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C $Header: /u/gcmpack/MITgcm/pkg/mom_vecinv/mom_vi_hdissip.F,v 1.24 2005/04/03 15:58:51 heimbach 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, |
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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,L2rdt,L4rdt |
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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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IF (useAnisotropicViscAGridMax) THEN |
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L2rdt=recip_dt/( 2.*(recip_DXF(I,J,bi,bj)**2 |
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& +recip_DYF(I,J,bi,bj)**2) ) |
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L4rdt=recip_dt/( 6.*(recip_DXF(I,J,bi,bj)**4 |
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& +recip_DYF(I,J,bi,bj)**4) |
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& +8.*((recip_DXF(I,J,bi,bj) |
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& *recip_DYF(I,J,bi,bj))**2) ) |
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ENDIF |
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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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IF ( (viscC2leith**2*grdVrt+viscC2leithD**2*grdDiv) |
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& .NE. 0. ) THEN |
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Alth2=sqrt(viscC2leith**2*grdVrt+viscC2leithD**2*grdDiv)*L3 |
111 |
ELSE |
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Alth2=0. _d 0 |
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ENDIF |
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IF ( (viscC4leith**2*grdVrt+viscC4leithD**2*grdDiv) |
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& .NE. 0. ) THEN |
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Alth4=sqrt(viscC4leith**2*grdVrt+viscC4leithD**2*grdDiv)*L5 |
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ELSE |
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Alth4=0. _d 0 |
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ENDIF |
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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 approximation is good to the same order as above... |
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Alth2=(viscC2leith*grdVrt+(viscC2leithD*grdDiv))*L3 |
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Alth4=(viscC4leith*grdVrt+(viscC4leithD*grdDiv))*L5 |
142 |
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 (useAnisotropicViscAGridMax) THEN |
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AlinMax=viscAhGridMax*L2rdt |
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viscAh_D(i,j)=min(AlinMax,viscAh_D(i,j)) |
150 |
ELSE |
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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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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 (useAnisotropicViscAGridMax) THEN |
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AlinMax=viscA4GridMax*L4rdt |
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viscA4_D(i,j)=min(AlinMax,viscA4_D(i,j)) |
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ELSE |
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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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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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IF (useAnisotropicViscAGridMax) THEN |
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L2rdt=recip_dt/( 2.*(recip_DXV(I,J,bi,bj)**2 |
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& +recip_DYU(I,J,bi,bj)**2) ) |
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L4rdt=recip_dt/( 6.*(recip_DXV(I,J,bi,bj)**4 |
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& +recip_DYU(I,J,bi,bj)**4) |
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& +8.*((recip_DXV(I,J,bi,bj) |
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& *recip_DYU(I,J,bi,bj))**2) ) |
186 |
ENDIF |
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|
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C This is the vector magnitude of the vorticity gradient squared |
189 |
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) |
195 |
|
