1 |
baylor |
1.1 |
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#include "MOM_COMMON_OPTIONS.h" |
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4 |
baylor |
1.5 |
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5 |
baylor |
1.1 |
SUBROUTINE MOM_CALC_VISC( |
6 |
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I bi,bj,k, |
7 |
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O viscAh_Z,viscAh_D,viscA4_Z,viscA4_D, |
8 |
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O harmonic,biharmonic,useVariableViscosity, |
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jmc |
1.12 |
I hDiv,vort3,tension,strain,KE,hFacZ, |
10 |
baylor |
1.1 |
I myThid) |
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12 |
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IMPLICIT NONE |
13 |
baylor |
1.5 |
C |
14 |
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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) |
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C +0.25*L**2*viscAhGrid/deltaT |
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C +sqrt(viscC2leith**2*grad(Vort3)**2 |
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C +viscC2leithD**2*grad(hDiv)**2)*L**3 |
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C +(viscC2smag/pi)**2*L**2*sqrt(Tension**2+Strain**2) |
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C |
22 |
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C biharmonic viscosity= |
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C viscA4 (or viscA4D on div pts and viscA4Z on zeta pts) |
24 |
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C +0.25*0.125*L**4*viscA4Grid/deltaT (approx) |
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C +0.125*L**5*sqrt(viscC4leith**2*grad(Vort3)**2 |
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C +viscC4leithD**2*grad(hDiv)**2) |
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C +0.125*L**4*(viscC4smag/pi)**2*sqrt(Tension**2+Strain**2) |
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C |
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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 |
34 |
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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 |
36 |
baylor |
1.9 |
C harmonic viscosity>sqrt(2*KE)*L/viscAhRemax |
37 |
baylor |
1.5 |
C |
38 |
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C viscA4Remax is min value for grid point biharmonic Reynolds num |
39 |
baylor |
1.9 |
C biharmonic viscosity>sqrt(2*KE)*L**3/8/viscA4Remax |
40 |
baylor |
1.5 |
C |
41 |
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C viscAhgridmax is CFL stability limiter for harmonic viscosity |
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C harmonic viscosity<0.25*viscAhgridmax*L**2/deltaT |
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C |
44 |
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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 |
47 |
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C viscAhgridmin and viscA4gridmin are lower limits for viscosity: |
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C harmonic viscosity>0.25*viscAhgridmax*L**2/deltaT |
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C biharmonic viscosity>viscA4gridmax*L**4/32/deltaT (approx) |
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C |
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C RECOMMENDED VALUES |
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C viscC2Leith=? |
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C viscC2LeithD=? |
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C viscC4Leith=? |
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C viscC4LeithD=? |
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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) |
59 |
baylor |
1.9 |
C viscAhRemax>=1, (<2 suppresses a computational mode) |
60 |
