) THEN !== trend diagnostics case : split the added trend in two parts ==! |
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116 | ! |
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117 | ALLOCATE( ztrdu(jpi,jpj,jpk), ztrdv(jpi,jpj,jpk) ) |
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118 | ! |
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119 | ztrdu(:,:,:) = ua(:,:,:) !* planetary vorticity trend (including Stokes-Coriolis force) |
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120 | ztrdv(:,:,:) = va(:,:,:) |
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121 | SELECT CASE( nvor_scheme ) |
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122 | CASE( np_ENS ) ; CALL vor_ens( kt, ncor, un , vn , ua, va ) ! enstrophy conserving scheme |
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123 | IF( ln_stcor ) CALL vor_ens( kt, ncor, usd, vsd, ua, va ) ! add the Stokes-Coriolis trend |
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124 | CASE( np_ENE, np_MIX ) ; CALL vor_ene( kt, ncor, un , vn , ua, va ) ! energy conserving scheme |
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125 | IF( ln_stcor ) CALL vor_ene( kt, ncor, usd, vsd, ua, va ) ! add the Stokes-Coriolis trend |
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126 | CASE( np_ENT ) ; CALL vor_enT( kt, ncor, un , vn , ua, va ) ! energy conserving scheme (T-pts) |
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127 | IF( ln_stcor ) CALL vor_enT( kt, ncor, usd, vsd, ua, va ) ! add the Stokes-Coriolis trend |
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128 | CASE( np_EET ) ; CALL vor_eeT( kt, ncor, un , vn , ua, va ) ! energy conserving scheme (een with e3t) |
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129 | IF( ln_stcor ) CALL vor_eeT( kt, ncor, usd, vsd, ua, va ) ! add the Stokes-Coriolis trend |
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130 | CASE( np_EEN ) ; CALL vor_een( kt, ncor, un , vn , ua, va ) ! energy & enstrophy scheme |
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131 | IF( ln_stcor ) CALL vor_een( kt, ncor, usd, vsd, ua, va ) ! add the Stokes-Coriolis trend |
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132 | END SELECT |
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133 | ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:) |
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134 | ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:) |
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135 | CALL trd_dyn( ztrdu, ztrdv, jpdyn_pvo, kt ) |
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136 | ! |
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137 | IF( n_dynadv /= np_LIN_dyn ) THEN !* relative vorticity or metric trend (only in non-linear case) |
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138 | ztrdu(:,:,:) = ua(:,:,:) |
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139 | ztrdv(:,:,:) = va(:,:,:) |
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140 | SELECT CASE( nvor_scheme ) |
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141 | CASE( np_ENT ) ; CALL vor_enT( kt, nrvm, un , vn , ua, va ) ! energy conserving scheme (T-pts) |
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142 | CASE( np_EET ) ; CALL vor_eeT( kt, nrvm, un , vn , ua, va ) ! energy conserving scheme (een with e3t) |
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143 | CASE( np_ENE ) ; CALL vor_ene( kt, nrvm, un , vn , ua, va ) ! energy conserving scheme |
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144 | CASE( np_ENS, np_MIX ) ; CALL vor_ens( kt, nrvm, un , vn , ua, va ) ! enstrophy conserving scheme |
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145 | CASE( np_EEN ) ; CALL vor_een( kt, nrvm, un , vn , ua, va ) ! energy & enstrophy scheme |
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146 | END SELECT |
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147 | ztrdu(:,:,:) = ua(:,:,:) - ztrdu(:,:,:) |
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148 | ztrdv(:,:,:) = va(:,:,:) - ztrdv(:,:,:) |
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149 | CALL trd_dyn( ztrdu, ztrdv, jpdyn_rvo, kt ) |
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150 | ENDIF |
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151 | ! |
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152 | DEALLOCATE( ztrdu, ztrdv ) |
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153 | ! |
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154 | ELSE !== total vorticity trend added to the general trend ==! |
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155 | ! |
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156 | SELECT CASE ( nvor_scheme ) !== vorticity trend added to the general trend ==! |
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157 | CASE( np_ENT ) !* energy conserving scheme (T-pts) |
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158 | CALL vor_enT( kt, ntot, un , vn , ua, va ) ! total vorticity trend |
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159 | IF( ln_stcor ) CALL vor_enT( kt, ncor, usd, vsd, ua, va ) ! add the Stokes-Coriolis trend |
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160 | CASE( np_EET ) !* energy conserving scheme (een scheme using e3t) |
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161 | CALL vor_eeT( kt, ntot, un , vn , ua, va ) ! total vorticity trend |
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162 | IF( ln_stcor ) CALL vor_eeT( kt, ncor, usd, vsd, ua, va ) ! add the Stokes-Coriolis trend |
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163 | CASE( np_ENE ) !* energy conserving scheme |
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164 | CALL vor_ene( kt, ntot, un , vn , ua, va ) ! total vorticity trend |
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165 | IF( ln_stcor ) CALL vor_ene( kt, ncor, usd, vsd, ua, va ) ! add the Stokes-Coriolis trend |
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166 | CASE( np_ENS ) !* enstrophy conserving scheme |
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167 | CALL vor_ens( kt, ntot, un , vn , ua, va ) ! total vorticity trend |
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168 | IF( ln_stcor ) CALL vor_ens( kt, ncor, usd, vsd, ua, va ) ! add the Stokes-Coriolis trend |
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169 | CASE( np_MIX ) !* mixed ene-ens scheme |
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170 | CALL vor_ens( kt, nrvm, un , vn , ua, va ) ! relative vorticity or metric trend (ens) |
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171 | CALL vor_ene( kt, ncor, un , vn , ua, va ) ! planetary vorticity trend (ene) |
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172 | IF( ln_stcor ) CALL vor_ene( kt, ncor, usd, vsd, ua, va ) ! add the Stokes-Coriolis trend |
