| 1 |
mlosch |
1.28 |
C $Header: /u/gcmpack/MITgcm/pkg/mom_common/mom_calc_visc.F,v 1.27 2007/08/16 02:20:40 jmc Exp $ |
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jmc |
1.14 |
C $Name: $ |
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baylor |
1.1 |
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#include "MOM_COMMON_OPTIONS.h" |
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baylor |
1.5 |
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baylor |
1.1 |
SUBROUTINE MOM_CALC_VISC( |
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I bi,bj,k, |
| 9 |
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O viscAh_Z,viscAh_D,viscA4_Z,viscA4_D, |
| 10 |
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O harmonic,biharmonic,useVariableViscosity, |
| 11 |
jmc |
1.12 |
I hDiv,vort3,tension,strain,KE,hFacZ, |
| 12 |
baylor |
1.1 |
I myThid) |
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IMPLICIT NONE |
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baylor |
1.5 |
C |
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C Calculate horizontal viscosities (L is typical grid width) |
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C harmonic viscosity= |
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C viscAh (or viscAhD on div pts and viscAhZ on zeta pts) |
| 19 |
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C +0.25*L**2*viscAhGrid/deltaT |
| 20 |
baylor |
1.17 |
C +sqrt((viscC2leith/pi)**6*grad(Vort3)**2 |
| 21 |
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C +(viscC2leithD/pi)**6*grad(hDiv)**2)*L**3 |
| 22 |
baylor |
1.5 |
C +(viscC2smag/pi)**2*L**2*sqrt(Tension**2+Strain**2) |
| 23 |
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C |
| 24 |
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C biharmonic viscosity= |
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C viscA4 (or viscA4D on div pts and viscA4Z on zeta pts) |
| 26 |
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C +0.25*0.125*L**4*viscA4Grid/deltaT (approx) |
| 27 |
baylor |
1.17 |
C +0.125*L**5*sqrt((viscC4leith/pi)**6*grad(Vort3)**2 |
| 28 |
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C +(viscC4leithD/pi)**6*grad(hDiv)**2) |
| 29 |
baylor |
1.5 |
C +0.125*L**4*(viscC4smag/pi)**2*sqrt(Tension**2+Strain**2) |
| 30 |
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C |
| 31 |
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C Note that often 0.125*L**2 is the scale between harmonic and |
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C biharmonic (see Griffies and Hallberg (2000)) |
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C This allows the same value of the coefficient to be used |
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C for roughly similar results with biharmonic and harmonic |
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C |
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C LIMITERS -- limit min and max values of viscosities |
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C viscAhRemax is min value for grid point harmonic Reynolds num |
| 38 |
baylor |
1.9 |
C harmonic viscosity>sqrt(2*KE)*L/viscAhRemax |
| 39 |
baylor |
1.5 |
C |
| 40 |
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C viscA4Remax is min value for grid point biharmonic Reynolds num |
| 41 |
baylor |
1.9 |
C biharmonic viscosity>sqrt(2*KE)*L**3/8/viscA4Remax |
| 42 |
baylor |
1.5 |
C |
| 43 |
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C viscAhgridmax is CFL stability limiter for harmonic viscosity |
| 44 |
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C harmonic viscosity<0.25*viscAhgridmax*L**2/deltaT |
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C |
| 46 |
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C viscA4gridmax is CFL stability limiter for biharmonic viscosity |
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C biharmonic viscosity<viscA4gridmax*L**4/32/deltaT (approx) |
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C |
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C viscAhgridmin and viscA4gridmin are lower limits for viscosity: |
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cnh |
1.25 |
C harmonic viscosity>0.25*viscAhgridmin*L**2/deltaT |
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C biharmonic viscosity>viscA4gridmin*L**4/32/deltaT (approx) |
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baylor |
1.5 |
C |
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C RECOMMENDED VALUES |
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baylor |
1.18 |
C viscC2Leith=1-3 |