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C viscA4Remax>=1, (<2 suppresses a computational mode) |
61 |
baylor |
1.5 |
C viscAhgridmax=1 |
62 |
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C viscA4gridmax=1 |
63 |
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C viscAhgrid<1 |
64 |
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C viscA4grid<1 |
65 |
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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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68 |
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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" |
73 |
baylor |
1.13 |
#ifdef ALLOW_EXCH2 |
74 |
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#include "W2_EXCH2_TOPOLOGY.h" |
75 |
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#include "W2_EXCH2_PARAMS.h" |
76 |
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#endif /* ALLOW_EXCH2 */ |
77 |
baylor |
1.1 |
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78 |
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C == Routine arguments == |
79 |
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INTEGER bi,bj,k |
80 |
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_RL viscAh_Z(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
81 |
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_RL viscAh_D(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
82 |
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_RL viscA4_Z(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
83 |
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_RL viscA4_D(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
84 |
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_RL hDiv(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
85 |
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_RL vort3(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
86 |
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_RL tension(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
87 |
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_RL strain(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
88 |
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_RL KE(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
89 |
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_RS hFacZ(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
90 |
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INTEGER myThid |
91 |
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LOGICAL harmonic,biharmonic,useVariableViscosity |
92 |
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93 |
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C == Local variables == |
94 |
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INTEGER I,J |
95 |
baylor |
1.5 |
_RL smag2fac, smag4fac |
96 |
baylor |
1.6 |
_RL viscAhRe_max, viscA4Re_max |
97 |
baylor |
1.13 |
_RL Alin,grdVrt,grdDiv |
98 |
baylor |
1.1 |
_RL recip_dt,L2,L3,L4,L5,L2rdt,L4rdt |
99 |
baylor |
1.5 |
_RL Uscl,U4scl |
100 |
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_RL viscAh_ZMax(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
101 |
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_RL viscAh_DMax(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
102 |
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_RL viscA4_ZMax(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
103 |
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_RL viscA4_DMax(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
104 |
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_RL viscAh_ZMin(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
105 |
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_RL viscAh_DMin(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
106 |
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_RL viscA4_ZMin(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
107 |
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_RL viscA4_DMin(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