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173 | CASE( np_EEN ) !* energy and enstrophy conserving scheme |
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174 | CALL vor_een( kt, ntot, un , vn , ua, va ) ! total vorticity trend |
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175 | IF( ln_stcor ) CALL vor_een( kt, ncor, usd, vsd, ua, va ) ! add the Stokes-Coriolis trend |
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176 | END SELECT |
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177 | ! |
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178 | ENDIF |
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179 | ! |
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180 | ! ! print sum trends (used for debugging) |
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181 | IF(ln_ctl) CALL prt_ctl( tab3d_1=ua, clinfo1=' vor - Ua: ', mask1=umask, & |
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182 | & tab3d_2=va, clinfo2= ' Va: ', mask2=vmask, clinfo3='dyn' ) |
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183 | ! |
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184 | IF( ln_timing ) CALL timing_stop('dyn_vor') |
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185 | ! |
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186 | END SUBROUTINE dyn_vor |
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187 | |
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188 | |
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189 | SUBROUTINE vor_enT( kt, kvor, pu, pv, pu_rhs, pv_rhs ) |
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190 | !!---------------------------------------------------------------------- |
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191 | !! *** ROUTINE vor_enT *** |
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192 | !! |
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193 | !! ** Purpose : Compute the now total vorticity trend and add it to |
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194 | !! the general trend of the momentum equation. |
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195 | !! |
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196 | !! ** Method : Trend evaluated using now fields (centered in time) |
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197 | !! and t-point evaluation of vorticity (planetary and relative). |
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198 | !! conserves the horizontal kinetic energy. |
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199 | !! The general trend of momentum is increased due to the vorticity |
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200 | !! term which is given by: |
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201 | !! voru = 1/bu mj[ ( mi(mj(bf*rvor))+bt*f_t)/e3t mj[vn] ] |
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202 | !! vorv = 1/bv mi[ ( mi(mj(bf*rvor))+bt*f_t)/e3f mj[un] ] |
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203 | !! where rvor is the relative vorticity at f-point |
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204 | !! |
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205 | !! ** Action : - Update (ua,va) with the now vorticity term trend |
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206 | !!---------------------------------------------------------------------- |
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207 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
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208 | INTEGER , INTENT(in ) :: kvor ! total, planetary, relative, or metric |
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209 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(inout) :: pu, pv ! now velocities |
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210 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(inout) :: pu_rhs, pv_rhs ! total v-trend |
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211 | ! |
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212 | INTEGER :: ji, jj, jk ! dummy loop indices |
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213 | REAL(wp) :: zx1, zy1, zx2, zy2 ! local scalars |
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214 | REAL(wp), DIMENSION(jpi,jpj) :: zwx, zwy, zwt ! 2D workspace |
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215 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwz ! 3D workspace |
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216 | !!---------------------------------------------------------------------- |
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217 | ! |
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218 | IF( kt == nit000 ) THEN |
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219 | IF(lwp) WRITE(numout,*) |
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220 | IF(lwp) WRITE(numout,*) 'dyn:vor_enT : vorticity term: t-point energy conserving scheme' |
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221 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~' |
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222 | ENDIF |
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223 | ! |
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224 | ! |
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225 | SELECT CASE( kvor ) !== volume weighted vorticity considered ==! |
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226 | CASE ( np_RVO ) !* relative vorticity |
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227 | DO jk = 1, jpkm1 ! Horizontal slab |
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228 | DO jj = 1, jpjm1 |
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229 | DO ji = 1, jpim1 |
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230 | zwz(ji,jj,jk) = ( e2v(ji+1,jj) * pv(ji+1,jj,jk) - e2v(ji,jj) * pv(ji,jj,jk) & |
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231 | & - e1u(ji,jj+1) * pu(ji,jj+1,jk) + e1u(ji,jj) * pu(ji,jj,jk) ) * r1_e1e2f(ji,jj) |
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232 | END DO |
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233 | END DO |
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234 | IF( ln_dynvor_msk ) THEN ! mask/unmask relative vorticity |
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235 | DO jj = 1, jpjm1 |
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236 | DO ji = 1, jpim1 |
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237 | zwz(ji,jj,jk) = zwz(ji,jj,jk) * fmask(ji,jj,jk) |
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238 | END DO |
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239 | END DO |
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240 | ENDIF |
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241 | END DO |
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242 | |