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C viscC2LeithD=1-3 |
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C viscC4Leith=1-3 |
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C viscC4LeithD=1.5-3 |
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baylor |
1.5 |
C viscC2smag=2.2-4 (Griffies and Hallberg,2000) |
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C 0.2-0.9 (Smagorinsky,1993) |
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C viscC4smag=2.2-4 (Griffies and Hallberg,2000) |
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baylor |
1.9 |
C viscAhRemax>=1, (<2 suppresses a computational mode) |
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C viscA4Remax>=1, (<2 suppresses a computational mode) |
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baylor |
1.5 |
C viscAhgridmax=1 |
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C viscA4gridmax=1 |
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C viscAhgrid<1 |
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C viscA4grid<1 |
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C viscAhgridmin<<1 |
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C viscA4gridmin<<1 |
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baylor |
1.1 |
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C == Global variables == |
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#include "SIZE.h" |
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#include "GRID.h" |
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#include "EEPARAMS.h" |
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#include "PARAMS.h" |
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baylor |
1.23 |
#ifdef ALLOW_NONHYDROSTATIC |
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#include "NH_VARS.h" |
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#endif |
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baylor |
1.1 |
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C == Routine arguments == |
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INTEGER bi,bj,k |
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_RL viscAh_Z(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 84 |
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_RL viscAh_D(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 85 |
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_RL viscA4_Z(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 86 |
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_RL viscA4_D(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 87 |
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_RL hDiv(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 88 |
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_RL vort3(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 89 |
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_RL tension(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 90 |
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_RL strain(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 91 |
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_RL KE(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 92 |
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_RS hFacZ(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 93 |
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INTEGER myThid |
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LOGICAL harmonic,biharmonic,useVariableViscosity |
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| 96 |
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C == Local variables == |
| 97 |
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INTEGER I,J |
| 98 |
baylor |
1.23 |
INTEGER kp1 |
| 99 |
baylor |
1.5 |
_RL smag2fac, smag4fac |
| 100 |
baylor |
1.17 |
_RL leith2fac, leith4fac |
| 101 |
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_RL leithD2fac, leithD4fac |
| 102 |
baylor |
1.6 |
_RL viscAhRe_max, viscA4Re_max |
| 103 |
jmc |
1.15 |
_RL Alin,grdVrt,grdDiv, keZpt |
| 104 |
baylor |
1.1 |
_RL recip_dt,L2,L3,L4,L5,L2rdt,L4rdt |
| 105 |
baylor |
1.5 |
_RL Uscl,U4scl |
| 106 |
jmc |
1.16 |
_RL divDx(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 107 |
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_RL divDy(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 108 |
jmc |
1.20 |
_RL vrtDx(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 109 |
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_RL vrtDy(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 110 |
baylor |
1.5 |
_RL viscAh_ZMax(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 111 |