108 |
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_RL viscAh_ZLth(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
109 |
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_RL viscAh_DLth(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
110 |
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_RL viscA4_ZLth(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
111 |
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_RL viscA4_DLth(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
112 |
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_RL viscAh_ZLthD(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
113 |
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_RL viscAh_DLthD(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
114 |
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_RL viscA4_ZLthD(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
115 |
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_RL viscA4_DLthD(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
116 |
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_RL viscAh_ZSmg(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
117 |
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_RL viscAh_DSmg(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
118 |
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_RL viscA4_ZSmg(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
119 |
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_RL viscA4_DSmg(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
120 |
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LOGICAL calcLeith,calcSmag |
121 |
baylor |
1.13 |
LOGICAL northWestCorner, northEastCorner, |
122 |
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& southWestCorner, southEastCorner |
123 |
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#ifdef ALLOW_EXCH2 |
124 |
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INTEGER myTile |
125 |
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#endif /* ALLOW_EXCH2 */ |
126 |
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127 |
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C Special stuff for Cubed Sphere |
128 |
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southWestCorner = .FALSE. |
129 |
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southEastCorner = .FALSE. |
130 |
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northWestCorner = .FALSE. |
131 |
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northEastCorner = .FALSE. |
132 |
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IF (useCubedSphereExchange) THEN |
133 |
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#ifdef ALLOW_EXCH2 |
134 |
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myTile = W2_myTileList(bi) |
135 |
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IF ( exch2_isWedge(myTile) .EQ. 1 .AND. |
136 |
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& exch2_isSedge(myTile) .EQ. 1 ) THEN |
137 |
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southWestCorner = .TRUE. |
138 |
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ENDIF |
139 |
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IF ( exch2_isEedge(myTile) .EQ. 1 .AND. |
140 |
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& exch2_isSedge(myTile) .EQ. 1 ) THEN |
141 |
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southEastCorner = .TRUE. |
142 |
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ENDIF |
143 |
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IF ( exch2_isEedge(myTile) .EQ. 1 .AND. |
144 |
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& exch2_isNedge(myTile) .EQ. 1 ) THEN |
145 |
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northEastCorner = .TRUE. |
146 |
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ENDIF |
147 |
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IF ( exch2_isWedge(myTile) .EQ. 1 .AND. |
148 |