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243 | CALL lbc_lnk( 'dynvor', zwz, 'F', 1. ) |
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244 | |
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245 | CASE ( np_CRV ) !* Coriolis + relative vorticity |
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246 | DO jk = 1, jpkm1 ! Horizontal slab |
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247 | DO jj = 1, jpjm1 |
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248 | DO ji = 1, jpim1 ! relative vorticity |
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249 | zwz(ji,jj,jk) = ( e2v(ji+1,jj) * pv(ji+1,jj,jk) - e2v(ji,jj) * pv(ji,jj,jk) & |
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250 | & - e1u(ji,jj+1) * pu(ji,jj+1,jk) + e1u(ji,jj) * pu(ji,jj,jk) ) * r1_e1e2f(ji,jj) |
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251 | END DO |
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252 | END DO |
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253 | IF( ln_dynvor_msk ) THEN ! mask/unmask relative vorticity |
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254 | DO jj = 1, jpjm1 |
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255 | DO ji = 1, jpim1 |
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256 | zwz(ji,jj,jk) = zwz(ji,jj,jk) * fmask(ji,jj,jk) |
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257 | END DO |
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258 | END DO |
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259 | ENDIF |
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260 | END DO |
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261 | |
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262 | CALL lbc_lnk( 'dynvor', zwz, 'F', 1. ) |
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263 | |
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264 | END SELECT |
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265 | |
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266 | ! ! =============== |
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267 | DO jk = 1, jpkm1 ! Horizontal slab |
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268 | ! ! =============== |
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269 | |
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270 | SELECT CASE( kvor ) !== volume weighted vorticity considered ==! |
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271 | CASE ( np_COR ) !* Coriolis (planetary vorticity) |
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272 | zwt(:,:) = ff_t(:,:) * e1e2t(:,:)*e3t_n(:,:,jk) |
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273 | CASE ( np_RVO ) !* relative vorticity |
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274 | DO jj = 2, jpj |
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275 | DO ji = 2, jpi ! vector opt. |
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276 | zwt(ji,jj) = r1_4 * ( zwz(ji-1,jj ,jk) + zwz(ji,jj ,jk) & |
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277 | & + zwz(ji-1,jj-1,jk) + zwz(ji,jj-1,jk) ) * e1e2t(ji,jj)*e3t_n(ji,jj,jk) |
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278 | END DO |
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279 | END DO |
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280 | CASE ( np_MET ) !* metric term |
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281 | DO jj = 2, jpj |
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282 | DO ji = 2, jpi |
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283 | zwt(ji,jj) = ( ( pv(ji,jj,jk) + pv(ji,jj-1,jk) ) * di_e2u_2(ji,jj) & |
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284 | & - ( pu(ji,jj,jk) + pu(ji-1,jj,jk) ) * dj_e1v_2(ji,jj) ) * e3t_n(ji,jj,jk) |
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285 | END DO |
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286 | END DO |
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287 | CASE ( np_CRV ) !* Coriolis + relative vorticity |
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288 | DO jj = 2, jpj |
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289 | DO ji = 2, jpi ! vector opt. |
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290 | zwt(ji,jj) = ( ff_t(ji,jj) + r1_4 * ( zwz(ji-1,jj ,jk) + zwz(ji,jj ,jk) & |
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291 | & + zwz(ji-1,jj-1,jk) + zwz(ji,jj-1,jk) ) ) * e1e2t(ji,jj)*e3t_n(ji,jj,jk) |
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292 | END DO |
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293 | END DO |
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294 | CASE ( np_CME ) !* Coriolis + metric |
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295 | DO jj = 2, jpj |
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296 | DO ji = 2, jpi ! vector opt. |
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297 | zwt(ji,jj) = ( ff_t(ji,jj) * e1e2t(ji,jj) & |
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298 | & + ( pv(ji,jj,jk) + pv(ji,jj-1,jk) ) * di_e2u_2(ji,jj) & |
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299 | & - ( pu(ji,jj,jk) + pu(ji-1,jj,jk) ) * dj_e1v_2(ji,jj) ) * e3t_n(ji,jj,jk) |
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300 | END DO |
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301 | END DO |
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302 | CASE DEFAULT ! error |
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303 | CALL ctl_stop('STOP','dyn_vor: wrong value for kvor' ) |
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304 | END SELECT |
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305 | ! |
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306 | ! !== compute and add the vorticity term trend =! |
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307 | DO jj = 2, jpjm1 |
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308 | DO ji = 2, jpim1 ! vector opt. |
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309 | pu_rhs(ji,jj,jk) = pu_rhs(ji,jj,jk) + r1_4 * r1_e1e2u(ji,jj) / e3u_n(ji,jj,jk) & |
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310 | & * ( zwt(ji+1,jj) * ( pv(ji+1,jj,jk) + pv(ji+1,jj-1,jk) ) & |
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311 | & + zwt(ji ,jj) * ( pv(ji ,jj,jk) + pv(ji ,jj-1,jk) ) ) |
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312 | ! |
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313 | pv_rhs(ji,jj,jk) = pv_rhs(ji,jj,jk) - r1_4 * r1_e1e2v(ji,jj) / e3v_n(ji,jj,jk) & |
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314 | & * ( zwt(ji,jj+1) * ( pu(ji,jj+1,jk) + pu(ji-1,jj+1,jk) ) & |
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315 | & + zwt(ji,jj ) * ( pu(ji,jj ,jk) + pu(ji-1,jj ,jk) ) ) |
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316 | END DO |
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317 | END DO |