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_RL viscAh_DMax(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 112 |
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_RL viscA4_ZMax(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 113 |
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_RL viscA4_DMax(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 114 |
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_RL viscAh_ZMin(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 115 |
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_RL viscAh_DMin(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 116 |
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_RL viscA4_ZMin(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 117 |
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_RL viscA4_DMin(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 118 |
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_RL viscAh_ZLth(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 119 |
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_RL viscAh_DLth(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 120 |
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_RL viscA4_ZLth(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 121 |
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_RL viscA4_DLth(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 122 |
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_RL viscAh_ZLthD(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 123 |
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_RL viscAh_DLthD(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 124 |
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_RL viscA4_ZLthD(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 125 |
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_RL viscA4_DLthD(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 126 |
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_RL viscAh_ZSmg(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 127 |
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_RL viscAh_DSmg(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 128 |
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_RL viscA4_ZSmg(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 129 |
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_RL viscA4_DSmg(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 130 |
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LOGICAL calcLeith,calcSmag |
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baylor |
1.1 |
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| 132 |
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useVariableViscosity= |
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& (viscAhGrid.NE.0.) |
| 134 |
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& .OR.(viscA4Grid.NE.0.) |
| 135 |
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& .OR.(viscC2leith.NE.0.) |
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& .OR.(viscC2leithD.NE.0.) |
| 137 |
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& .OR.(viscC4leith.NE.0.) |
| 138 |
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& .OR.(viscC4leithD.NE.0.) |
| 139 |
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& .OR.(viscC2smag.NE.0.) |
| 140 |
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& .OR.(viscC4smag.NE.0.) |
| 141 |
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| 142 |
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harmonic= |
| 143 |
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& (viscAh.NE.0.) |
| 144 |
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& .OR.(viscAhD.NE.0.) |
| 145 |
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& .OR.(viscAhZ.NE.0.) |
| 146 |
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& .OR.(viscAhGrid.NE.0.) |
| 147 |
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& .OR.(viscC2leith.NE.0.) |
| 148 |
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& .OR.(viscC2leithD.NE.0.) |
| 149 |
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& .OR.(viscC2smag.NE.0.) |
| 150 |
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| 151 |
baylor |
1.9 |
IF ((harmonic).and.(viscAhremax.ne.0.)) THEN |
| 152 |
jmc |
1.10 |
viscAhre_max=sqrt(2. _d 0)/viscAhRemax |
| 153 |
baylor |
1.9 |
ELSE |
| 154 |
jmc |
1.10 |
viscAhre_max=0. _d 0 |
| 155 |
baylor |
1.9 |
ENDIF |
| 156 |
baylor |
1.5 |
|
| 157 |
baylor |
1.1 |
biharmonic= |
| 158 |
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& (viscA4.NE.0.) |