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& exch2_isNedge(myTile) .EQ. 1 ) THEN |
149 |
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northWestCorner = .TRUE. |
150 |
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ENDIF |
151 |
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#else |
152 |
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southWestCorner = .TRUE. |
153 |
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southEastCorner = .TRUE. |
154 |
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northWestCorner = .TRUE. |
155 |
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northEastCorner = .TRUE. |
156 |
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#endif /* ALLOW_EXCH2 */ |
157 |
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ENDIF |
158 |
baylor |
1.1 |
|
159 |
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useVariableViscosity= |
160 |
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& (viscAhGrid.NE.0.) |
161 |
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& .OR.(viscA4Grid.NE.0.) |
162 |
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& .OR.(viscC2leith.NE.0.) |
163 |
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& .OR.(viscC2leithD.NE.0.) |
164 |
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& .OR.(viscC4leith.NE.0.) |
165 |
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& .OR.(viscC4leithD.NE.0.) |
166 |
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& .OR.(viscC2smag.NE.0.) |
167 |
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& .OR.(viscC4smag.NE.0.) |
168 |
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169 |
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harmonic= |
170 |
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& (viscAh.NE.0.) |
171 |
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& .OR.(viscAhD.NE.0.) |
172 |
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& .OR.(viscAhZ.NE.0.) |
173 |
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& .OR.(viscAhGrid.NE.0.) |
174 |
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& .OR.(viscC2leith.NE.0.) |
175 |
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& .OR.(viscC2leithD.NE.0.) |
176 |
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& .OR.(viscC2smag.NE.0.) |
177 |
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178 |
baylor |
1.9 |
IF ((harmonic).and.(viscAhremax.ne.0.)) THEN |
179 |
jmc |
1.10 |
viscAhre_max=sqrt(2. _d 0)/viscAhRemax |
180 |
baylor |
1.9 |
ELSE |
181 |
jmc |
1.10 |
viscAhre_max=0. _d 0 |
182 |
baylor |
1.9 |
ENDIF |
183 |
baylor |
1.5 |
|
184 |
baylor |
1.1 |
biharmonic= |
185 |
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& (viscA4.NE.0.) |
186 |
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& .OR.(viscA4D.NE.0.) |
187 |
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& .OR.(viscA4Z.NE.0.) |
188 |
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& .OR.(viscA4Grid.NE.0.) |
189 |
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& .OR.(viscC4leith.NE.0.) |
190 |
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& .OR.(viscC4leithD.NE.0.) |
191 |
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& .OR.(viscC4smag.NE.0.) |
192 |
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193 |
baylor |
1.9 |
IF ((biharmonic).and.(viscA4remax.ne.0.)) THEN |
194 |
jmc |
1.10 |
viscA4re_max=0.125 _d 0*sqrt(2. _d 0)/viscA4Remax |
195 |
baylor |
1.9 |
ELSE |
196 |
jmc |
1.10 |
viscA4re_max=0. _d 0 |
197 |
baylor |
1.9 |
ENDIF |
198 |
baylor |
1.5 |
|
199 |
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calcleith= |
200 |
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& (viscC2leith.NE.0.) |
201 |
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& .OR.(viscC2leithD.NE.0.) |
202 |
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& .OR.(viscC4leith.NE.0.) |
203 |
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& .OR.(viscC4leithD.NE.0.) |
204 |