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318 | ! ! =============== |
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319 | END DO ! End of slab |
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320 | ! ! =============== |
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321 | END SUBROUTINE vor_enT |
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322 | |
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323 | |
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324 | SUBROUTINE vor_ene( kt, kvor, pun, pvn, pua, pva ) |
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325 | !!---------------------------------------------------------------------- |
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326 | !! *** ROUTINE vor_ene *** |
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327 | !! |
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328 | !! ** Purpose : Compute the now total vorticity trend and add it to |
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329 | !! the general trend of the momentum equation. |
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330 | !! |
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331 | !! ** Method : Trend evaluated using now fields (centered in time) |
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332 | !! and the Sadourny (1975) flux form formulation : conserves the |
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333 | !! horizontal kinetic energy. |
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334 | !! The general trend of momentum is increased due to the vorticity |
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335 | !! term which is given by: |
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336 | !! voru = 1/e1u mj-1[ (rvor+f)/e3f mi(e1v*e3v vn) ] |
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337 | !! vorv = 1/e2v mi-1[ (rvor+f)/e3f mj(e2u*e3u un) ] |
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338 | !! where rvor is the relative vorticity |
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339 | !! |
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340 | !! ** Action : - Update (ua,va) with the now vorticity term trend |
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341 | !! |
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342 | !! References : Sadourny, r., 1975, j. atmos. sciences, 32, 680-689. |
---|
343 | !!---------------------------------------------------------------------- |
---|
344 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
---|
345 | INTEGER , INTENT(in ) :: kvor ! total, planetary, relative, or metric |
---|
346 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(inout) :: pun, pvn ! now velocities |
---|
347 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(inout) :: pua, pva ! total v-trend |
---|
348 | ! |
---|
349 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
350 | REAL(wp) :: zx1, zy1, zx2, zy2 ! local scalars |
---|
351 | REAL(wp), DIMENSION(jpi,jpj) :: zwx, zwy, zwz ! 2D workspace |
---|
352 | !!---------------------------------------------------------------------- |
---|
353 | ! |
---|
354 | IF( kt == nit000 ) THEN |
---|
355 | IF(lwp) WRITE(numout,*) |
---|
356 | IF(lwp) WRITE(numout,*) 'dyn:vor_ene : vorticity term: energy conserving scheme' |
---|
357 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~' |
---|
358 | ENDIF |
---|
359 | ! |
---|
360 | ! ! =============== |
---|
361 | DO jk = 1, jpkm1 ! Horizontal slab |
---|
362 | ! ! =============== |
---|
363 | ! |
---|
364 | SELECT CASE( kvor ) !== vorticity considered ==! |
---|
365 | CASE ( np_COR ) !* Coriolis (planetary vorticity) |
---|
366 | zwz(:,:) = ff_f(:,:) |
---|
367 | CASE ( np_RVO ) !* relative vorticity |
---|
368 | DO jj = 1, jpjm1 |
---|
369 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
370 | zwz(ji,jj) = ( e2v(ji+1,jj ) * pvn(ji+1,jj ,jk) - e2v(ji,jj) * pvn(ji,jj,jk) & |
---|
371 | & - e1u(ji ,jj+1) * pun(ji ,jj+1,jk) + e1u(ji,jj) * pun(ji,jj,jk) ) * r1_e1e2f(ji,jj) |
---|
372 | END DO |
---|
373 | END DO |
---|
374 | CASE ( np_MET ) !* metric term |
---|
375 | DO jj = 1, jpjm1 |
---|
376 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
377 | zwz(ji,jj) = ( pvn(ji+1,jj ,jk) + pvn(ji,jj,jk) ) * di_e2v_2e1e2f(ji,jj) & |
---|
378 | & - ( pun(ji ,jj+1,jk) + pun(ji,jj,jk) ) * dj_e1u_2e1e2f(ji,jj) |
---|
379 | END DO |
---|
380 | END DO |
---|
381 | CASE ( np_CRV ) !* Coriolis + relative vorticity |
---|
382 | DO jj = 1, jpjm1 |
---|
383 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
384 | zwz(ji,jj) = ff_f(ji,jj) + ( e2v(ji+1,jj) * pvn(ji+1,jj,jk) - e2v(ji,jj) * pvn(ji,jj,jk) & |
---|
385 | & - e1u(ji,jj+1) * pun(ji,jj+1,jk) + e1u(ji,jj) * pun(ji,jj,jk) ) * r1_e1e2f(ji,jj) |
---|
386 | END DO |
---|
387 | END DO |
---|
388 | CASE ( np_CME ) !* Coriolis + metric |
---|
389 | DO jj = 1, jpjm1 |
---|
390 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
391 | zwz(ji,jj) = ff_f(ji,jj) + ( pvn(ji+1,jj ,jk) + pvn(ji,jj,jk) ) * di_e2v_2e1e2f(ji,jj) & |
---|
392 | & - ( pun(ji ,jj+1,jk) + pun(ji,jj,jk) ) * dj_e1u_2e1e2f(ji,jj) |
---|
393 | END DO |
---|
394 | END DO |
---|
395 | CASE DEFAULT ! error |
---|
396 | CALL ctl_stop('STOP','dyn_vor: wrong value for kvor' ) |
---|
397 | END SELECT |
---|
398 | ! |
---|
399 | IF( ln_dynvor_msk ) THEN !== mask/unmask vorticity ==! |
---|
400 | DO jj = 1, jpjm1 |
---|
401 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
402 | zwz(ji,jj) = zwz(ji,jj) * fmask(ji,jj,jk) |
---|
403 | END DO |
---|
404 | END DO |
---|
405 | ENDIF |
---|
406 | |
---|
407 | IF( ln_sco ) THEN |
---|
408 | zwz(:,:) = zwz(:,:) / e3f_n(:,:,jk) |
---|
409 | zwx(:,:) = e2u(:,:) * e3u_n(:,:,jk) * pun(:,:,jk) |
---|
410 | zwy(:,:) = e1v(:,:) * e3v_n(:,:,jk) * pvn(:,:,jk) |
---|
411 | ELSE |
---|
412 | zwx(:,:) = e2u(:,:) * pun(:,:,jk) |
---|
413 | zwy(:,:) = e1v(:,:) * pvn(:,:,jk) |
---|
414 | ENDIF |
---|
415 | ! !== compute and add the vorticity term trend =! |
---|
416 | DO jj = 2, jpjm1 |
---|
417 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
418 | zy1 = zwy(ji,jj-1) + zwy(ji+1,jj-1) |
---|
419 | zy2 = zwy(ji,jj ) + zwy(ji+1,jj ) |
---|
420 | zx1 = zwx(ji-1,jj) + zwx(ji-1,jj+1) |
---|
421 | zx2 = zwx(ji ,jj) + zwx(ji ,jj+1) |
---|
422 | pua(ji,jj,jk) = pua(ji,jj,jk) + r1_4 * r1_e1u(ji,jj) * ( zwz(ji ,jj-1) * zy1 + zwz(ji,jj) * zy2 ) |
---|
423 | pva(ji,jj,jk) = pva(ji,jj,jk) - r1_4 * r1_e2v(ji,jj) * ( zwz(ji-1,jj ) * zx1 + zwz(ji,jj) * zx2 ) |
---|
424 | END DO |
---|
425 | END DO |
---|
426 | ! ! =============== |
---|
427 | END DO ! End of slab |
---|
428 | ! ! =============== |
---|
429 | END SUBROUTINE vor_ene |
---|
430 | |
---|
431 | |
---|
432 | SUBROUTINE vor_ens( kt, kvor, pun, pvn, pua, pva ) |
---|
433 | !!---------------------------------------------------------------------- |
---|
434 | !! *** ROUTINE vor_ens *** |
---|
435 | !! |
---|