| 159 |
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& .OR.(viscA4D.NE.0.) |
| 160 |
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& .OR.(viscA4Z.NE.0.) |
| 161 |
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& .OR.(viscA4Grid.NE.0.) |
| 162 |
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& .OR.(viscC4leith.NE.0.) |
| 163 |
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& .OR.(viscC4leithD.NE.0.) |
| 164 |
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& .OR.(viscC4smag.NE.0.) |
| 165 |
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| 166 |
baylor |
1.9 |
IF ((biharmonic).and.(viscA4remax.ne.0.)) THEN |
| 167 |
jmc |
1.10 |
viscA4re_max=0.125 _d 0*sqrt(2. _d 0)/viscA4Remax |
| 168 |
baylor |
1.9 |
ELSE |
| 169 |
jmc |
1.10 |
viscA4re_max=0. _d 0 |
| 170 |
baylor |
1.9 |
ENDIF |
| 171 |
baylor |
1.5 |
|
| 172 |
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calcleith= |
| 173 |
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& (viscC2leith.NE.0.) |
| 174 |
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& .OR.(viscC2leithD.NE.0.) |
| 175 |
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& .OR.(viscC4leith.NE.0.) |
| 176 |
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& .OR.(viscC4leithD.NE.0.) |
| 177 |
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| 178 |
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calcsmag= |
| 179 |
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& (viscC2smag.NE.0.) |
| 180 |
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& .OR.(viscC4smag.NE.0.) |
| 181 |
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| 182 |
baylor |
1.1 |
IF (deltaTmom.NE.0.) THEN |
| 183 |
jmc |
1.10 |
recip_dt=1. _d 0/deltaTmom |
| 184 |
baylor |
1.1 |
ELSE |
| 185 |
jmc |
1.10 |
recip_dt=0. _d 0 |
| 186 |
baylor |
1.1 |
ENDIF |
| 187 |
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| 188 |
baylor |
1.5 |
IF (calcsmag) THEN |
| 189 |
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smag2fac=(viscC2smag/pi)**2 |
| 190 |
jmc |
1.10 |
smag4fac=0.125 _d 0*(viscC4smag/pi)**2 |
| 191 |
baylor |
1.9 |
ELSE |
| 192 |
jmc |
1.10 |
smag2fac=0. _d 0 |
| 193 |
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smag4fac=0. _d 0 |
| 194 |
baylor |
1.5 |
ENDIF |
| 195 |
baylor |
1.1 |
|
| 196 |
baylor |
1.17 |
IF (calcleith) THEN |
| 197 |
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IF (useFullLeith) THEN |
| 198 |
baylor |
1.19 |
leith2fac =(viscC2leith /pi)**6 |
| 199 |
baylor |
1.17 |
leithD2fac=(viscC2leithD/pi)**6 |
| 200 |
baylor |
1.19 |
leith4fac =0.015625 _d 0*(viscC4leith /pi)**6 |
| 201 |
baylor |
1.17 |
leithD4fac=0.015625 _d 0*(viscC4leithD/pi)**6 |
| 202 |
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ELSE |
| 203 |
baylor |
1.19 |
leith2fac =(viscC2leith /pi)**3 |
| 204 |
baylor |
1.17 |
leithD2fac=(viscC2leithD/pi)**3 |
| 205 |
baylor |
1.19 |
leith4fac =0.125 _d 0*(viscC4leith /pi)**3 |
| 206 |
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leithD4fac=0.125 _d 0*(viscC4leithD/pi)**3 |
| 207 |
baylor |
1.17 |
ENDIF |
| 208 |
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ELSE |
| 209 |
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leith2fac=0. _d 0 |
| 210 |
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leith4fac=0. _d 0 |
| 211 |
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leithD2fac=0. _d 0 |
| 212 |
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leithD4fac=0. _d 0 |
| 213 |
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ENDIF |
| 214 |
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| 215 |
heimbach |
1.21 |
#ifdef ALLOW_AUTODIFF_TAMC |
| 216 |
heimbach |
1.22 |
IF ( calcLeith .OR. calcSmag ) THEN |
| 217 |
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STOP 'calcLeith or calcSmag not implemented for ADJOINT' |
| 218 |
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ENDIF |
| 219 |
mlosch |
1.24 |
#endif |
| 220 |
heimbach |
1.22 |
DO j=1-Oly,sNy+Oly |
| 221 |
heimbach |
1.21 |
DO i=1-Olx,sNx+Olx |
| 222 |
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viscAh_D(i,j)=viscAhD |
| 223 |
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viscAh_Z(i,j)=viscAhZ |
| 224 |
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viscA4_D(i,j)=viscA4D |
| 225 |
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viscA4_Z(i,j)=viscA4Z |
| 226 |
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c |
| 227 |
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visca4_zsmg(i,j) = 0. _d 0 |
| 228 |
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viscah_zsmg(i,j) = 0. _d 0 |