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205 |
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calcsmag= |
206 |
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& (viscC2smag.NE.0.) |
207 |
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& .OR.(viscC4smag.NE.0.) |
208 |
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209 |
baylor |
1.1 |
IF (deltaTmom.NE.0.) THEN |
210 |
jmc |
1.10 |
recip_dt=1. _d 0/deltaTmom |
211 |
baylor |
1.1 |
ELSE |
212 |
jmc |
1.10 |
recip_dt=0. _d 0 |
213 |
baylor |
1.1 |
ENDIF |
214 |
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215 |
baylor |
1.5 |
IF (calcsmag) THEN |
216 |
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smag2fac=(viscC2smag/pi)**2 |
217 |
jmc |
1.10 |
smag4fac=0.125 _d 0*(viscC4smag/pi)**2 |
218 |
baylor |
1.9 |
ELSE |
219 |
jmc |
1.10 |
smag2fac=0. _d 0 |
220 |
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smag4fac=0. _d 0 |
221 |
baylor |
1.5 |
ENDIF |
222 |
baylor |
1.1 |
|
223 |
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C - Viscosity |
224 |
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IF (useVariableViscosity) THEN |
225 |
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DO j=2-Oly,sNy+Oly-1 |
226 |
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DO i=2-Olx,sNx+Olx-1 |
227 |
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CCCCCCCCCCCCCCC Divergence Point CalculationsCCCCCCCCCCCCCCCCCCCC |
228 |
baylor |
1.5 |
|
229 |
baylor |
1.1 |
C These are (powers of) length scales |
230 |
baylor |
1.11 |
IF (useAreaViscLength) THEN |
231 |
jmc |
1.12 |
L2=rA(i,j,bi,bj) |
232 |
baylor |
1.11 |
ELSE |
233 |
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L2=2. _d 0/((recip_DXF(I,J,bi,bj)**2+recip_DYF(I,J,bi,bj)**2)) |
234 |
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ENDIF |
235 |
baylor |
1.1 |
L3=(L2**1.5) |
236 |
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L4=(L2**2) |
237 |
baylor |
1.5 |
L5=(L2**2.5) |
238 |
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|
239 |
jmc |
1.10 |
L2rdt=0.25 _d 0*recip_dt*L2 |
240 |
baylor |
1.5 |
|
241 |
baylor |
1.11 |
IF (useAreaViscLength) THEN |
242 |
jmc |
1.12 |
L4rdt=0.125 _d 0*recip_dt*rA(i,j,bi,bj)**2 |
243 |
baylor |
1.11 |
ELSE |
244 |
|
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L4rdt=recip_dt/( 6. _d 0*(recip_DXF(I,J,bi,bj)**4 |
245 |
jmc |
1.10 |
& +recip_DYF(I,J,bi,bj)**4) |
246 |
|
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& +8. _d 0*((recip_DXF(I,J,bi,bj) |
247 |
|
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& *recip_DYF(I,J,bi,bj))**2) ) |
248 |
baylor |
1.11 |
ENDIF |
249 |
baylor |
1.1 |
|
250 |
baylor |
1.5 |
C Velocity Reynolds Scale |
251 |
baylor |
1.9 |
Uscl=sqrt(KE(i,j)*L2)*viscAhRe_max |
252 |
|
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U4scl=sqrt(KE(i,j))*L3*viscA4Re_max |
253 |
baylor |
1.5 |
|
254 |
|
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IF (useFullLeith.and.calcleith) THEN |
255 |
baylor |
1.1 |
C This is the vector magnitude of the vorticity gradient squared |
256 |
jmc |
1.10 |
grdVrt=0.25 _d 0*( |
257 |
baylor |
1.1 |
& ((vort3(i+1,j)-vort3(i,j))*recip_DXG(i,j,bi,bj))**2 |
258 |
|
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& +((vort3(i,j+1)-vort3(i,j))*recip_DYG(i,j,bi,bj))**2 |
259 |
baylor |
1.8 |
& +((vort3(i+1,j+1)-vort3(i,j+1)) |
260 |
|
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& *recip_DXG(i,j+1,bi,bj))**2 |
261 |
|
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& +((vort3(i+1,j+1)-vort3(i+1,j)) |
262 |
|
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& *recip_DYG(i+1,j,bi,bj))**2) |
263 |
baylor |
1.1 |
|
264 |
|
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C This is the vector magnitude of grad (div.v) squared |
265 |
|
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C Using it in Leith serves to damp instabilities in w. |
266 |
jmc |
1.10 |
grdDiv=0.25 _d 0*( |
267 |
baylor |
1.5 |