436 | !! ** Purpose : Compute the now total vorticity trend and add it to |
---|
437 | !! the general trend of the momentum equation. |
---|
438 | !! |
---|
439 | !! ** Method : Trend evaluated using now fields (centered in time) |
---|
440 | !! and the Sadourny (1975) flux FORM formulation : conserves the |
---|
441 | !! potential enstrophy of a horizontally non-divergent flow. the |
---|
442 | !! trend of the vorticity term is given by: |
---|
443 | !! voru = 1/e1u mj-1[ (rvor+f)/e3f ] mj-1[ mi(e1v*e3v vn) ] |
---|
444 | !! vorv = 1/e2v mi-1[ (rvor+f)/e3f ] mi-1[ mj(e2u*e3u un) ] |
---|
445 | !! Add this trend to the general momentum trend (ua,va): |
---|
446 | !! (ua,va) = (ua,va) + ( voru , vorv ) |
---|
447 | !! |
---|
448 | !! ** Action : - Update (ua,va) arrays with the now vorticity term trend |
---|
449 | !! |
---|
450 | !! References : Sadourny, r., 1975, j. atmos. sciences, 32, 680-689. |
---|
451 | !!---------------------------------------------------------------------- |
---|
452 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
---|
453 | INTEGER , INTENT(in ) :: kvor ! total, planetary, relative, or metric |
---|
454 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(inout) :: pun, pvn ! now velocities |
---|
455 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(inout) :: pua, pva ! total v-trend |
---|
456 | ! |
---|
457 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
458 | REAL(wp) :: zuav, zvau ! local scalars |
---|
459 | REAL(wp), DIMENSION(jpi,jpj) :: zwx, zwy, zwz, zww ! 2D workspace |
---|
460 | !!---------------------------------------------------------------------- |
---|
461 | ! |
---|
462 | IF( kt == nit000 ) THEN |
---|
463 | IF(lwp) WRITE(numout,*) |
---|
464 | IF(lwp) WRITE(numout,*) 'dyn:vor_ens : vorticity term: enstrophy conserving scheme' |
---|
465 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~' |
---|
466 | ENDIF |
---|
467 | ! ! =============== |
---|
468 | DO jk = 1, jpkm1 ! Horizontal slab |
---|
469 | ! ! =============== |
---|
470 | ! |
---|
471 | SELECT CASE( kvor ) !== vorticity considered ==! |
---|
472 | CASE ( np_COR ) !* Coriolis (planetary vorticity) |
---|
473 | zwz(:,:) = ff_f(:,:) |
---|
474 | CASE ( np_RVO ) !* relative vorticity |
---|
475 | DO jj = 1, jpjm1 |
---|
476 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
477 | zwz(ji,jj) = ( e2v(ji+1,jj ) * pvn(ji+1,jj ,jk) - e2v(ji,jj) * pvn(ji,jj,jk) & |
---|
478 | & - e1u(ji ,jj+1) * pun(ji ,jj+1,jk) + e1u(ji,jj) * pun(ji,jj,jk) ) * r1_e1e2f(ji,jj) |
---|
479 | END DO |
---|
480 | END DO |
---|
481 | CASE ( np_MET ) !* metric term |
---|
482 | DO jj = 1, jpjm1 |
---|
483 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
484 | zwz(ji,jj) = ( pvn(ji+1,jj ,jk) + pvn(ji,jj,jk) ) * di_e2v_2e1e2f(ji,jj) & |
---|
485 | & - ( pun(ji ,jj+1,jk) + pun(ji,jj,jk) ) * dj_e1u_2e1e2f(ji,jj) |
---|
486 | END DO |
---|
487 | END DO |
---|
488 | CASE ( np_CRV ) !* Coriolis + relative vorticity |
---|
489 | DO jj = 1, jpjm1 |
---|
490 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
491 | zwz(ji,jj) = ff_f(ji,jj) + ( e2v(ji+1,jj ) * pvn(ji+1,jj ,jk) - e2v(ji,jj) * pvn(ji,jj,jk) & |
---|
492 | & - e1u(ji ,jj+1) * pun(ji ,jj+1,jk) + e1u(ji,jj) * pun(ji,jj,jk) ) * r1_e1e2f(ji,jj) |
---|
493 | END DO |
---|
494 | END DO |
---|
495 | CASE ( np_CME ) !* Coriolis + metric |
---|
496 | DO jj = 1, jpjm1 |
---|
497 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
498 | zwz(ji,jj) = ff_f(ji,jj) + ( pvn(ji+1,jj ,jk) + pvn(ji,jj,jk) ) * di_e2v_2e1e2f(ji,jj) & |
---|
499 | & - ( pun(ji ,jj+1,jk) + pun(ji,jj,jk) ) * dj_e1u_2e1e2f(ji,jj) |
---|
500 | END DO |
---|
501 | END DO |
---|
502 | CASE DEFAULT ! error |
---|
503 | CALL ctl_stop('STOP','dyn_vor: wrong value for kvor' ) |
---|
504 | END SELECT |
---|
505 | ! |
---|
506 | IF( ln_dynvor_msk ) THEN !== mask/unmask vorticity ==! |
---|
507 | DO jj = 1, jpjm1 |
---|
508 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
509 | zwz(ji,jj) = zwz(ji,jj) * fmask(ji,jj,jk) |
---|
510 | END DO |
---|
511 | END DO |
---|
512 | ENDIF |
---|
513 | ! |
---|
514 | IF( ln_sco ) THEN !== horizontal fluxes ==! |
---|
515 | zwz(:,:) = zwz(:,:) / e3f_n(:,:,jk) |
---|
516 | zwx(:,:) = e2u(:,:) * e3u_n(:,:,jk) * pun(:,:,jk) |
---|
517 | zwy(:,:) = e1v(:,:) * e3v_n(:,:,jk) * pvn(:,:,jk) |
---|
518 | ELSE |
---|
519 | zwx(:,:) = e2u(:,:) * pun(:,:,jk) |
---|
520 | zwy(:,:) = e1v(:,:) * pvn(:,:,jk) |
---|
521 | ENDIF |
---|
522 | ! !== compute and add the vorticity term trend =! |
---|
523 | DO jj = 2, jpjm1 |
---|
524 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
525 | zuav = r1_8 * r1_e1u(ji,jj) * ( zwy(ji ,jj-1) + zwy(ji+1,jj-1) & |
---|
526 | & + zwy(ji ,jj ) + zwy(ji+1,jj ) ) |
---|
527 | zvau =-r1_8 * r1_e2v(ji,jj) * ( zwx(ji-1,jj ) + zwx(ji-1,jj+1) & |
---|
528 | & + zwx(ji ,jj ) + zwx(ji ,jj+1) ) |
---|
529 | pua(ji,jj,jk) = pua(ji,jj,jk) + zuav * ( zwz(ji ,jj-1) + zwz(ji,jj) ) |
---|
530 | pva(ji,jj,jk) = pva(ji,jj,jk) + zvau * ( zwz(ji-1,jj ) + zwz(ji,jj) ) |
---|
531 | END DO |
---|
532 | END DO |
---|
533 | ! ! =============== |
---|
534 | END DO ! End of slab |
---|
535 | ! ! =============== |
---|
536 | END SUBROUTINE vor_ens |
---|
537 | |
---|
538 | |
---|
539 | SUBROUTINE vor_een( kt, kvor, pun, pvn, pua, pva ) |
---|
540 | !!---------------------------------------------------------------------- |
---|
541 | !! *** ROUTINE vor_een *** |
---|
542 | !! |
---|
543 | !! ** Purpose : Compute the now total vorticity trend and add it to |
---|
544 | !! the general trend of the momentum equation. |
---|
545 | !! |
---|
546 | !! ** Method : Trend evaluated using now fields (centered in time) |
---|
547 | !! and the Arakawa and Lamb (1980) flux form formulation : conserves |
---|
548 | !! both the horizontal kinetic energy and the potential enstrophy |
---|
549 | !! when horizontal divergence is zero (see the NEMO documentation) |
---|
550 | !! Add this trend to the general momentum trend (ua,va). |
---|
551 | !! |
---|
552 | !! ** Action : - Update (ua,va) with the now vorticity term trend |
---|
553 | !! |
---|
554 | !! References : Arakawa and Lamb 1980, Mon. Wea. Rev., 109, 18-36 |
---|
555 | !!---------------------------------------------------------------------- |
---|
556 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
---|
557 | INTEGER , INTENT(in ) :: kvor ! total, planetary, relative, or metric |
---|
558 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(inout) :: pun, pvn ! now velocities |
---|
559 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(inout) :: pua, pva ! total v-trend |
---|
560 | ! |
---|
561 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
562 | INTEGER :: ierr ! local integer |
---|
563 | REAL(wp) :: zua, zva ! local scalars |
---|
564 | REAL(wp) :: zmsk, ze3f ! local scalars |
---|
565 | REAL(wp), DIMENSION(jpi,jpj) :: zwx , zwy , z1_e3f |
---|
566 | REAL(wp), DIMENSION(jpi,jpj) :: ztnw, ztne, ztsw, ztse |