| 229 |
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c |
| 230 |
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viscAh_Dlth(i,j) = 0. _d 0 |
| 231 |
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viscA4_Dlth(i,j) = 0. _d 0 |
| 232 |
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viscAh_DlthD(i,j)= 0. _d 0 |
| 233 |
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viscA4_DlthD(i,j)= 0. _d 0 |
| 234 |
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c |
| 235 |
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viscAh_DSmg(i,j) = 0. _d 0 |
| 236 |
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viscA4_DSmg(i,j) = 0. _d 0 |
| 237 |
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c |
| 238 |
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viscAh_ZLth(i,j) = 0. _d 0 |
| 239 |
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viscA4_ZLth(i,j) = 0. _d 0 |
| 240 |
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viscAh_ZLthD(i,j)= 0. _d 0 |
| 241 |
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viscA4_ZLthD(i,j)= 0. _d 0 |
| 242 |
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ENDDO |
| 243 |
heimbach |
1.22 |
ENDDO |
| 244 |
heimbach |
1.21 |
|
| 245 |
baylor |
1.1 |
C - Viscosity |
| 246 |
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IF (useVariableViscosity) THEN |
| 247 |
jmc |
1.16 |
|
| 248 |
jmc |
1.20 |
C- Initialise to zero gradient of vorticity & divergence: |
| 249 |
jmc |
1.16 |
DO j=1-Oly,sNy+Oly |
| 250 |
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DO i=1-Olx,sNx+Olx |
| 251 |
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divDx(i,j) = 0. |
| 252 |
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divDy(i,j) = 0. |
| 253 |
jmc |
1.20 |
vrtDx(i,j) = 0. |
| 254 |
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vrtDy(i,j) = 0. |
| 255 |
jmc |
1.16 |
ENDDO |
| 256 |
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ENDDO |
| 257 |
jmc |
1.20 |
|
| 258 |
jmc |
1.16 |
IF (calcleith) THEN |
| 259 |
jmc |
1.20 |
C horizontal gradient of horizontal divergence: |
| 260 |
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| 261 |
jmc |
1.16 |
C- gradient in x direction: |
| 262 |
heimbach |
1.26 |
cph-exch2#ifndef ALLOW_AUTODIFF_TAMC |
| 263 |
jmc |
1.16 |
IF (useCubedSphereExchange) THEN |
| 264 |
|
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C to compute d/dx(hDiv), fill corners with appropriate values: |
| 265 |
jmc |
1.27 |
CALL FILL_CS_CORNER_TR_RL( .TRUE., .FALSE., |
| 266 |
|
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& hDiv, bi,bj, myThid ) |
| 267 |
jmc |
1.16 |
ENDIF |
| 268 |
heimbach |
1.26 |
cph-exch2#endif |
| 269 |
jmc |
1.16 |
DO j=2-Oly,sNy+Oly-1 |
| 270 |
|
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DO i=2-Olx,sNx+Olx-1 |
| 271 |
|
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divDx(i,j) = (hDiv(i,j)-hDiv(i-1,j))*recip_DXC(i,j,bi,bj) |
| 272 |
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ENDDO |
| 273 |
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ENDDO |
| 274 |
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| 275 |
|
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C- gradient in y direction: |
| 276 |
heimbach |
1.26 |
cph-exch2#ifndef ALLOW_AUTODIFF_TAMC |
| 277 |
jmc |
1.16 |
IF (useCubedSphereExchange) THEN |
| 278 |
|
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C to compute d/dy(hDiv), fill corners with appropriate values: |
| 279 |
jmc |
1.27 |
CALL FILL_CS_CORNER_TR_RL(.FALSE., .FALSE., |
| 280 |
|
|
& hDiv, bi,bj, myThid ) |
| 281 |
jmc |
1.16 |
ENDIF |
| 282 |
heimbach |
1.26 |
cph-exch2#endif |
| 283 |
jmc |
1.16 |
DO j=2-Oly,sNy+Oly-1 |
| 284 |
|
|
DO i=2-Olx,sNx+Olx-1 |
| 285 |
|
|
divDy(i,j) = (hDiv(i,j)-hDiv(i,j-1))*recip_DYC(i,j,bi,bj) |
| 286 |
|
|
ENDDO |
| 287 |
|
|
ENDDO |
| 288 |
jmc |
1.20 |
|
| 289 |
|
|
C horizontal gradient of vertical vorticity: |
| 290 |
|
|
C- gradient in x direction: |
| 291 |
|
|
DO j=2-Oly,sNy+Oly |
| 292 |
|
|
DO i=2-Olx,sNx+Olx-1 |
| 293 |
|
|
vrtDx(i,j) = (vort3(i+1,j)-vort3(i,j)) |
| 294 |
|
|
& *recip_DXG(i,j,bi,bj) |
| 295 |
|
|
& *maskS(i,j,k,bi,bj) |
| 296 |
|
|
ENDDO |
| 297 |
|
|
ENDDO |
| 298 |
|
|
C- gradient in y direction: |
| 299 |
|
|
DO j=2-Oly,sNy+Oly-1 |
| 300 |
|
|
DO i=2-Olx,sNx+Olx |
| 301 |
|
|
vrtDy(i,j) = (vort3(i,j+1)-vort3(i,j)) |
| 302 |
|
|
& *recip_DYG(i,j,bi,bj) |
| 303 |
|
|
& *maskW(i,j,k,bi,bj) |
| 304 |
|
|
ENDDO |
| 305 |
|
|
ENDDO |
| 306 |
|
|
|
| 307 |
jmc |
1.16 |
ENDIF |
| 308 |
|
|
|
| 309 |
baylor |
1.1 |
DO j=2-Oly,sNy+Oly-1 |
| 310 |
|
|
DO i=2-Olx,sNx+Olx-1 |
| 311 |