& ((hDiv(i+1,j)-hDiv(i,j))*recip_DXC(i+1,j,bi,bj))**2 |
268 |
|
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& +((hDiv(i,j+1)-hDiv(i,j))*recip_DYC(i,j+1,bi,bj))**2 |
269 |
|
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& +((hDiv(i,j)-hDiv(i-1,j))*recip_DXC(i,j,bi,bj))**2 |
270 |
|
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& +((hDiv(i,j)-hDiv(i,j-1))*recip_DYC(i,j,bi,bj))**2) |
271 |
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272 |
|
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viscAh_DLth(i,j)= |
273 |
|
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& sqrt(viscC2leith**2*grdVrt+viscC2leithD**2*grdDiv)*L3 |
274 |
jmc |
1.10 |
viscA4_DLth(i,j)=0.125 _d 0* |
275 |
baylor |
1.5 |
& sqrt(viscC4leith**2*grdVrt+viscC4leithD**2*grdDiv)*L5 |
276 |
|
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viscAh_DLthd(i,j)= |
277 |
|
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& sqrt(viscC2leithD**2*grdDiv)*L3 |
278 |
jmc |
1.10 |
viscA4_DLthd(i,j)=0.125 _d 0* |
279 |
baylor |
1.5 |
& sqrt(viscC4leithD**2*grdDiv)*L5 |
280 |
|
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ELSEIF (calcleith) THEN |
281 |
baylor |
1.1 |
C but this approximation will work on cube |
282 |
|
|
c (and differs by as much as 4X) |
283 |
baylor |
1.5 |
grdVrt=abs((vort3(i+1,j)-vort3(i,j))*recip_DXG(i,j,bi,bj)) |
284 |
|
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grdVrt=max(grdVrt, |
285 |
|
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& abs((vort3(i,j+1)-vort3(i,j))*recip_DYG(i,j,bi,bj))) |
286 |
|
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grdVrt=max(grdVrt, |
287 |
|
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& abs((vort3(i+1,j+1)-vort3(i,j+1))*recip_DXG(i,j+1,bi,bj))) |
288 |
|
|
grdVrt=max(grdVrt, |
289 |
|
|
& abs((vort3(i+1,j+1)-vort3(i+1,j))*recip_DYG(i+1,j,bi,bj))) |
290 |
|
|
|
291 |
|
|
grdDiv=abs((hDiv(i+1,j)-hDiv(i,j))*recip_DXC(i+1,j,bi,bj)) |
292 |
|
|
grdDiv=max(grdDiv, |
293 |
|
|
& abs((hDiv(i,j+1)-hDiv(i,j))*recip_DYC(i,j+1,bi,bj))) |
294 |
|
|
grdDiv=max(grdDiv, |
295 |
|
|
& abs((hDiv(i,j)-hDiv(i-1,j))*recip_DXC(i,j,bi,bj))) |
296 |
|
|
grdDiv=max(grdDiv, |
297 |
|
|
& abs((hDiv(i,j)-hDiv(i,j-1))*recip_DYC(i,j,bi,bj))) |
298 |
baylor |
1.1 |
|
299 |
|
|
c This approximation is good to the same order as above... |
300 |
baylor |
1.5 |
viscAh_Dlth(i,j)= |
301 |
|
|
& (viscC2leith*grdVrt+(viscC2leithD*grdDiv))*L3 |
302 |
jmc |
1.10 |
viscA4_Dlth(i,j)=0.125 _d 0* |
303 |
baylor |
1.5 |
& (viscC4leith*grdVrt+(viscC4leithD*grdDiv))*L5 |
304 |
|
|
viscAh_DlthD(i,j)= |
305 |
|
|
& ((viscC2leithD*grdDiv))*L3 |
306 |
jmc |
1.10 |
viscA4_DlthD(i,j)=0.125 _d 0* |
307 |
baylor |
1.5 |
& ((viscC4leithD*grdDiv))*L5 |
308 |
baylor |
1.1 |
ELSE |
309 |
jmc |
1.10 |
viscAh_Dlth(i,j)=0. _d 0 |
310 |
|
|
viscA4_Dlth(i,j)=0. _d 0 |
311 |
|
|
viscAh_DlthD(i,j)=0. _d 0 |
312 |
|
|
viscA4_DlthD(i,j)=0. _d 0 |
313 |
baylor |
1.1 |
ENDIF |
314 |
|
|
|
315 |
baylor |
1.5 |
IF (calcsmag) THEN |
316 |
|
|
viscAh_DSmg(i,j)=L2 |
317 |
|
|
& *sqrt(tension(i,j)**2 |
318 |
jmc |
1.10 |
& +0.25 _d 0*(strain(i+1, j )**2+strain( i ,j+1)**2 |
319 |
|
|
& +strain(i , j )**2+strain(i+1,j+1)**2)) |
320 |
baylor |
1.5 |
viscA4_DSmg(i,j)=smag4fac*L2*viscAh_DSmg(i,j) |
321 |
|
|
viscAh_DSmg(i,j)=smag2fac*viscAh_DSmg(i,j) |
322 |
baylor |
1.1 |
ELSE |
323 |
jmc |
1.10 |
viscAh_DSmg(i,j)=0. _d 0 |
324 |
|
|
viscA4_DSmg(i,j)=0. _d 0 |
325 |
baylor |
1.1 |
ENDIF |
326 |
|
|
|
327 |
|
|
C Harmonic on Div.u points |
328 |
baylor |
1.5 |
Alin=viscAhD+viscAhGrid*L2rdt |
329 |
|
|
& +viscAh_DLth(i,j)+viscAh_DSmg(i,j) |
330 |
|
|
viscAh_DMin(i,j)=max(viscAhGridMin*L2rdt,Uscl) |
331 |
|
|
viscAh_D(i,j)=max(viscAh_DMin(i,j),Alin) |
332 |
|
|
viscAh_DMax(i,j)=min(viscAhGridMax*L2rdt,viscAhMax) |
333 |
|
|
viscAh_D(i,j)=min(viscAh_DMax(i,j),viscAh_D(i,j)) |
334 |
baylor |
1.1 |
|
335 |
|
|
C BiHarmonic on Div.u points |
336 |
baylor |
1.5 |
Alin=viscA4D+viscA4Grid*L4rdt |
337 |
|
|
& +viscA4_DLth(i,j)+viscA4_DSmg(i,j) |
338 |
|
|
