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C $Header: /u/gcmpack/MITgcm/pkg/mom_vecinv/mom_vi_hdissip.F,v 1.20 2005/03/23 18:21:06 adcroft Exp $ |
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C $Name: $ |
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|
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#include "MOM_VECINV_OPTIONS.h" |
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|
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SUBROUTINE MOM_VI_HDISSIP( |
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I bi,bj,k, |
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I hDiv,vort3,hFacZ,dStar,zStar, |
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O uDissip,vDissip, |
| 10 |
I myThid) |
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|
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cph( |
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cph The following line was commented in the argument list |
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cph TAMC cannot digest commented lines within continuing lines |
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c I viscAh_Z,viscAh_D,viscA4_Z,viscA4_D, |
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cph) |
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|
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IMPLICIT NONE |
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C |
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C Calculate horizontal dissipation terms |
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C [del^2 - del^4] (u,v) |
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C |
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|
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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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|
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C == Routine arguments == |
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INTEGER bi,bj,k |
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_RL hDiv(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL vort3(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RS hFacZ(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL dStar(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL zStar(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL uDissip(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL vDissip(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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INTEGER myThid |
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|
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C == Local variables == |
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_RL viscAh_Z(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL viscAh_D(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL viscA4_Z(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL viscA4_D(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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INTEGER I,J |
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_RL Zip,Zij,Zpj,Dim,Dij,Dmj,uD2,vD2,uD4,vD4 |
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_RL Alin,AlinMin,AlinMax,Alth2,Alth4,grdVrt,grdDiv |
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_RL vg2,vg2Min,vg2Max,vg4,vg4Min,vg4Max |
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_RL recip_dt,L2,L3,L4,L5 |
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LOGICAL useVariableViscosity |
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|
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useVariableViscosity= |
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& (viscAhGrid.NE.0.) |
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& .OR.(viscA4Grid.NE.0.) |
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& .OR.(viscC2leith.NE.0.) |
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& .OR.(viscC2leithD.NE.0.) |
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& .OR.(viscC4leith.NE.0.) |
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& .OR.(viscC4leithD.NE.0.) |
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|
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IF (deltaTmom.NE.0.) THEN |
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recip_dt=1./deltaTmom |
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ELSE |
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recip_dt=0. |
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ENDIF |
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|
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vg2=viscAhGrid*recip_dt |
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vg2Min=viscAhGridMin*recip_dt |