|
|
CCCCCCCCCCCCCCC Divergence Point CalculationsCCCCCCCCCCCCCCCCCCCC |
| 312 |
baylor |
1.5 |
|
| 313 |
baylor |
1.1 |
C These are (powers of) length scales |
| 314 |
baylor |
1.11 |
IF (useAreaViscLength) THEN |
| 315 |
jmc |
1.12 |
L2=rA(i,j,bi,bj) |
| 316 |
mlosch |
1.28 |
L4rdt=0.03125 _d 0*recip_dt*L2**2 |
| 317 |
baylor |
1.11 |
ELSE |
| 318 |
|
|
L2=2. _d 0/((recip_DXF(I,J,bi,bj)**2+recip_DYF(I,J,bi,bj)**2)) |
| 319 |
mlosch |
1.28 |
L4rdt=recip_dt/( 6. _d 0*(recip_DXF(I,J,bi,bj)**4 |
| 320 |
|
|
& +recip_DYF(I,J,bi,bj)**4) |
| 321 |
|
|
& +8. _d 0*((recip_DXF(I,J,bi,bj) |
| 322 |
|
|
& *recip_DYF(I,J,bi,bj))**2) ) |
| 323 |
baylor |
1.11 |
ENDIF |
| 324 |
baylor |
1.1 |
L3=(L2**1.5) |
| 325 |
|
|
L4=(L2**2) |
| 326 |
mlosch |
1.28 |
L5=(L2*L3) |
| 327 |
baylor |
1.5 |
|
| 328 |
jmc |
1.10 |
L2rdt=0.25 _d 0*recip_dt*L2 |
| 329 |
baylor |
1.5 |
|
| 330 |
|
|
C Velocity Reynolds Scale |
| 331 |
jmc |
1.15 |
IF ( viscAhRe_max.GT.0. .AND. KE(i,j).GT.0. ) THEN |
| 332 |
|
|
Uscl=sqrt(KE(i,j)*L2)*viscAhRe_max |
| 333 |
|
|
ELSE |
| 334 |
|
|
Uscl=0. |
| 335 |
|
|
ENDIF |
| 336 |
|
|
IF ( viscA4Re_max.GT.0. .AND. KE(i,j).GT.0. ) THEN |
| 337 |
|
|
U4scl=sqrt(KE(i,j))*L3*viscA4Re_max |
| 338 |
|
|
ELSE |
| 339 |
|
|
U4scl=0. |
| 340 |
|
|
ENDIF |
| 341 |
baylor |
1.5 |
|
| 342 |
heimbach |
1.22 |
#ifndef ALLOW_AUTODIFF_TAMC |
| 343 |
baylor |
1.5 |
IF (useFullLeith.and.calcleith) THEN |
| 344 |
baylor |
1.1 |
C This is the vector magnitude of the vorticity gradient squared |
| 345 |
jmc |
1.20 |
grdVrt=0.25 _d 0*( (vrtDx(i,j+1)*vrtDx(i,j+1) |
| 346 |
|
|
& + vrtDx(i,j)*vrtDx(i,j) ) |
| 347 |
|
|
& + (vrtDy(i+1,j)*vrtDy(i+1,j) |
| 348 |
|
|
& + vrtDy(i,j)*vrtDy(i,j) ) ) |
| 349 |
baylor |
1.1 |
|
| 350 |
|
|
C This is the vector magnitude of grad (div.v) squared |
| 351 |
|
|
C Using it in Leith serves to damp instabilities in w. |
| 352 |
jmc |
1.16 |
grdDiv=0.25 _d 0*( (divDx(i+1,j)*divDx(i+1,j) |
| 353 |
|
|
& + divDx(i,j)*divDx(i,j) ) |
| 354 |
|
|
& + (divDy(i,j+1)*divDy(i,j+1) |
| 355 |
|
|
& + divDy(i,j)*divDy(i,j) ) ) |
| 356 |
baylor |
1.5 |
|
| 357 |
|
|
viscAh_DLth(i,j)= |
| 358 |
baylor |
1.17 |
& sqrt(leith2fac*grdVrt+leithD2fac*grdDiv)*L3 |
| 359 |
|
|
viscA4_DLth(i,j)= |
| 360 |
|
|
& sqrt(leith4fac*grdVrt+leithD4fac*grdDiv)*L5 |
| 361 |
baylor |
1.5 |
viscAh_DLthd(i,j)= |
| 362 |
baylor |
1.17 |
& sqrt(leithD2fac*grdDiv)*L3 |
| 363 |
|
|
viscA4_DLthd(i,j)= |
| 364 |
|
|
& sqrt(leithD4fac*grdDiv)*L5 |
| 365 |
baylor |
1.5 |
ELSEIF (calcleith) THEN |
| 366 |
baylor |
1.1 |
C but this approximation will work on cube |
| 367 |
|
|
c (and differs by as much as 4X) |
| 368 |
jmc |
1.20 |
grdVrt=max( abs(vrtDx(i,j+1)), abs(vrtDx(i,j)) ) |
| 369 |
|
|
grdVrt=max( grdVrt, abs(vrtDy(i+1,j)) ) |
| 370 |
|
|
grdVrt=max( grdVrt, abs(vrtDy(i,j)) ) |
| 371 |
baylor |
1.5 |
|
| 372 |
jmc |
1.20 |
c This approximation is good to the same order as above... |
| 373 |
jmc |
1.16 |
grdDiv=max( abs(divDx(i+1,j)), abs(divDx(i,j)) ) |
| 374 |
|
|
grdDiv=max( grdDiv, abs(divDy(i,j+1)) ) |
| 375 |
|
|
grdDiv=max( grdDiv, abs(divDy(i,j)) ) |
| 376 |
baylor |
1.1 |
|
| 377 |
baylor |
1.17 |
viscAh_Dlth(i,j)=(leith2fac*grdVrt+(leithD2fac*grdDiv))*L3 |
| 378 |
|
|
viscA4_Dlth(i,j)=(leith4fac*grdVrt+(leithD4fac*grdDiv))*L5 |
| 379 |
|
|
viscAh_DlthD(i,j)=((leithD2fac*grdDiv))*L3 |
| 380 |
|
|
viscA4_DlthD(i,j)=((leithD4fac*grdDiv))*L5 |
| 381 |
baylor |
1.1 |
ELSE |
| 382 |
jmc |
1.10 |
viscAh_Dlth(i,j)=0. _d 0 |
| 383 |
|
|
viscA4_Dlth(i,j)=0. _d 0 |
| 384 |
|
|
viscAh_DlthD(i,j)=0. _d 0 |
| 385 |
|
|
viscA4_DlthD(i,j)=0. _d 0 |
| 386 |
baylor |
1.1 |
ENDIF |
| 387 |
|
|
|
| 388 |
baylor |
1.5 |
IF (calcsmag) THEN |
| 389 |
|
|
viscAh_DSmg(i,j)=L2 |
| 390 |
|
|
& *sqrt(tension(i,j)**2 |
| 391 |
jmc |
1.10 |
& +0.25 _d 0*(strain(i+1, j )**2+strain( i ,j+1)**2 |
| 392 |
|
|
& +strain(i , j )**2+strain(i+1,j+1)**2)) |
| 393 |
baylor |
1.5 |
viscA4_DSmg(i,j)=smag4fac*L2*viscAh_DSmg(i,j) |
| 394 |
|
|
viscAh_DSmg(i,j)=smag2fac*viscAh_DSmg(i,j) |
| 395 |
baylor |
1.1 |
ELSE |
| 396 |
jmc |
1.10 |
viscAh_DSmg(i,j)=0. _d 0 |
| 397 |
|
|
viscA4_DSmg(i,j)=0. _d 0 |
| 398 |
baylor |
1.1 |
ENDIF |
| 399 |
heimbach |
1.22 |
#endif /* ALLOW_AUTODIFF_TAMC */ |
| 400 |
baylor |
1.1 |
|
| 401 |
|
|
C Harmonic on Div.u points |
| 402 |
baylor |
1.5 |
Alin=viscAhD+viscAhGrid*L2rdt |
| 403 |
|
|
& +viscAh_DLth(i,j)+viscAh_DSmg(i,j) |
| 404 |
|
|
viscAh_DMin(i,j)=max(viscAhGridMin*L2rdt,Uscl) |
| 405 |
|
|
viscAh_D(i,j)=max(viscAh_DMin(i,j),Alin) |
| 406 |
|
|
viscAh_DMax(i,j)=min(viscAhGridMax*L2rdt,viscAhMax) |
| 407 |
|
|
viscAh_D(i,j)=min(viscAh_DMax(i,j),viscAh_D(i,j)) |
| 408 |
baylor |