viscA4_DMin(i,j)=max(viscA4GridMin*L4rdt,U4scl) |
339 |
|
|
viscA4_D(i,j)=max(viscA4_DMin(i,j),Alin) |
340 |
|
|
viscA4_DMax(i,j)=min(viscA4GridMax*L4rdt,viscA4Max) |
341 |
|
|
viscA4_D(i,j)=min(viscA4_DMax(i,j),viscA4_D(i,j)) |
342 |
baylor |
1.1 |
|
343 |
|
|
CCCCCCCCCCCCC Vorticity Point CalculationsCCCCCCCCCCCCCCCCCC |
344 |
|
|
C These are (powers of) length scales |
345 |
baylor |
1.11 |
IF (useAreaViscLength) THEN |
346 |
jmc |
1.12 |
L2=rAz(i,j,bi,bj) |
347 |
baylor |
1.11 |
ELSE |
348 |
jmc |
1.12 |
L2=2. _d 0/((recip_DXV(I,J,bi,bj)**2+recip_DYU(I,J,bi,bj)**2)) |
349 |
baylor |
1.11 |
ENDIF |
350 |
|
|
|
351 |
baylor |
1.1 |
L3=(L2**1.5) |
352 |
|
|
L4=(L2**2) |
353 |
baylor |
1.5 |
L5=(L2**2.5) |
354 |
|
|
|
355 |
jmc |
1.10 |
L2rdt=0.25 _d 0*recip_dt*L2 |
356 |
baylor |
1.11 |
IF (useAreaViscLength) THEN |
357 |
baylor |
1.13 |
L4rdt=0.125 _d 0*recip_dt*RaZ(i,j,bi,bj)**2 |
358 |
baylor |
1.11 |
ELSE |
359 |
|
|
L4rdt=recip_dt/ |
360 |
|
|
& ( 6. _d 0*(recip_DXV(I,J,bi,bj)**4+recip_DYU(I,J,bi,bj)**4) |
361 |
|
|
& +8. _d 0*((recip_DXV(I,J,bi,bj)*recip_DYU(I,J,bi,bj))**2)) |
362 |
|
|
ENDIF |
363 |
baylor |
1.5 |
|
364 |
|
|
C Velocity Reynolds Scale |
365 |
jmc |
1.10 |
Uscl=sqrt(0.25 _d 0*(KE(i,j)+KE(i,j+1)+KE(i+1,j)+KE(i+1,j+1)) |
366 |
baylor |
1.9 |
& *L2)*viscAhRe_max |
367 |
jmc |
1.10 |
U4scl=sqrt(0.25 _d 0*(KE(i,j)+KE(i,j+1)+KE(i+1,j)+KE(i+1,j+1))) |
368 |
baylor |
1.9 |
& *L3*viscA4Re_max |
369 |
baylor |
1.1 |
|
370 |
|
|
C This is the vector magnitude of the vorticity gradient squared |
371 |
baylor |
1.5 |
IF (useFullLeith.and.calcleith) THEN |
372 |
jmc |
1.10 |
grdVrt=0.25 _d 0*( |
373 |
baylor |
1.5 |
& ((vort3(i+1,j)-vort3(i,j))*recip_DXG(i,j,bi,bj))**2 |
374 |
|
|
& +((vort3(i,j+1)-vort3(i,j))*recip_DYG(i,j,bi,bj))**2 |
375 |
|
|
& +((vort3(i-1,j)-vort3(i,j))*recip_DXG(i-1,j,bi,bj))**2 |
376 |
|
|
& +((vort3(i,j-1)-vort3(i,j))*recip_DYG(i,j-1,bi,bj))**2) |
377 |
baylor |
1.1 |
|
378 |
|
|
C This is the vector magnitude of grad(div.v) squared |
379 |
jmc |
1.10 |
grdDiv=0.25 _d 0*( |
380 |
baylor |
1.5 |
& ((hDiv(i,j)-hDiv(i-1,j))*recip_DXC(i,j,bi,bj))**2 |
381 |
|
|
& +((hDiv(i,j)-hDiv(i,j-1))*recip_DYC(i,j,bi,bj))**2 |
382 |
|
|
& +((hDiv(i,j-1)-hDiv(i-1,j-1))*recip_DXC(i,j-1,bi,bj))**2 |
383 |
|
|
& +((hDiv(i-1,j)-hDiv(i-1,j-1))*recip_DYC(i-1,j,bi,bj))**2) |
384 |
|
|
|
385 |
|
|
viscAh_ZLth(i,j)= |
386 |
|
|
& sqrt(viscC2leith**2*grdVrt+viscC2leithD**2*grdDiv)*L3 |
387 |
jmc |
1.10 |
viscA4_ZLth(i,j)=0.125 _d 0* |
388 |
baylor |
1.5 |
& sqrt(viscC4leith**2*grdVrt+viscC4leithD**2*grdDiv)*L5 |
389 |
|
|
viscAh_ZLthD(i,j)= |
390 |
|
|
& sqrt(viscC2leithD**2*grdDiv)*L3 |
391 |
jmc |
1.10 |
viscA4_ZLthD(i,j)=0.125 _d 0* |
392 |
baylor |
1.5 |
& sqrt(viscC4leithD**2*grdDiv)*L5 |
393 |
|
|
|
394 |
|
|
ELSEIF (calcleith) THEN |
395 |
baylor |
1.1 |
C but this approximation will work on cube (and differs by 4X) |
396 |
baylor |
1.5 |
grdVrt=abs((vort3(i+1,j)-vort3(i,j))*recip_DXG(i,j,bi,bj)) |
397 |
|
|
grdVrt=max(grdVrt, |
398 |
|
|
& abs((vort3(i,j+1)-vort3(i,j))*recip_DYG(i,j,bi,bj))) |
399 |
|
|
grdVrt=max(grdVrt, |
400 |
|
|
& abs((vort3(i-1,j)-vort3(i,j))*recip_DXG(i-1,j,bi,bj))) |
401 |
|
|
grdVrt=max(grdVrt, |
402 |
|
|
& abs((vort3(i,j-1)-vort3(i,j))*recip_DYG(i,j-1,bi,bj))) |
403 |
|
|
|
404 |
|
|
grdDiv=abs((hDiv(i,j)-hDiv(i-1,j))*recip_DXC(i,j,bi,bj)) |
405 |
|
|
grdDiv=max(grdDiv, |
406 |
|
|
& abs((hDiv(i,j)-hDiv(i,j-1))*recip_DYC(i,j,bi,bj))) |
407 |
|
|
grdDiv=max(grdDiv, |
408 |
jmc |
1.10 |
& abs((hDiv(i,j-1)-hDiv(i-1,j-1))*recip_DXC(i,j-1,bi,bj))) |
409 |
baylor |
1.5 |
grdDiv=max(grdDiv, |
410 |
jmc |
1.10 |
& abs((hDiv(i-1,j)-hDiv(i-1,j-1))*recip_DYC(i-1,j,bi,bj))) |
411 |
baylor |
1.5 |
|
412 |
|
|
viscAh_ZLth(i,j)=(viscC2leith*grdVrt |
413 |
|
|
& +(viscC2leithD*grdDiv))*L3 |
414 |
jmc |
1.10 |
viscA4_ZLth(i,j)=0.125 _d 0*(viscC4leith*grdVrt |
415 |
baylor |
1.5 |
& +(viscC4leithD*grdDiv))*L5 |
416 |
|
|
viscAh_ZLthD(i,j)=((viscC2leithD*grdDiv))*L3 |
417 |
jmc |
1.10 |
viscA4_ZLthD(i,j)=0.125 _d 0*((viscC4leithD*grdDiv))*L5 |