---|
567 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwz |
---|
568 | !!---------------------------------------------------------------------- |
---|
569 | ! |
---|
570 | IF( kt == nit000 ) THEN |
---|
571 | IF(lwp) WRITE(numout,*) |
---|
572 | IF(lwp) WRITE(numout,*) 'dyn:vor_een : vorticity term: energy and enstrophy conserving scheme' |
---|
573 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~' |
---|
574 | ENDIF |
---|
575 | ! |
---|
576 | ! ! =============== |
---|
577 | DO jk = 1, jpkm1 ! Horizontal slab |
---|
578 | ! ! =============== |
---|
579 | ! |
---|
580 | SELECT CASE( nn_een_e3f ) ! == reciprocal of e3 at F-point |
---|
581 | CASE ( 0 ) ! original formulation (masked averaging of e3t divided by 4) |
---|
582 | DO jj = 1, jpjm1 |
---|
583 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
584 | ze3f = ( e3t_n(ji,jj+1,jk)*tmask(ji,jj+1,jk) + e3t_n(ji+1,jj+1,jk)*tmask(ji+1,jj+1,jk) & |
---|
585 | & + e3t_n(ji,jj ,jk)*tmask(ji,jj ,jk) + e3t_n(ji+1,jj ,jk)*tmask(ji+1,jj ,jk) ) |
---|
586 | IF( ze3f /= 0._wp ) THEN ; z1_e3f(ji,jj) = 4._wp / ze3f |
---|
587 | ELSE ; z1_e3f(ji,jj) = 0._wp |
---|
588 | ENDIF |
---|
589 | END DO |
---|
590 | END DO |
---|
591 | CASE ( 1 ) ! new formulation (masked averaging of e3t divided by the sum of mask) |
---|
592 | DO jj = 1, jpjm1 |
---|
593 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
594 | ze3f = ( e3t_n(ji,jj+1,jk)*tmask(ji,jj+1,jk) + e3t_n(ji+1,jj+1,jk)*tmask(ji+1,jj+1,jk) & |
---|
595 | & + e3t_n(ji,jj ,jk)*tmask(ji,jj ,jk) + e3t_n(ji+1,jj ,jk)*tmask(ji+1,jj ,jk) ) |
---|
596 | zmsk = ( tmask(ji,jj+1,jk) + tmask(ji+1,jj+1,jk) & |
---|
597 | & + tmask(ji,jj ,jk) + tmask(ji+1,jj ,jk) ) |
---|
598 | IF( ze3f /= 0._wp ) THEN ; z1_e3f(ji,jj) = zmsk / ze3f |
---|
599 | ELSE ; z1_e3f(ji,jj) = 0._wp |
---|
600 | ENDIF |
---|
601 | END DO |
---|
602 | END DO |
---|
603 | END SELECT |
---|
604 | ! |
---|
605 | SELECT CASE( kvor ) !== vorticity considered ==! |
---|
606 | CASE ( np_COR ) !* Coriolis (planetary vorticity) |
---|
607 | DO jj = 1, jpjm1 |
---|
608 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
609 | zwz(ji,jj,jk) = ff_f(ji,jj) * z1_e3f(ji,jj) |
---|
610 | END DO |
---|
611 | END DO |
---|
612 | CASE ( np_RVO ) !* relative vorticity |
---|
613 | DO jj = 1, jpjm1 |
---|
614 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
615 | zwz(ji,jj,jk) = ( e2v(ji+1,jj ) * pvn(ji+1,jj,jk) - e2v(ji,jj) * pvn(ji,jj,jk) & |
---|
616 | & - e1u(ji ,jj+1) * pun(ji,jj+1,jk) + e1u(ji,jj) * pun(ji,jj,jk) ) * r1_e1e2f(ji,jj)*z1_e3f(ji,jj) |
---|
617 | END DO |
---|
618 | END DO |
---|
619 | CASE ( np_MET ) !* metric term |
---|
620 | DO jj = 1, jpjm1 |
---|
621 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
622 | zwz(ji,jj,jk) = ( ( pvn(ji+1,jj,jk) + pvn(ji,jj,jk) ) * di_e2v_2e1e2f(ji,jj) & |
---|
623 | & - ( pun(ji,jj+1,jk) + pun(ji,jj,jk) ) * dj_e1u_2e1e2f(ji,jj) ) * z1_e3f(ji,jj) |
---|
624 | END DO |
---|
625 | END DO |
---|
626 | CASE ( np_CRV ) !* Coriolis + relative vorticity |
---|
627 | DO jj = 1, jpjm1 |
---|
628 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
629 | zwz(ji,jj,jk) = ( ff_f(ji,jj) + ( e2v(ji+1,jj ) * pvn(ji+1,jj,jk) - e2v(ji,jj) * pvn(ji,jj,jk) & |
---|
630 | & - e1u(ji ,jj+1) * pun(ji,jj+1,jk) + e1u(ji,jj) * pun(ji,jj,jk) ) & |
---|
631 | & * r1_e1e2f(ji,jj) ) * z1_e3f(ji,jj) |
---|
632 | END DO |
---|
633 | END DO |
---|
634 | CASE ( np_CME ) !* Coriolis + metric |
---|
635 | DO jj = 1, jpjm1 |
---|
636 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
637 | zwz(ji,jj,jk) = ( ff_f(ji,jj) + ( pvn(ji+1,jj ,jk) + pvn(ji,jj,jk) ) * di_e2v_2e1e2f(ji,jj) & |
---|
638 | & - ( pun(ji ,jj+1,jk) + pun(ji,jj,jk) ) * dj_e1u_2e1e2f(ji,jj) ) * z1_e3f(ji,jj) |
---|
639 | END DO |
---|
640 | END DO |
---|
641 | CASE DEFAULT ! error |
---|
642 | CALL ctl_stop('STOP','dyn_vor: wrong value for kvor' ) |
---|
643 | END SELECT |
---|
644 | ! |
---|
645 | IF( ln_dynvor_msk ) THEN !== mask/unmask vorticity ==! |
---|
646 | DO jj = 1, jpjm1 |
---|
647 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
648 | zwz(ji,jj,jk) = zwz(ji,jj,jk) * fmask(ji,jj,jk) |
---|
649 | END DO |
---|
650 | END DO |
---|
651 | ENDIF |
---|
652 | END DO ! End of slab |
---|
653 | ! |
---|
654 | CALL lbc_lnk( 'dynvor', zwz, 'F', 1. ) |
---|
655 | |
---|
656 | DO jk = 1, jpkm1 ! Horizontal slab |
---|
657 | ! |
---|
658 | ! !== horizontal fluxes ==! |
---|
659 | zwx(:,:) = e2u(:,:) * e3u_n(:,:,jk) * pun(:,:,jk) |
---|
660 | zwy(:,:) = e1v(:,:) * e3v_n(:,:,jk) * pvn(:,:,jk) |
---|
661 | |
---|
662 | ! !== compute and add the vorticity term trend =! |
---|
663 | jj = 2 |
---|
664 | ztne(1,:) = 0 ; ztnw(1,:) = 0 ; ztse(1,:) = 0 ; ztsw(1,:) = 0 |
---|
665 | DO ji = 2, jpi ! split in 2 parts due to vector opt. |
---|
666 | ztne(ji,jj) = zwz(ji-1,jj ,jk) + zwz(ji ,jj ,jk) + zwz(ji ,jj-1,jk) |
---|
667 | ztnw(ji,jj) = zwz(ji-1,jj-1,jk) + zwz(ji-1,jj ,jk) + zwz(ji ,jj ,jk) |
---|
668 | ztse(ji,jj) = zwz(ji ,jj ,jk) + zwz(ji ,jj-1,jk) + zwz(ji-1,jj-1,jk) |
---|
669 | ztsw(ji,jj) = zwz(ji ,jj-1,jk) + zwz(ji-1,jj-1,jk) + zwz(ji-1,jj ,jk) |
---|
670 | END DO |
---|
671 | DO jj = 3, jpj |
---|
672 | DO ji = fs_2, jpi ! vector opt. ok because we start at jj = 3 |
---|
673 | ztne(ji,jj) = zwz(ji-1,jj ,jk) + zwz(ji ,jj ,jk) + zwz(ji ,jj-1,jk) |
---|
674 | ztnw(ji,jj) = zwz(ji-1,jj-1,jk) + zwz(ji-1,jj ,jk) + zwz(ji ,jj ,jk) |
---|
675 | ztse(ji,jj) = zwz(ji ,jj ,jk) + zwz(ji ,jj-1,jk) + zwz(ji-1,jj-1,jk) |
---|
676 | ztsw(ji,jj) = zwz(ji ,jj-1,jk) + zwz(ji-1,jj-1,jk) + zwz(ji-1,jj ,jk) |
---|
677 | END DO |
---|
678 | END DO |
---|
679 | DO jj = 2, jpjm1 |
---|
680 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
681 | zua = + r1_12 * r1_e1u(ji,jj) * ( ztne(ji,jj ) * zwy(ji ,jj ) + ztnw(ji+1,jj) * zwy(ji+1,jj ) & |
---|
682 | & + ztse(ji,jj ) * zwy(ji ,jj-1) + ztsw(ji+1,jj) * zwy(ji+1,jj-1) ) |
---|
683 | zva = - r1_12 * r1_e2v(ji,jj) * ( ztsw(ji,jj+1) * zwx(ji-1,jj+1) + ztse(ji,jj+1) * zwx(ji ,jj+1) & |
---|
684 | & + ztnw(ji,jj ) * zwx(ji-1,jj ) + ztne(ji,jj ) * zwx(ji ,jj ) ) |
---|
685 | pua(ji,jj,jk) = pua(ji,jj,jk) + zua |
---|
686 | pva(ji,jj,jk) = pva(ji,jj,jk) + zva |
---|
687 | END DO |
---|
688 | END DO |
---|
689 | ! ! =============== |
---|
690 | END DO ! End of slab |
---|
691 | ! ! =============== |
---|
692 | END SUBROUTINE vor_een |
---|
693 | |
---|
694 | |
---|
695 | |
---|
696 | SUBROUTINE vor_eeT( kt, kvor, pun, pvn, pua, pva ) |
---|
697 | !!---------------------------------------------------------------------- |
---|
698 | !! *** ROUTINE vor_eeT *** |
---|
699 | !! |
---|
700 | !! ** Purpose : Compute the now total vorticity trend and add it to |
---|
701 | !! the general trend of the momentum equation. |
---|
702 | !! |
---|
703 | !! ** Method : Trend evaluated using now fields (centered in time) |
---|
704 | !! and the Arakawa and Lamb (1980) vector form formulation using |
---|
705 | !! a modified version of Arakawa and Lamb (1980) scheme (see vor_een). |