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vg2Max=viscAhGridMax*recip_dt |
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vg4=viscA4Grid*recip_dt |
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vg4Min=viscA4GridMin*recip_dt |
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vg4Max=viscA4GridMax*recip_dt |
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|
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C - Viscosity |
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IF (useVariableViscosity) THEN |
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DO j=2-Oly,sNy+Oly-1 |
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DO i=2-Olx,sNx+Olx-1 |
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C These are (powers of) length scales used in the Leith viscosity calculation |
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L2=rA(i,j,bi,bj) |
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L3=(L2**1.5) |
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L4=(L2**2) |
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L5=0.125*(L2**2.5) |
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|
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|
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IF (useFullLeith) THEN |
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C This is the vector magnitude of the vorticity gradient squared |
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grdVrt=0.25*( |
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& ((vort3(i+1,j)-vort3(i,j))*recip_DXG(i,j,bi,bj))**2 |
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& +((vort3(i,j+1)-vort3(i,j))*recip_DYG(i,j,bi,bj))**2 |
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& +((vort3(i+1,j+1)-vort3(i,j+1))*recip_DXG(i,j+1,bi,bj))**2 |
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& +((vort3(i+1,j+1)-vort3(i+1,j))*recip_DYG(i+1,j,bi,bj))**2) |
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|
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C This is the vector magnitude of grad (div.v) squared |
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C Using it in Leith serves to damp instabilities in w. |
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grdDiv=0.25*( |
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& ((hDiv(i+1,j)-hDiv(i,j))*recip_DXG(i,j,bi,bj))**2 |
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& +((hDiv(i,j+1)-hDiv(i,j))*recip_DYG(i,j,bi,bj))**2 |
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& +((hDiv(i-1,j)-hDiv(i,j))*recip_DXG(i-1,j,bi,bj))**2 |
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& +((hDiv(i,j-1)-hDiv(i,j))*recip_DYG(i,j-1,bi,bj))**2) |
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|
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Alth2=sqrt(viscC2leith**2*grdVrt+viscC2leithD**2*grdDiv)*L3 |
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Alth4=sqrt(viscC4leith**2*grdVrt+viscC4leithD**2*grdDiv)*L5 |
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ELSE |
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C but this approximation will work on cube |
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c (and differs by as much as 4X) |
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grdVrt=abs((vort3(i+1,j)-vort3(i,j))*recip_DXG(i,j,bi,bj)) |
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grdVrt=max(grdVrt, |
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& abs((vort3(i,j+1)-vort3(i,j))*recip_DYG(i,j,bi,bj))) |
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grdVrt=max(grdVrt, |
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& abs((vort3(i+1,j+1)-vort3(i,j+1))*recip_DXG(i,j+1,bi,bj))) |
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grdVrt=max(grdVrt, |
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& abs((vort3(i+1,j+1)-vort3(i+1,j))*recip_DYG(i+1,j,bi,bj))) |
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|
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grdDiv=abs((hDiv(i+1,j)-hDiv(i,j))*recip_DXG(i,j,bi,bj)) |
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grdDiv=max(grdDiv, |
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& abs((hDiv(i,j+1)-hDiv(i,j))*recip_DYG(i,j,bi,bj))) |
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grdDiv=max(grdDiv, |
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& abs((hDiv(i-1,j)-hDiv(i,j))*recip_DXG(i-1,j,bi,bj))) |
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grdDiv=max(grdDiv, |
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& abs((hDiv(i,j-1)-hDiv(i,j))*recip_DYG(i,j-1,bi,bj))) |
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|