418 |
baylor |
1.1 |
ELSE |
419 |
jmc |
1.10 |
viscAh_ZLth(i,j)=0. _d 0 |
420 |
|
|
viscA4_ZLth(i,j)=0. _d 0 |
421 |
|
|
viscAh_ZLthD(i,j)=0. _d 0 |
422 |
|
|
viscA4_ZLthD(i,j)=0. _d 0 |
423 |
baylor |
1.1 |
ENDIF |
424 |
|
|
|
425 |
baylor |
1.5 |
IF (calcsmag) THEN |
426 |
|
|
viscAh_ZSmg(i,j)=L2 |
427 |
|
|
& *sqrt(strain(i,j)**2 |
428 |
jmc |
1.10 |
& +0.25 _d 0*(tension( i , j )**2+tension( i ,j-1)**2 |
429 |
|
|
& +tension(i-1, j )**2+tension(i-1,j-1)**2)) |
430 |
baylor |
1.5 |
viscA4_ZSmg(i,j)=smag4fac*L2*viscAh_ZSmg(i,j) |
431 |
|
|
viscAh_ZSmg(i,j)=smag2fac*viscAh_ZSmg(i,j) |
432 |
baylor |
1.1 |
ENDIF |
433 |
|
|
|
434 |
|
|
C Harmonic on Zeta points |
435 |
baylor |
1.5 |
Alin=viscAhZ+viscAhGrid*L2rdt |
436 |
|
|
& +viscAh_ZLth(i,j)+viscAh_ZSmg(i,j) |
437 |
|
|
viscAh_ZMin(i,j)=max(viscAhGridMin*L2rdt,Uscl) |
438 |
|
|
viscAh_Z(i,j)=max(viscAh_ZMin(i,j),Alin) |
439 |
|
|
viscAh_ZMax(i,j)=min(viscAhGridMax*L2rdt,viscAhMax) |
440 |
|
|
viscAh_Z(i,j)=min(viscAh_ZMax(i,j),viscAh_Z(i,j)) |
441 |
|
|
|
442 |
|
|
C BiHarmonic on Zeta points |
443 |
|
|
Alin=viscA4Z+viscA4Grid*L4rdt |
444 |
|
|
& +viscA4_ZLth(i,j)+viscA4_ZSmg(i,j) |
445 |
|
|
viscA4_ZMin(i,j)=max(viscA4GridMin*L4rdt,U4scl) |
446 |
|
|
viscA4_Z(i,j)=max(viscA4_ZMin(i,j),Alin) |
447 |
|
|
viscA4_ZMax(i,j)=min(viscA4GridMax*L4rdt,viscA4Max) |
448 |
|
|
viscA4_Z(i,j)=min(viscA4_ZMax(i,j),viscA4_Z(i,j)) |
449 |
baylor |
1.1 |
ENDDO |
450 |
|
|
ENDDO |
451 |
|
|
ELSE |
452 |
|
|
DO j=1-Oly,sNy+Oly |
453 |
|
|
DO i=1-Olx,sNx+Olx |
454 |
|
|
viscAh_D(i,j)=viscAhD |
455 |
|
|
viscAh_Z(i,j)=viscAhZ |
456 |
|
|
viscA4_D(i,j)=viscA4D |
457 |
|
|
viscA4_Z(i,j)=viscA4Z |
458 |
|
|
ENDDO |
459 |
|
|
ENDDO |
460 |
|
|
ENDIF |
461 |
|
|
|
462 |
|
|
#ifdef ALLOW_DIAGNOSTICS |
463 |
|
|
IF (useDiagnostics) THEN |
464 |
|
|
CALL DIAGNOSTICS_FILL(viscAh_D,'VISCAHD ',k,1,2,bi,bj,myThid) |
465 |
|
|
CALL DIAGNOSTICS_FILL(viscA4_D,'VISCA4D ',k,1,2,bi,bj,myThid) |
466 |
|
|
CALL DIAGNOSTICS_FILL(viscAh_Z,'VISCAHZ ',k,1,2,bi,bj,myThid) |
467 |
|
|
CALL DIAGNOSTICS_FILL(viscA4_Z,'VISCA4Z ',k,1,2,bi,bj,myThid) |
468 |
baylor |
1.5 |
|
469 |
|
|
CALL DIAGNOSTICS_FILL(viscAh_DMax,'VAHDMAX ',k,1,2,bi,bj,myThid) |
470 |
|
|
CALL DIAGNOSTICS_FILL(viscA4_DMax,'VA4DMAX ',k,1,2,bi,bj,myThid) |
471 |
|
|
CALL DIAGNOSTICS_FILL(viscAh_ZMax,'VAHZMAX ',k,1,2,bi,bj,myThid) |
472 |
|
|
CALL DIAGNOSTICS_FILL(viscA4_ZMax,'VA4ZMAX ',k,1,2,bi,bj,myThid) |
473 |
|
|
|
474 |
|
|
CALL DIAGNOSTICS_FILL(viscAh_DMin,'VAHDMIN ',k,1,2,bi,bj,myThid) |
475 |
|
|
CALL DIAGNOSTICS_FILL(viscA4_DMin,'VA4DMIN ',k,1,2,bi,bj,myThid) |
476 |
|
|
CALL DIAGNOSTICS_FILL(viscAh_ZMin,'VAHZMIN ',k,1,2,bi,bj,myThid) |
477 |
|
|
CALL DIAGNOSTICS_FILL(viscA4_ZMin,'VA4ZMIN ',k,1,2,bi,bj,myThid) |
478 |
|
|
|
479 |
|
|
CALL DIAGNOSTICS_FILL(viscAh_DLth,'VAHDLTH ',k,1,2,bi,bj,myThid) |
480 |
|
|
CALL DIAGNOSTICS_FILL(viscA4_DLth,'VA4DLTH ',k,1,2,bi,bj,myThid) |
481 |
|
|
CALL DIAGNOSTICS_FILL(viscAh_ZLth,'VAHZLTH ',k,1,2,bi,bj,myThid) |
482 |
|
|
CALL DIAGNOSTICS_FILL(viscA4_ZLth,'VA4ZLTH ',k,1,2,bi,bj,myThid) |
483 |
|
|
|
484 |
baylor |
1.7 |
CALL DIAGNOSTICS_FILL(viscAh_DLthD,'VAHDLTHD' |
485 |
baylor |
1.8 |
& ,k,1,2,bi,bj,myThid) |
486 |
baylor |
1.7 |
CALL DIAGNOSTICS_FILL(viscA4_DLthD,'VA4DLTHD' |
487 |
baylor |
1.8 |
& ,k,1,2,bi,bj,myThid) |
488 |
baylor |
1.7 |
CALL DIAGNOSTICS_FILL(viscAh_ZLthD,'VAHZLTHD' |
489 |
baylor |
1.8 |
& ,k,1,2,bi,bj,myThid) |
490 |
baylor |
1.7 |
CALL DIAGNOSTICS_FILL(viscA4_ZLthD,'VA4ZLTHD' |
491 |
baylor |
1.8 |
& ,k,1,2,bi,bj,myThid) |
492 |
baylor |
1.5 |
|
493 |
|
|
CALL DIAGNOSTICS_FILL(viscAh_DSmg,'VAHDSMAG',k,1,2,bi,bj,myThid) |
494 |
|
|
CALL DIAGNOSTICS_FILL(viscA4_DSmg,'VA4DSMAG',k,1,2,bi,bj,myThid) |
495 |
|
|
CALL DIAGNOSTICS_FILL(viscAh_ZSmg,'VAHZSMAG',k,1,2,bi,bj,myThid) |
496 |
|
|
CALL DIAGNOSTICS_FILL(viscA4_ZSmg,'VA4ZSMAG',k,1,2,bi,bj,myThid) |
497 |
baylor |
1.1 |
ENDIF |
498 |
|
|
#endif |
499 |
|
|
|
500 |
|
|
RETURN |
501 |
|
|
END |
502 |
baylor |
1.5 |
|