---|
706 | !! The change consists in |
---|
707 | !! Add this trend to the general momentum trend (ua,va). |
---|
708 | !! |
---|
709 | !! ** Action : - Update (ua,va) with the now vorticity term trend |
---|
710 | !! |
---|
711 | !! References : Arakawa and Lamb 1980, Mon. Wea. Rev., 109, 18-36 |
---|
712 | !!---------------------------------------------------------------------- |
---|
713 | INTEGER , INTENT(in ) :: kt ! ocean time-step index |
---|
714 | INTEGER , INTENT(in ) :: kvor ! total, planetary, relative, or metric |
---|
715 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(inout) :: pun, pvn ! now velocities |
---|
716 | REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(inout) :: pua, pva ! total v-trend |
---|
717 | ! |
---|
718 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
719 | INTEGER :: ierr ! local integer |
---|
720 | REAL(wp) :: zua, zva ! local scalars |
---|
721 | REAL(wp) :: zmsk, z1_e3t ! local scalars |
---|
722 | REAL(wp), DIMENSION(jpi,jpj) :: zwx , zwy |
---|
723 | REAL(wp), DIMENSION(jpi,jpj) :: ztnw, ztne, ztsw, ztse |
---|
724 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwz |
---|
725 | !!---------------------------------------------------------------------- |
---|
726 | ! |
---|
727 | IF( kt == nit000 ) THEN |
---|
728 | IF(lwp) WRITE(numout,*) |
---|
729 | IF(lwp) WRITE(numout,*) 'dyn:vor_een : vorticity term: energy and enstrophy conserving scheme' |
---|
730 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~' |
---|
731 | ENDIF |
---|
732 | ! |
---|
733 | ! ! =============== |
---|
734 | DO jk = 1, jpkm1 ! Horizontal slab |
---|
735 | ! ! =============== |
---|
736 | ! |
---|
737 | ! |
---|
738 | SELECT CASE( kvor ) !== vorticity considered ==! |
---|
739 | CASE ( np_COR ) !* Coriolis (planetary vorticity) |
---|
740 | DO jj = 1, jpjm1 |
---|
741 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
742 | zwz(ji,jj,jk) = ff_f(ji,jj) |
---|
743 | END DO |
---|
744 | END DO |
---|
745 | CASE ( np_RVO ) !* relative vorticity |
---|
746 | DO jj = 1, jpjm1 |
---|
747 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
748 | zwz(ji,jj,jk) = ( e2v(ji+1,jj ) * pvn(ji+1,jj ,jk) - e2v(ji,jj) * pvn(ji,jj,jk) & |
---|
749 | & - e1u(ji ,jj+1) * pun(ji ,jj+1,jk) + e1u(ji,jj) * pun(ji,jj,jk) ) & |
---|
750 | & * r1_e1e2f(ji,jj) |
---|
751 | END DO |
---|
752 | END DO |
---|
753 | CASE ( np_MET ) !* metric term |
---|
754 | DO jj = 1, jpjm1 |
---|
755 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
756 | zwz(ji,jj,jk) = ( pvn(ji+1,jj ,jk) + pvn(ji,jj,jk) ) * di_e2v_2e1e2f(ji,jj) & |
---|
757 | & - ( pun(ji ,jj+1,jk) + pun(ji,jj,jk) ) * dj_e1u_2e1e2f(ji,jj) |
---|
758 | END DO |
---|
759 | END DO |
---|
760 | CASE ( np_CRV ) !* Coriolis + relative vorticity |
---|
761 | DO jj = 1, jpjm1 |
---|
762 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
763 | zwz(ji,jj,jk) = ( ff_f(ji,jj) + ( e2v(ji+1,jj ) * pvn(ji+1,jj ,jk) - e2v(ji,jj) * pvn(ji,jj,jk) & |
---|
764 | & - e1u(ji ,jj+1) * pun(ji ,jj+1,jk) + e1u(ji,jj) * pun(ji,jj,jk) ) & |
---|
765 | & * r1_e1e2f(ji,jj) ) |
---|
766 | END DO |
---|
767 | END DO |
---|
768 | CASE ( np_CME ) !* Coriolis + metric |
---|
769 | DO jj = 1, jpjm1 |
---|
770 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
771 | zwz(ji,jj,jk) = ff_f(ji,jj) + ( pvn(ji+1,jj ,jk) + pvn(ji,jj,jk) ) * di_e2v_2e1e2f(ji,jj) & |
---|
772 | & - ( pun(ji ,jj+1,jk) + pun(ji,jj,jk) ) * dj_e1u_2e1e2f(ji,jj) |
---|
773 | END DO |
---|
774 | END DO |
---|
775 | CASE DEFAULT ! error |
---|
776 | CALL ctl_stop('STOP','dyn_vor: wrong value for kvor' ) |
---|
777 | END SELECT |
---|
778 | ! |
---|
779 | IF( ln_dynvor_msk ) THEN !== mask/unmask vorticity ==! |
---|
780 | DO jj = 1, jpjm1 |
---|
781 | DO ji = 1, fs_jpim1 ! vector opt. |
---|
782 | zwz(ji,jj,jk) = zwz(ji,jj,jk) * fmask(ji,jj,jk) |
---|
783 | END DO |
---|
784 | END DO |
---|
785 | ENDIF |
---|
786 | END DO |
---|
787 | ! |
---|
788 | CALL lbc_lnk( 'dynvor', zwz, 'F', 1. ) |
---|
789 | ! |
---|
790 | DO jk = 1, jpkm1 ! Horizontal slab |
---|
791 | |
---|
792 | ! !== horizontal fluxes ==! |
---|
793 | zwx(:,:) = e2u(:,:) * e3u_n(:,:,jk) * pun(:,:,jk) |
---|
794 | zwy(:,:) = e1v(:,:) * e3v_n(:,:,jk) * pvn(:,:,jk) |
---|
795 | |
---|
796 | ! !== compute and add the vorticity term trend =! |
---|
797 | jj = 2 |
---|
798 | ztne(1,:) = 0 ; ztnw(1,:) = 0 ; ztse(1,:) = 0 ; ztsw(1,:) = 0 |
---|
799 | DO ji = 2, jpi ! split in 2 parts due to vector opt. |
---|
800 | z1_e3t = 1._wp / e3t_n(ji,jj,jk) |
---|
801 | ztne(ji,jj) = ( zwz(ji-1,jj ,jk) + zwz(ji ,jj ,jk) + zwz(ji ,jj-1,jk) ) * z1_e3t |
---|
802 | ztnw(ji,jj) = ( zwz(ji-1,jj-1,jk) + zwz(ji-1,jj ,jk) + zwz(ji ,jj ,jk) ) * z1_e3t |
---|
803 | ztse(ji,jj) = ( zwz(ji ,jj ,jk) + zwz(ji ,jj-1,jk) + zwz(ji-1,jj-1,jk) ) * z1_e3t |
---|
804 | ztsw(ji,jj) = ( zwz(ji ,jj-1,jk) + zwz(ji-1,jj-1,jk) + zwz(ji-1,jj ,jk) ) * z1_e3t |
---|
805 | END DO |
---|
806 | DO jj = 3, jpj |
---|
807 | DO ji = fs_2, jpi ! vector opt. ok because we start at jj = 3 |
---|
808 | z1_e3t = 1._wp / e3t_n(ji,jj,jk) |
---|
809 | ztne(ji,jj) = ( zwz(ji-1,jj ,jk) + zwz(ji ,jj ,jk) + zwz(ji ,jj-1,jk) ) * z1_e3t |
---|
810 | ztnw(ji,jj) = ( zwz(ji-1,jj-1,jk) + zwz(ji-1,jj ,jk) + zwz(ji ,jj ,jk) ) * z1_e3t |
---|
811 | ztse(ji,jj) = ( zwz(ji ,jj ,jk) + zwz(ji ,jj-1,jk) + zwz(ji-1,jj-1,jk) ) * z1_e3t |
---|
812 | ztsw(ji,jj) = ( zwz(ji ,jj-1,jk) + zwz(ji-1,jj-1,jk) + zwz(ji-1,jj ,jk) ) * z1_e3t |
---|
813 | END DO |
---|
814 | END DO |
---|
815 | DO jj = 2, jpjm1 |
---|
816 | DO ji = fs_2, fs_jpim1 ! vector opt. |
---|
817 | zua = + r1_12 * r1_e1u(ji,jj) * ( ztne(ji,jj ) * zwy(ji ,jj ) + ztnw(ji+1,jj) * zwy(ji+1,jj ) & |
---|
818 | & + ztse(ji,jj ) * zwy(ji ,jj-1) + ztsw(ji+1,jj) * zwy(ji+1,jj-1) ) |
---|
819 | zva = - r1_12 * r1_e2v(ji,jj) * ( ztsw(ji,jj+1) * zwx(ji-1,jj+1) + ztse(ji,jj+1) * zwx(ji ,jj+1) & |
---|
820 | & + ztnw(ji,jj ) * zwx(ji-1,jj ) + ztne(ji,jj ) * zwx(ji ,jj ) ) |
---|
821 | pua(ji,jj,jk) = pua(ji,jj,jk) + zua |
---|
822 | pva(ji,jj,jk) = pva(ji,jj,jk) + zva |
---|
823 | END DO |
---|
824 | END DO |
---|
825 | ! ! =============== |
---|
826 | END DO ! End of slab |
---|
827 | ! ! =============== |
---|
828 | END SUBROUTINE vor_eeT |
---|
829 | |
---|
830 | |
---|
831 | SUBROUTINE dyn_vor_init |
---|
832 | !!--------------------------------------------------------------------- |
---|
833 | !! *** ROUTINE dyn_vor_init *** |
---|
834 | !! |
---|
835 | !! ** Purpose : Control the consistency between cpp options for |
---|
836 | !! tracer advection schemes |
---|
837 | !!---------------------------------------------------------------------- |
---|
838 | INTEGER :: ji, jj, jk ! dummy loop indices |
---|
839 | INTEGER :: ioptio, ios ! local integer |
---|
840 | !! |
---|
841 | NAMELIST/namdyn_vor/ ln_dynvor_ens, ln_dynvor_ene, ln_dynvor_enT, ln_dynvor_eeT, & |
---|
842 | & ln_dynvor_een, nn_een_e3f , ln_dynvor_mix, ln_dynvor_msk |