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C This if statement is just to prevent bitwise changes when leithd=0 |
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IF ((viscC2leithd.eq.0).and.(viscc4leithd.eq.0)) THEN |
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Alth2=viscC2leith*grdVrt*L3 |
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Alth4=viscC4leith*grdVrt*L5 |
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ELSE |
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Alth2=sqrt(viscC2leith**2*grdVrt+viscC2leithD**2*grdDiv)*L3 |
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Alth4=sqrt(viscC4leith**2*grdVrt+viscC4leithD**2*grdDiv)*L5 |
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ENDIF |
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ENDIF |
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|
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C Harmonic Modified Leith on Div.u points |
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Alin=viscAhD+vg2*L2+Alth2 |
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viscAh_D(i,j)=min(viscAhMax,Alin) |
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IF (vg2Max.GT.0.) THEN |
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AlinMax=vg2Max*L2 |
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viscAh_D(i,j)=min(AlinMax,viscAh_D(i,j)) |
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ENDIF |
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AlinMin=vg2Min*L2 |
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viscAh_D(i,j)=max(AlinMin,viscAh_D(i,j)) |
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|
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C BiHarmonic Modified Leith on Div.u points |
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Alin=viscA4D+vg4*L4+Alth4 |
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viscA4_D(i,j)=min(viscA4Max,Alin) |
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IF (vg4Max.GT.0.) THEN |
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AlinMax=vg4Max*L4 |
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viscA4_D(i,j)=min(AlinMax,viscA4_D(i,j)) |
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ENDIF |
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AlinMin=vg4Min*L4 |
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viscA4_D(i,j)=max(AlinMin,viscA4_D(i,j)) |
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|
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C These are (powers of) length scales used in the Leith viscosity calculation |
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L2=rAz(i,j,bi,bj) |
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L3=(L2**1.5) |
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L4=(L2**2) |
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L5=0.125*(L2**2.5) |
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|
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C This is the vector magnitude of the vorticity gradient squared |
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IF (useFullLeith) THEN |
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grdVrt=0.25*( |
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& ((vort3(i+1,j)-vort3(i,j))*recip_DXG(i,j,bi,bj))**2 |
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& +((vort3(i,j+1)-vort3(i,j))*recip_DYG(i,j,bi,bj))**2 |
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& +((vort3(i-1,j)-vort3(i,j))*recip_DXG(i-1,j,bi,bj))**2 |
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& +((vort3(i,j-1)-vort3(i,j))*recip_DYG(i,j-1,bi,bj))**2) |
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|
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C This is the vector magnitude of grad(div.v) squared |
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grdDiv=0.25*( |
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& ((hDiv(i+1,j)-hDiv(i,j))*recip_DXG(i,j,bi,bj))**2 |
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& +((hDiv(i,j+1)-hDiv(i,j))*recip_DYG(i,j,bi,bj))**2 |
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& +((hDiv(i+1,j+1)-hDiv(i,j+1))*recip_DXG(i,j+1,bi,bj))**2 |
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& +((hDiv(i+1,j+1)-hDiv(i+1,j))*recip_DYG(i+1,j,bi,bj))**2) |
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|
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Alth2=sqrt(viscC2leith**2*grdVrt+viscC2leithD**2*grdDiv)*L3 |
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Alth4=sqrt(viscC4leith**2*grdVrt+viscC4leithD**2*grdDiv)*L5 |
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ELSE |
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C but this approximation will work on cube (and differs by as much as 4X) |