1.1 |
|
| 409 |
|
|
C BiHarmonic on Div.u points |
| 410 |
baylor |
1.5 |
Alin=viscA4D+viscA4Grid*L4rdt |
| 411 |
|
|
& +viscA4_DLth(i,j)+viscA4_DSmg(i,j) |
| 412 |
|
|
viscA4_DMin(i,j)=max(viscA4GridMin*L4rdt,U4scl) |
| 413 |
|
|
viscA4_D(i,j)=max(viscA4_DMin(i,j),Alin) |
| 414 |
|
|
viscA4_DMax(i,j)=min(viscA4GridMax*L4rdt,viscA4Max) |
| 415 |
|
|
viscA4_D(i,j)=min(viscA4_DMax(i,j),viscA4_D(i,j)) |
| 416 |
baylor |
1.1 |
|
| 417 |
jmc |
1.27 |
#ifdef ALLOW_NONHYDROSTATIC |
| 418 |
baylor |
1.23 |
C /* Pass Viscosities to calc_gw, if constant, not necessary */ |
| 419 |
|
|
|
| 420 |
|
|
kp1 = MIN(k+1,Nr) |
| 421 |
|
|
|
| 422 |
|
|
if (k .eq. 1) then |
| 423 |
|
|
viscAh_W(i,j,kp1,bi,bj)=0.5*viscAh_D(i,j) |
| 424 |
|
|
viscA4_W(i,j,kp1,bi,bj)=0.5*viscA4_D(i,j) |
| 425 |
|
|
|
| 426 |
jmc |
1.27 |
C /* These values dont get used */ |
| 427 |
|
|
viscAh_W(i,j,k,bi,bj)=viscAh_D(i,j) |
| 428 |
baylor |
1.23 |
viscA4_W(i,j,k,bi,bj)=viscA4_D(i,j) |
| 429 |
|
|
else |
| 430 |
|
|
C Note that previous call of this function has already added half. |
| 431 |
|
|
viscAh_W(i,j,kp1,bi,bj)=0.5*viscAh_D(i,j) |
| 432 |
|
|
viscA4_W(i,j,kp1,bi,bj)=0.5*viscA4_D(i,j) |
| 433 |
|
|
|
| 434 |
|
|
viscAh_W(i,j,k,bi,bj)=viscAh_W(i,j,k,bi,bj)+0.5*viscAh_D(i,j) |
| 435 |
|
|
viscA4_W(i,j,k,bi,bj)=viscA4_W(i,j,k,bi,bj)+0.5*viscA4_D(i,j) |
| 436 |
|
|
endif |
| 437 |
|
|
#endif /* ALLOW_NONHYDROSTATIC */ |
| 438 |
|
|
|
| 439 |
baylor |
1.1 |
CCCCCCCCCCCCC Vorticity Point CalculationsCCCCCCCCCCCCCCCCCC |
| 440 |
|
|
C These are (powers of) length scales |
| 441 |
baylor |
1.11 |
IF (useAreaViscLength) THEN |
| 442 |
jmc |
1.12 |
L2=rAz(i,j,bi,bj) |
| 443 |
mlosch |
1.28 |
L4rdt=0.125 _d 0*recip_dt*rAz(i,j,bi,bj)**2 |
| 444 |
baylor |
1.11 |
ELSE |
| 445 |
jmc |
1.12 |
L2=2. _d 0/((recip_DXV(I,J,bi,bj)**2+recip_DYU(I,J,bi,bj)**2)) |
| 446 |
mlosch |
1.28 |
L4rdt=recip_dt/ |
| 447 |
|
|
& ( 6. _d 0*(recip_DXV(I,J,bi,bj)**4+recip_DYU(I,J,bi,bj)**4) |
| 448 |
|
|
& +8. _d 0*((recip_DXV(I,J,bi,bj)*recip_DYU(I,J,bi,bj))**2)) |
| 449 |
baylor |
1.11 |
ENDIF |
| 450 |
|
|
|
| 451 |
baylor |
1.1 |
L3=(L2**1.5) |
| 452 |
|
|
L4=(L2**2) |
| 453 |
mlosch |
1.28 |
L5=(L2*L3) |
| 454 |
baylor |
1.5 |
|
| 455 |
jmc |
1.10 |
L2rdt=0.25 _d 0*recip_dt*L2 |
| 456 |
baylor |
1.5 |
|
| 457 |
jmc |
1.15 |
C Velocity Reynolds Scale (Pb here at CS-grid corners !) |
| 458 |
|
|
IF ( viscAhRe_max.GT.0. .OR. viscA4Re_max.GT.0. ) THEN |
| 459 |
|
|
keZpt=0.25 _d 0*( (KE(i,j)+KE(i-1,j-1)) |
| 460 |
|
|
& +(KE(i-1,j)+KE(i,j-1)) ) |
| 461 |
|
|
IF ( keZpt.GT.0. ) THEN |
| 462 |
|
|
Uscl = sqrt(keZpt*L2)*viscAhRe_max |
| 463 |
|
|
U4scl= sqrt(keZpt)*L3*viscA4Re_max |
| 464 |
|
|
ELSE |
| 465 |
|
|
Uscl =0. |
| 466 |
|
|
U4scl=0. |
| 467 |
|
|
ENDIF |
| 468 |
|
|
ELSE |
| 469 |
|
|
Uscl =0. |
| 470 |
|
|
U4scl=0. |
| 471 |
|
|
ENDIF |
| 472 |
baylor |
1.1 |
|
| 473 |
heimbach |
1.22 |
#ifndef ALLOW_AUTODIFF_TAMC |
| 474 |
baylor |
1.1 |
C This is the vector magnitude of the vorticity gradient squared |
| 475 |
baylor |
1.5 |
IF (useFullLeith.and.calcleith) THEN |
| 476 |
jmc |
1.20 |
grdVrt=0.25 _d 0*( (vrtDx(i-1,j)*vrtDx(i-1,j) |
| 477 |
|
|
& + vrtDx(i,j)*vrtDx(i,j) ) |
| 478 |
|
|
& + (vrtDy(i,j-1)*vrtDy(i,j-1) |
| 479 |
|
|
& + vrtDy(i,j)*vrtDy(i,j) ) ) |
| 480 |
baylor |
1.1 |
|
| 481 |
|
|
C This is the vector magnitude of grad(div.v) squared |
| 482 |
jmc |
1.16 |
grdDiv=0.25 _d 0*( (divDx(i,j-1)*divDx(i,j-1) |
| 483 |
|
|
& + divDx(i,j)*divDx(i,j) ) |
| 484 |
|
|
& + (divDy(i-1,j)*divDy(i-1,j) |
| 485 |
|
|
& + divDy(i,j)*divDy(i,j) ) ) |
| 486 |
baylor |
1.5 |
|
| 487 |
|
|
viscAh_ZLth(i,j)= |
| 488 |
baylor |
1.17 |
& sqrt(leith2fac*grdVrt+leithD2fac*grdDiv)*L3 |
| 489 |
|
|
viscA4_ZLth(i,j)= |
| 490 |
|
|
& sqrt(leith4fac*grdVrt+leithD4fac*grdDiv)*L5 |
| 491 |
baylor |
1.5 |
viscAh_ZLthD(i,j)= |
| 492 |
baylor |
1.17 |
& sqrt(leithD2fac*grdDiv)*L3 |
| 493 |
|
|
viscA4_ZLthD(i,j)= |
| 494 |
|
|
& sqrt(leithD4fac*grdDiv)*L5 |
| 495 |
baylor |
1.5 |
|
| 496 |
|
|
ELSEIF (calcleith) THEN |
| 497 |
baylor |
1.1 |
C but this approximation will work on cube (and differs by 4X) |
| 498 |
jmc |
1.20 |
grdVrt=max( abs(vrtDx(i-1,j)), abs(vrtDx(i,j)) ) |
| 499 |
|
|
grdVrt=max( grdVrt, abs(vrtDy(i,j-1)) ) |
| 500 |
|
|
grdVrt=max( grdVrt, abs(vrtDy(i,j)) ) |
| 501 |
baylor |
1.5 |
|
| 502 |
jmc |
1.16 |
grdDiv=max( abs(divDx(i,j)), abs(divDx(i,j-1)) ) |
| 503 |
|
|
grdDiv=max( grdDiv, abs(divDy(i,j)) ) |
| 504 |
|
|
grdDiv=max( grdDiv, abs(divDy(i-1,j)) ) |
| 505 |
baylor |
1.5 |
|
| 506 |
baylor |
1.17 |
viscAh_ZLth(i,j)=(leith2fac*grdVrt+(leithD2fac*grdDiv))*L3 |
| 507 |
|
|
viscA4_ZLth(i,j)=(leith4fac*grdVrt+(leithD4fac*grdDiv))*L5 |