---|
843 | !!---------------------------------------------------------------------- |
---|
844 | ! |
---|
845 | IF(lwp) THEN |
---|
846 | WRITE(numout,*) |
---|
847 | WRITE(numout,*) 'dyn_vor_init : vorticity term : read namelist and control the consistency' |
---|
848 | WRITE(numout,*) '~~~~~~~~~~~~' |
---|
849 | ENDIF |
---|
850 | ! |
---|
851 | REWIND( numnam_ref ) ! Namelist namdyn_vor in reference namelist : Vorticity scheme options |
---|
852 | READ ( numnam_ref, namdyn_vor, IOSTAT = ios, ERR = 901) |
---|
853 | 901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'namdyn_vor in reference namelist', lwp ) |
---|
854 | REWIND( numnam_cfg ) ! Namelist namdyn_vor in configuration namelist : Vorticity scheme options |
---|
855 | READ ( numnam_cfg, namdyn_vor, IOSTAT = ios, ERR = 902 ) |
---|
856 | 902 IF( ios > 0 ) CALL ctl_nam ( ios , 'namdyn_vor in configuration namelist', lwp ) |
---|
857 | IF(lwm) WRITE ( numond, namdyn_vor ) |
---|
858 | ! |
---|
859 | IF(lwp) THEN ! Namelist print |
---|
860 | WRITE(numout,*) ' Namelist namdyn_vor : choice of the vorticity term scheme' |
---|
861 | WRITE(numout,*) ' enstrophy conserving scheme ln_dynvor_ens = ', ln_dynvor_ens |
---|
862 | WRITE(numout,*) ' f-point energy conserving scheme ln_dynvor_ene = ', ln_dynvor_ene |
---|
863 | WRITE(numout,*) ' t-point energy conserving scheme ln_dynvor_enT = ', ln_dynvor_enT |
---|
864 | WRITE(numout,*) ' energy conserving scheme (een using e3t) ln_dynvor_eeT = ', ln_dynvor_eeT |
---|
865 | WRITE(numout,*) ' enstrophy and energy conserving scheme ln_dynvor_een = ', ln_dynvor_een |
---|
866 | WRITE(numout,*) ' e3f = averaging /4 (=0) or /sum(tmask) (=1) nn_een_e3f = ', nn_een_e3f |
---|
867 | WRITE(numout,*) ' mixed enstrophy/energy conserving scheme ln_dynvor_mix = ', ln_dynvor_mix |
---|
868 | WRITE(numout,*) ' masked (=T) or unmasked(=F) vorticity ln_dynvor_msk = ', ln_dynvor_msk |
---|
869 | ENDIF |
---|
870 | |
---|
871 | IF( ln_dynvor_msk ) CALL ctl_stop( 'dyn_vor_init: masked vorticity is not currently not available') |
---|
872 | |
---|
873 | !!gm this should be removed when choosing a unique strategy for fmask at the coast |
---|
874 | ! If energy, enstrophy or mixed advection of momentum in vector form change the value for masks |
---|
875 | ! at angles with three ocean points and one land point |
---|
876 | IF(lwp) WRITE(numout,*) |
---|
877 | IF(lwp) WRITE(numout,*) ' change fmask value in the angles (T) ln_vorlat = ', ln_vorlat |
---|
878 | IF( ln_vorlat .AND. ( ln_dynvor_ene .OR. ln_dynvor_ens .OR. ln_dynvor_mix ) ) THEN |
---|
879 | DO jk = 1, jpk |
---|
880 | DO jj = 1, jpjm1 |
---|
881 | DO ji = 1, jpim1 |
---|
882 | IF( tmask(ji,jj+1,jk) + tmask(ji+1,jj+1,jk) & |
---|
883 | & + tmask(ji,jj ,jk) + tmask(ji+1,jj+1,jk) == 3._wp ) fmask(ji,jj,jk) = 1._wp |
---|
884 | END DO |
---|
885 | END DO |
---|
886 | END DO |
---|
887 | ! |
---|
888 | CALL lbc_lnk( 'dynvor', fmask, 'F', 1._wp ) ! Lateral boundary conditions on fmask |
---|
889 | ! |
---|
890 | ENDIF |
---|
891 | !!gm end |
---|
892 | |
---|
893 | ioptio = 0 ! type of scheme for vorticity (set nvor_scheme) |
---|
894 | IF( ln_dynvor_ens ) THEN ; ioptio = ioptio + 1 ; nvor_scheme = np_ENS ; ENDIF |
---|
895 | IF( ln_dynvor_ene ) THEN ; ioptio = ioptio + 1 ; nvor_scheme = np_ENE ; ENDIF |
---|
896 | IF( ln_dynvor_enT ) THEN ; ioptio = ioptio + 1 ; nvor_scheme = np_ENT ; ENDIF |
---|
897 | IF( ln_dynvor_eeT ) THEN ; ioptio = ioptio + 1 ; nvor_scheme = np_EET ; ENDIF |
---|
898 | IF( ln_dynvor_een ) THEN ; ioptio = ioptio + 1 ; nvor_scheme = np_EEN ; ENDIF |
---|
899 | IF( ln_dynvor_mix ) THEN ; ioptio = ioptio + 1 ; nvor_scheme = np_MIX ; ENDIF |
---|
900 | ! |
---|
901 | IF( ioptio /= 1 ) CALL ctl_stop( ' use ONE and ONLY one vorticity scheme' ) |
---|
902 | ! |
---|
903 | IF(lwp) WRITE(numout,*) ! type of calculated vorticity (set ncor, nrvm, ntot) |
---|
904 | ncor = np_COR ! planetary vorticity |
---|
905 | SELECT CASE( n_dynadv ) |
---|
906 | CASE( np_LIN_dyn ) |
---|
907 | IF(lwp) WRITE(numout,*) ' ==>>> linear dynamics : total vorticity = Coriolis' |
---|
908 | nrvm = np_COR ! planetary vorticity |
---|
909 | ntot = np_COR ! - - |
---|
910 | CASE( np_VEC_c2 ) |
---|
911 | IF(lwp) WRITE(numout,*) ' ==>>> vector form dynamics : total vorticity = Coriolis + relative vorticity' |
---|
912 | nrvm = np_RVO ! relative vorticity |
---|
913 | ntot = np_CRV ! relative + planetary vorticity |
---|
914 | CASE( np_FLX_c2 , np_FLX_ubs ) |
---|
915 | IF(lwp) WRITE(numout,*) ' ==>>> flux form dynamics : total vorticity = Coriolis + metric term' |
---|
916 | nrvm = np_MET ! metric term |
---|
917 | ntot = np_CME ! Coriolis + metric term |
---|
918 | ! |
---|
919 | SELECT CASE( nvor_scheme ) ! pre-computed gradients for the metric term: |
---|
920 | CASE( np_ENT ) !* T-point metric term : pre-compute di(e2u)/2 and dj(e1v)/2 |
---|
921 | ALLOCATE( di_e2u_2(jpi,jpj), dj_e1v_2(jpi,jpj) ) |
---|
922 | DO jj = 2, jpjm1 |
---|
923 | DO ji = 2, jpim1 |
---|
924 | di_e2u_2(ji,jj) = ( e2u(ji,jj) - e2u(ji-1,jj ) ) * 0.5_wp |
---|
925 | dj_e1v_2(ji,jj) = ( e1v(ji,jj) - e1v(ji ,jj-1) ) * 0.5_wp |
---|
926 | END DO |
---|
927 | END DO |
---|
928 | CALL lbc_lnk_multi( 'dynvor', di_e2u_2, 'T', -1. , dj_e1v_2, 'T', -1. ) ! Lateral boundary conditions |
---|
929 | ! |
---|
930 | CASE DEFAULT !* F-point metric term : pre-compute di(e2u)/(2*e1e2f) and dj(e1v)/(2*e1e2f) |
---|
931 | ALLOCATE( di_e2v_2e1e2f(jpi,jpj), dj_e1u_2e1e2f(jpi,jpj) ) |
---|
932 | DO jj = 1, jpjm1 |
---|
933 | DO ji = 1, jpim1 |
---|
934 | di_e2v_2e1e2f(ji,jj) = ( e2v(ji+1,jj ) - e2v(ji,jj) ) * 0.5 * r1_e1e2f(ji,jj) |
---|
935 | dj_e1u_2e1e2f(ji,jj) = ( e1u(ji ,jj+1) - e1u(ji,jj) ) * 0.5 * r1_e1e2f(ji,jj) |
---|
936 | END DO |
---|
937 | END DO |
---|
938 | CALL lbc_lnk_multi( 'dynvor', di_e2v_2e1e2f, 'F', -1. , dj_e1u_2e1e2f, 'F', -1. ) ! Lateral boundary conditions |
---|
939 | END SELECT |
---|
940 | ! |
---|
941 | END SELECT |
---|
942 | |
---|
943 | IF(lwp) THEN ! Print the choice |
---|
944 | WRITE(numout,*) |
---|
945 | SELECT CASE( nvor_scheme ) |
---|
946 | CASE( np_ENS ) ; WRITE(numout,*) ' ==>>> enstrophy conserving scheme (ENS)' |
---|
947 | CASE( np_ENE ) ; WRITE(numout,*) ' ==>>> energy conserving scheme (Coriolis at F-points) (ENE)' |
---|
948 | CASE( np_ENT ) ; WRITE(numout,*) ' ==>>> energy conserving scheme (Coriolis at T-points) (ENT)' |
---|
949 | CASE( np_EET ) ; WRITE(numout,*) ' ==>>> energy conserving scheme (EEN scheme using e3t) (EET)' |
---|
950 | CASE( np_EEN ) ; WRITE(numout,*) ' ==>>> energy and enstrophy conserving scheme (EEN)' |
---|
951 | CASE( np_MIX ) ; WRITE(numout,*) ' ==>>> mixed enstrophy/energy conserving scheme (MIX)' |
---|
952 | END SELECT |
---|
953 | ENDIF |
---|
954 | ! |
---|
955 | END SUBROUTINE dyn_vor_init |
---|
956 | |
---|
957 | !!============================================================================== |
---|
958 | END MODULE dynvor |
---|