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grdVrt=abs((vort3(i+1,j)-vort3(i,j))*recip_DXG(i,j,bi,bj)) |
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grdVrt=max(grdVrt, |
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& abs((vort3(i,j+1)-vort3(i,j))*recip_DYG(i,j,bi,bj))) |
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grdVrt=max(grdVrt, |
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& abs((vort3(i-1,j)-vort3(i,j))*recip_DXG(i-1,j,bi,bj))) |
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grdVrt=max(grdVrt, |
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& abs((vort3(i,j-1)-vort3(i,j))*recip_DYG(i,j-1,bi,bj))) |
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|
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grdDiv=abs((hDiv(i+1,j)-hDiv(i,j))*recip_DXG(i,j,bi,bj)) |
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grdDiv=max(grdDiv, |
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& abs((hDiv(i,j+1)-hDiv(i,j))*recip_DYG(i,j,bi,bj))) |
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grdDiv=max(grdDiv, |
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& abs((hDiv(i+1,j+1)-hDiv(i,j+1))*recip_DXG(i-1,j,bi,bj))) |
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grdDiv=max(grdDiv, |
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& abs((hDiv(i+1,j+1)-hDiv(i+1,j))*recip_DYG(i,j-1,bi,bj))) |
| 192 |
|
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C This if statement is just to prevent bitwise changes when leithd=0 |
| 194 |
IF ((viscC2leithd.eq.0).and.(viscc4leithd.eq.0)) THEN |
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Alth2=viscC2leith*grdVrt*L3 |
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Alth4=viscC4leith*grdVrt*L5 |
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ELSE |
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Alth2=sqrt(viscC2leith**2*grdVrt+viscC2leithD**2*grdDiv)*L3 |
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Alth4=sqrt(viscC4leith**2*grdVrt+viscC4leithD**2*grdDiv)*L5 |
| 200 |
ENDIF |
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ENDIF |
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|
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C Harmonic Modified Leith on Zeta points |
| 204 |
Alin=viscAhZ+vg2*L2+Alth2 |
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viscAh_Z(i,j)=min(viscAhMax,Alin) |
| 206 |
IF (vg2Max.GT.0.) THEN |
| 207 |
AlinMax=vg2Max*L2 |
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viscAh_Z(i,j)=min(AlinMax,viscAh_Z(i,j)) |
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ENDIF |
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AlinMin=vg2Min*L2 |
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viscAh_Z(i,j)=max(AlinMin,viscAh_Z(i,j)) |
| 212 |
|
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C BiHarmonic Modified Leith on Zeta Points |
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Alin=viscA4Z+vg4*L4+Alth4 |
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viscA4_Z(i,j)=min(viscA4Max,Alin) |
| 216 |
IF (vg4Max.GT.0.) THEN |
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AlinMax=vg4Max*L4 |
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viscA4_Z(i,j)=min(AlinMax,viscA4_Z(i,j)) |
| 219 |
ENDIF |
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AlinMin=vg4Min*L4 |
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viscA4_Z(i,j)=max(AlinMin,viscA4_Z(i,j)) |
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ENDDO |
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ENDDO |
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ELSE |
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DO j=1-Oly,sNy+Oly |
| 226 |
DO i=1-Olx,sNx+Olx |
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viscAh_D(i,j)=viscAhD |
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viscAh_Z(i,j)=viscAhZ |
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viscA4_D(i,j)=viscA4D |
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viscA4_Z(i,j)=viscA4Z |
| 231 |
ENDDO |
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ENDDO |
| 233 |
ENDIF |
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|
| 235 |
C - Laplacian terms |
| 236 |
IF ( viscC2leith.NE.0. .OR. viscAhGrid.NE.0. |
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& .OR. viscAhD.NE.0. .OR. viscAhZ.NE.0. ) THEN |
| 238 |
DO j=2-Oly,sNy+Oly-1 |
| 239 |
DO i=2-Olx,sNx+Olx-1 |
| 240 |
|
| 241 |
Dim=hDiv( i ,j-1) |
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Dij=hDiv( i , j ) |
| 243 |
Dmj=hDiv(i-1, j ) |
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Zip=hFacZ( i ,j+1)*vort3( i ,j+1) |
| 245 |
Zij=hFacZ( i , j )*vort3( i , j ) |
| 246 |
Zpj=hFacZ(i+1, j )*vort3(i+1, j ) |