| 508 |
|
|
viscAh_ZLthD(i,j)=(leithD2fac*grdDiv)*L3 |
| 509 |
|
|
viscA4_ZLthD(i,j)=(leithD4fac*grdDiv)*L5 |
| 510 |
baylor |
1.1 |
ELSE |
| 511 |
jmc |
1.10 |
viscAh_ZLth(i,j)=0. _d 0 |
| 512 |
|
|
viscA4_ZLth(i,j)=0. _d 0 |
| 513 |
|
|
viscAh_ZLthD(i,j)=0. _d 0 |
| 514 |
|
|
viscA4_ZLthD(i,j)=0. _d 0 |
| 515 |
baylor |
1.1 |
ENDIF |
| 516 |
|
|
|
| 517 |
baylor |
1.5 |
IF (calcsmag) THEN |
| 518 |
|
|
viscAh_ZSmg(i,j)=L2 |
| 519 |
|
|
& *sqrt(strain(i,j)**2 |
| 520 |
jmc |
1.10 |
& +0.25 _d 0*(tension( i , j )**2+tension( i ,j-1)**2 |
| 521 |
|
|
& +tension(i-1, j )**2+tension(i-1,j-1)**2)) |
| 522 |
baylor |
1.5 |
viscA4_ZSmg(i,j)=smag4fac*L2*viscAh_ZSmg(i,j) |
| 523 |
|
|
viscAh_ZSmg(i,j)=smag2fac*viscAh_ZSmg(i,j) |
| 524 |
baylor |
1.1 |
ENDIF |
| 525 |
heimbach |
1.22 |
#endif /* ALLOW_AUTODIFF_TAMC */ |
| 526 |
baylor |
1.1 |
|
| 527 |
|
|
C Harmonic on Zeta points |
| 528 |
baylor |
1.5 |
Alin=viscAhZ+viscAhGrid*L2rdt |
| 529 |
|
|
& +viscAh_ZLth(i,j)+viscAh_ZSmg(i,j) |
| 530 |
|
|
viscAh_ZMin(i,j)=max(viscAhGridMin*L2rdt,Uscl) |
| 531 |
|
|
viscAh_Z(i,j)=max(viscAh_ZMin(i,j),Alin) |
| 532 |
|
|
viscAh_ZMax(i,j)=min(viscAhGridMax*L2rdt,viscAhMax) |
| 533 |
|
|
viscAh_Z(i,j)=min(viscAh_ZMax(i,j),viscAh_Z(i,j)) |
| 534 |
|
|
|
| 535 |
|
|
C BiHarmonic on Zeta points |
| 536 |
|
|
Alin=viscA4Z+viscA4Grid*L4rdt |
| 537 |
|
|
& +viscA4_ZLth(i,j)+viscA4_ZSmg(i,j) |
| 538 |
|
|
viscA4_ZMin(i,j)=max(viscA4GridMin*L4rdt,U4scl) |
| 539 |
|
|
viscA4_Z(i,j)=max(viscA4_ZMin(i,j),Alin) |
| 540 |
|
|
viscA4_ZMax(i,j)=min(viscA4GridMax*L4rdt,viscA4Max) |
| 541 |
|
|
viscA4_Z(i,j)=min(viscA4_ZMax(i,j),viscA4_Z(i,j)) |
| 542 |
baylor |
1.1 |
ENDDO |
| 543 |
|
|
ENDDO |
| 544 |
|
|
ELSE |
| 545 |
|
|
DO j=1-Oly,sNy+Oly |
| 546 |
|
|
DO i=1-Olx,sNx+Olx |
| 547 |
|
|
viscAh_D(i,j)=viscAhD |
| 548 |
|
|
viscAh_Z(i,j)=viscAhZ |
| 549 |
|
|
viscA4_D(i,j)=viscA4D |
| 550 |
|
|
viscA4_Z(i,j)=viscA4Z |
| 551 |
|
|
ENDDO |
| 552 |
|
|
ENDDO |
| 553 |
|
|
ENDIF |
| 554 |
|
|
|
| 555 |
|
|
#ifdef ALLOW_DIAGNOSTICS |
| 556 |
|
|
IF (useDiagnostics) THEN |
| 557 |
|
|
CALL DIAGNOSTICS_FILL(viscAh_D,'VISCAHD ',k,1,2,bi,bj,myThid) |
| 558 |
|
|
CALL DIAGNOSTICS_FILL(viscA4_D,'VISCA4D ',k,1,2,bi,bj,myThid) |
| 559 |
|
|
CALL DIAGNOSTICS_FILL(viscAh_Z,'VISCAHZ ',k,1,2,bi,bj,myThid) |
| 560 |
|
|
CALL DIAGNOSTICS_FILL(viscA4_Z,'VISCA4Z ',k,1,2,bi,bj,myThid) |
| 561 |
baylor |
1.23 |
#ifdef ALLOW_NONHYDROSTATIC |
| 562 |
|
|
CALL DIAGNOSTICS_FILL(viscAh_W,'VISCAHW ',k,1,2,bi,bj,myThid) |
| 563 |
|
|
CALL DIAGNOSTICS_FILL(viscA4_W,'VISCA4W ',k,1,2,bi,bj,myThid) |
| 564 |
|
|
#endif |
| 565 |
baylor |
1.5 |
|
| 566 |
|
|
CALL DIAGNOSTICS_FILL(viscAh_DMax,'VAHDMAX ',k,1,2,bi,bj,myThid) |
| 567 |
|
|
CALL DIAGNOSTICS_FILL(viscA4_DMax,'VA4DMAX ',k,1,2,bi,bj,myThid) |
| 568 |
|
|
CALL DIAGNOSTICS_FILL(viscAh_ZMax,'VAHZMAX ',k,1,2,bi,bj,myThid) |
| 569 |
|
|
CALL DIAGNOSTICS_FILL(viscA4_ZMax,'VA4ZMAX ',k,1,2,bi,bj,myThid) |
| 570 |
|
|
|
| 571 |
|
|
CALL DIAGNOSTICS_FILL(viscAh_DMin,'VAHDMIN ',k,1,2,bi,bj,myThid) |
| 572 |
|
|
CALL DIAGNOSTICS_FILL(viscA4_DMin,'VA4DMIN ',k,1,2,bi,bj,myThid) |
| 573 |
|
|
CALL DIAGNOSTICS_FILL(viscAh_ZMin,'VAHZMIN ',k,1,2,bi,bj,myThid) |
| 574 |
|
|
CALL DIAGNOSTICS_FILL(viscA4_ZMin,'VA4ZMIN ',k,1,2,bi,bj,myThid) |
| 575 |
|
|
|
| 576 |
|
|
CALL DIAGNOSTICS_FILL(viscAh_DLth,'VAHDLTH ',k,1,2,bi,bj,myThid) |
| 577 |
|
|
CALL DIAGNOSTICS_FILL(viscA4_DLth,'VA4DLTH ',k,1,2,bi,bj,myThid) |
| 578 |
|
|
CALL DIAGNOSTICS_FILL(viscAh_ZLth,'VAHZLTH ',k,1,2,bi,bj,myThid) |
| 579 |
|
|
CALL DIAGNOSTICS_FILL(viscA4_ZLth,'VA4ZLTH ',k,1,2,bi,bj,myThid) |
| 580 |
|
|
|
| 581 |
baylor |
1.7 |
CALL DIAGNOSTICS_FILL(viscAh_DLthD,'VAHDLTHD' |
| 582 |
baylor |
1.8 |
& ,k,1,2,bi,bj,myThid) |
| 583 |
baylor |
1.7 |
CALL DIAGNOSTICS_FILL(viscA4_DLthD,'VA4DLTHD' |
| 584 |
baylor |
1.8 |
& ,k,1,2,bi,bj,myThid) |
| 585 |
baylor |
1.7 |
CALL DIAGNOSTICS_FILL(viscAh_ZLthD,'VAHZLTHD' |
| 586 |
baylor |
1.8 |
& ,k,1,2,bi,bj,myThid) |
| 587 |
baylor |
1.7 |
CALL DIAGNOSTICS_FILL(viscA4_ZLthD,'VA4ZLTHD' |
| 588 |
baylor |
1.8 |
& ,k,1,2,bi,bj,myThid) |
| 589 |
baylor |
1.5 |
|
| 590 |
|
|
CALL DIAGNOSTICS_FILL(viscAh_DSmg,'VAHDSMAG',k,1,2,bi,bj,myThid) |
| 591 |
|
|
CALL DIAGNOSTICS_FILL(viscA4_DSmg,'VA4DSMAG',k,1,2,bi,bj,myThid) |
| 592 |
|
|
CALL DIAGNOSTICS_FILL(viscAh_ZSmg,'VAHZSMAG',k,1,2,bi,bj,myThid) |
| 593 |
|
|
CALL DIAGNOSTICS_FILL(viscA4_ZSmg,'VA4ZSMAG',k,1,2,bi,bj,myThid) |
| 594 |
baylor |
1.1 |
ENDIF |
| 595 |
|
|
#endif |
| 596 |
|
|
|
| 597 |
|
|
RETURN |
| 598 |
|
|
END |
| 599 |
baylor |
1.5 |
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