| 247 |
|
| 248 |
C This bit scales the harmonic dissipation operator to be proportional |
| 249 |
C to the grid-cell area over the time-step. viscAh is then non-dimensional |
| 250 |
C and should be less than 1/8, for example viscAh=0.01 |
| 251 |
IF (useVariableViscosity) THEN |
| 252 |
Dij=Dij*viscAh_D(i,j) |
| 253 |
Dim=Dim*viscAh_D(i,j-1) |
| 254 |
Dmj=Dmj*viscAh_D(i-1,j) |
| 255 |
Zij=Zij*viscAh_Z(i,j) |
| 256 |
Zip=Zip*viscAh_Z(i,j+1) |
| 257 |
Zpj=Zpj*viscAh_Z(i+1,j) |
| 258 |
uD2 = ( |
| 259 |
& cosFacU(j,bi,bj)*( Dij-Dmj )*recip_DXC(i,j,bi,bj) |
| 260 |
& -recip_hFacW(i,j,k,bi,bj)*( Zip-Zij )*recip_DYG(i,j,bi,bj) ) |
| 261 |
vD2 = ( |
| 262 |
& recip_hFacS(i,j,k,bi,bj)*( Zpj-Zij )*recip_DXG(i,j,bi,bj) |
| 263 |
& *cosFacV(j,bi,bj) |
| 264 |
& +( Dij-Dim )*recip_DYC(i,j,bi,bj) ) |
| 265 |
ELSE |
| 266 |
uD2 = viscAhD* |
| 267 |
& cosFacU(j,bi,bj)*( Dij-Dmj )*recip_DXC(i,j,bi,bj) |
| 268 |
& - viscAhZ*recip_hFacW(i,j,k,bi,bj)* |
| 269 |
& ( Zip-Zij )*recip_DYG(i,j,bi,bj) |
| 270 |
vD2 = viscAhZ*recip_hFacS(i,j,k,bi,bj)* |
| 271 |
& cosFacV(j,bi,bj)*( Zpj-Zij )*recip_DXG(i,j,bi,bj) |
| 272 |
& + viscAhD* ( Dij-Dim )*recip_DYC(i,j,bi,bj) |
| 273 |
ENDIF |
| 274 |
|
| 275 |
uDissip(i,j) = uD2 |
| 276 |
vDissip(i,j) = vD2 |
| 277 |
|
| 278 |
ENDDO |
| 279 |
ENDDO |
| 280 |
ELSE |
| 281 |
DO j=2-Oly,sNy+Oly-1 |
| 282 |
DO i=2-Olx,sNx+Olx-1 |
| 283 |
uDissip(i,j) = 0. |
| 284 |
vDissip(i,j) = 0. |
| 285 |
ENDDO |
| 286 |
ENDDO |
| 287 |
ENDIF |
| 288 |
|
| 289 |
C - Bi-harmonic terms |
| 290 |
IF ( viscC4leith.NE.0. .OR. viscA4Grid.NE.0. |
| 291 |
& .OR. viscA4D.NE.0. .OR. viscA4Z.NE.0. ) THEN |
| 292 |
DO j=2-Oly,sNy+Oly-1 |
| 293 |
DO i=2-Olx,sNx+Olx-1 |
| 294 |
|
| 295 |
#ifdef MOM_VI_ORIGINAL_VISCA4 |
| 296 |
Dim=dyF( i ,j-1,bi,bj)*dStar( i ,j-1) |
| 297 |
Dij=dyF( i , j ,bi,bj)*dStar( i , j ) |
| 298 |
Dmj=dyF(i-1, j ,bi,bj)*dStar(i-1, j ) |
| 299 |
|
| 300 |
Zip=dxV( i ,j+1,bi,bj)*hFacZ( i ,j+1)*zStar( i ,j+1) |
| 301 |
Zij=dxV( i , j ,bi,bj)*hFacZ( i , j )*zStar( i , j ) |
| 302 |
Zpj=dxV(i+1, j ,bi,bj)*hFacZ(i+1, j )*zStar(i+1, j ) |
| 303 |
#else |
| 304 |
Dim=dStar( i ,j-1) |
| 305 |
Dij=dStar( i , j ) |
| 306 |
Dmj=dStar(i-1, j ) |
| 307 |
|
| 308 |
Zip=hFacZ( i ,j+1)*zStar( i ,j+1) |
| 309 |
Zij=hFacZ( i , j )*zStar( i , j ) |
| 310 |
Zpj=hFacZ(i+1, j )*zStar(i+1, j ) |
| 311 |
#endif |
| 312 |
|
| 313 |
C This bit scales the harmonic dissipation operator to be proportional |
| 314 |
C to the grid-cell area over the time-step. viscAh is then non-dimensional |
| 315 |
C and should be less than 1/8, for example viscAh=0.01 |
| 316 |
IF (useVariableViscosity) THEN |
| 317 |
Dij=Dij*viscA4_D(i,j) |
| 318 |
Dim=Dim*viscA4_D(i,j-1) |
| 319 |
Dmj=Dmj*viscA4_D(i-1,j) |
| 320 |
Zij=Zij*viscA4_Z(i,j) |
| 321 |
Zip=Zip*viscA4_Z(i,j+1) |
| 322 |
Zpj=Zpj*viscA4_Z(i+1,j) |
| 323 |
|
| 324 |
#ifdef MOM_VI_ORIGINAL_VISCA4 |
| 325 |
uD4 = recip_rAw(i,j,bi,bj)*( |
| 326 |
& ( (Dij-Dmj)*cosFacU(j,bi,bj) ) |
| 327 |
& -recip_hFacW(i,j,k,bi,bj)*( Zip-Zij ) ) |
| 328 |
vD4 = recip_rAs(i,j,bi,bj)*( |
| 329 |
& recip_hFacS(i,j,k,bi,bj)*( (Zpj-Zij)*cosFacV(j,bi,bj) ) |
| 330 |
& + ( Dij-Dim ) ) |
| 331 |
ELSE |
| 332 |
uD4 = recip_rAw(i,j,bi,bj)*( |
| 333 |
& viscA4*( (Dij-Dmj)*cosFacU(j,bi,bj) ) |
| 334 |
& -recip_hFacW(i,j,k,bi,bj)*viscA4*( Zip-Zij ) ) |
| 335 |
vD4 = recip_rAs(i,j,bi,bj)*( |
| 336 |
& recip_hFacS(i,j,k,bi,bj)*viscA4*( (Zpj-Zij)*cosFacV(j,bi,bj) ) |
| 337 |
& + viscA4*( Dij-Dim ) ) |
| 338 |
#else /* MOM_VI_ORIGINAL_VISCA4 */ |
| 339 |
uD4 = ( |
| 340 |
& cosFacU(j,bi,bj)*( Dij-Dmj )*recip_DXC(i,j,bi,bj) |
| 341 |
& -recip_hFacW(i,j,k,bi,bj)*( Zip-Zij )*recip_DYG(i,j,bi,bj) ) |
| 342 |
vD4 = ( |
| 343 |
& recip_hFacS(i,j,k,bi,bj)*( Zpj-Zij )*recip_DXG(i,j,bi,bj) |
| 344 |
& *cosFacV(j,bi,bj) |
| 345 |
& +( Dij-Dim )*recip_DYC(i,j,bi,bj) ) |
| 346 |
ELSE |
| 347 |
uD4 = viscA4D* |
| 348 |
& cosFacU(j,bi,bj)*( Dij-Dmj )*recip_DXC(i,j,bi,bj) |
| 349 |
& - viscA4Z*recip_hFacW(i,j,k,bi,bj)* |
| 350 |
& ( Zip-Zij )*recip_DYG(i,j,bi,bj) |
| 351 |
vD4 = viscA4Z*recip_hFacS(i,j,k,bi,bj)* |
| 352 |
& cosFacV(j,bi,bj)*( Zpj-Zij )*recip_DXG(i,j,bi,bj) |
| 353 |
& + viscA4D* ( Dij-Dim )*recip_DYC(i,j,bi,bj) |
| 354 |
#endif /* MOM_VI_ORIGINAL_VISCA4 */ |
| 355 |
ENDIF |
| 356 |
|
| 357 |
uDissip(i,j) = uDissip(i,j) - uD4 |
| 358 |
vDissip(i,j) = vDissip(i,j) - vD4 |
| 359 |
|
| 360 |
ENDDO |
| 361 |
ENDDO |
| 362 |
ENDIF |
| 363 |
|
| 364 |
#ifdef ALLOW_DIAGNOSTICS |
| 365 |
IF (useDiagnostics) THEN |
| 366 |
CALL DIAGNOSTICS_FILL(viscAh_D,'VISCAH ',k,1,2,bi,bj,myThid) |
| 367 |
CALL DIAGNOSTICS_FILL(viscA4_D,'VISCA4 ',k,1,2,bi,bj,myThid) |
| 368 |
ENDIF |
| 369 |
#endif |
| 370 |
|
| 371 |
RETURN |
| 372 |
END |
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