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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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|
203 |
IF ( (viscC2leith**2*grdVrt+viscC2leithD**2*grdDiv) |
204 |
& .NE. 0. ) THEN |
205 |
Alth2=sqrt(viscC2leith**2*grdVrt+viscC2leithD**2*grdDiv)*L3 |
206 |
ELSE |
207 |
Alth2=0. _d 0 |
208 |
ENDIF |
209 |
IF ( (viscC4leith**2*grdVrt+viscC4leithD**2*grdDiv) |
210 |
& .NE. 0. ) THEN |
211 |
Alth4=sqrt(viscC4leith**2*grdVrt+viscC4leithD**2*grdDiv)*L5 |
212 |
ELSE |
213 |
Alth4=0. _d 0 |
214 |
ENDIF |
215 |
ELSE |
216 |
C but this approximation will work on cube (and differs by as much as 4X) |
217 |
grdVrt=abs((vort3(i+1,j)-vort3(i,j))*recip_DXG(i,j,bi,bj)) |
218 |
grdVrt=max(grdVrt, |
219 |
& abs((vort3(i,j+1)-vort3(i,j))*recip_DYG(i,j,bi,bj))) |
220 |
grdVrt=max(grdVrt, |
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& abs((vort3(i-1,j)-vort3(i,j))*recip_DXG(i-1,j,bi,bj))) |
222 |
grdVrt=max(grdVrt, |
223 |
& abs((vort3(i,j-1)-vort3(i,j))*recip_DYG(i,j-1,bi,bj))) |
224 |
|
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grdDiv=abs((hDiv(i+1,j)-hDiv(i,j))*recip_DXG(i,j,bi,bj)) |
226 |
grdDiv=max(grdDiv, |
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& abs((hDiv(i,j+1)-hDiv(i,j))*recip_DYG(i,j,bi,bj))) |
228 |
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))) |
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|
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C This if statement is just to prevent bitwise changes when leithd=0 |
234 |
Alth2=(viscC2leith*grdVrt+(viscC2leithD*grdDiv))*L3 |
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Alth4=(viscC4leith*grdVrt+(viscC4leithD*grdDiv))*L5 |
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ENDIF |
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|
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C Harmonic Modified Leith on Zeta points |
239 |
Alin=viscAhZ+vg2*L2+Alth2 |
240 |
viscAh_Z(i,j)=min(viscAhMax,Alin) |
241 |
IF (useAnisotropicViscAGridMax) THEN |
242 |
AlinMax=viscAhGridMax*L2rdt |
243 |
viscAh_Z(i,j)=min(AlinMax,viscAh_Z(i,j)) |
244 |
ELSE |
245 |
IF (vg2Max.GT.0.) THEN |
246 |
AlinMax=vg2Max*L2 |
247 |
viscAh_Z(i,j)=min(AlinMax,viscAh_Z(i,j)) |
248 |
ENDIF |
249 |
ENDIF |
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AlinMin=vg2Min*L2 |
251 |
viscAh_Z(i,j)=max(AlinMin,viscAh_Z(i,j)) |
252 |
|
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C BiHarmonic Modified Leith on Zeta Points |
254 |
Alin=viscA4Z+vg4*L4+Alth4 |
255 |
viscA4_Z(i,j)=min(viscA4Max,Alin) |
256 |
IF (useAnisotropicViscAGridMax) THEN |
257 |
AlinMax=viscA4GridMax*L4rdt |
258 |
viscA4_Z(i,j)=min(AlinMax,viscA4_Z(i,j)) |
259 |
ELSE |
260 |
IF (vg4Max.GT.0.) THEN |
261 |
AlinMax=vg4Max*L4 |
262 |
viscA4_Z(i,j)=min(AlinMax,viscA4_Z(i,j)) |
263 |
ENDIF |
264 |
ENDIF |
265 |
AlinMin=vg4Min*L4 |
266 |
viscA4_Z(i,j)=max(AlinMin,viscA4_Z(i,j)) |
267 |
ENDDO |
268 |
ENDDO |
269 |
ELSE |
270 |
DO j=1-Oly,sNy+Oly |
271 |
DO i=1-Olx,sNx+Olx |
272 |
viscAh_D(i,j)=viscAhD |
273 |
viscAh_Z(i,j)=viscAhZ |
274 |
viscA4_D(i,j)=viscA4D |
275 |
viscA4_Z(i,j)=viscA4Z |
276 |
ENDDO |
277 |
ENDDO |
278 |
ENDIF |
279 |
|
280 |
C - Laplacian terms |
281 |
IF ( viscC2leith.NE.0. .OR. viscAhGrid.NE.0. |
282 |
& .OR. viscAhD.NE.0. .OR. viscAhZ.NE.0. ) THEN |
283 |
DO j=2-Oly,sNy+Oly-1 |
284 |
DO i=2-Olx,sNx+Olx-1 |
285 |
|
286 |
Dim=hDiv( i ,j-1) |
287 |
Dij=hDiv( i , j ) |
288 |
Dmj=hDiv(i-1, j ) |
289 |
Zip=hFacZ( i ,j+1)*vort3( i ,j+1) |
290 |
Zij=hFacZ( i , j )*vort3( i , j ) |
291 |
Zpj=hFacZ(i+1, j )*vort3(i+1, j ) |
292 |
|
293 |
C This bit scales the harmonic dissipation operator to be proportional |
294 |
C to the grid-cell area over the time-step. viscAh is then non-dimensional |
295 |
C and should be less than 1/8, for example viscAh=0.01 |
296 |
IF (useVariableViscosity) THEN |
297 |
Dij=Dij*viscAh_D(i,j) |
298 |
Dim=Dim*viscAh_D(i,j-1) |
299 |
Dmj=Dmj*viscAh_D(i-1,j) |
300 |
Zij=Zij*viscAh_Z(i,j) |
301 |
Zip=Zip*viscAh_Z(i,j+1) |
302 |
Zpj=Zpj*viscAh_Z(i+1,j) |
303 |
uD2 = ( |
304 |
& cosFacU(j,bi,bj)*( Dij-Dmj )*recip_DXC(i,j,bi,bj) |
305 |
& -recip_hFacW(i,j,k,bi,bj)*( Zip-Zij )*recip_DYG(i,j,bi,bj) ) |
306 |
vD2 = ( |
307 |
& recip_hFacS(i,j,k,bi,bj)*( Zpj-Zij )*recip_DXG(i,j,bi,bj) |
308 |
& *cosFacV(j,bi,bj) |
309 |
& +( Dij-Dim )*recip_DYC(i,j,bi,bj) ) |
310 |
ELSE |
311 |
uD2 = viscAhD* |
312 |
& cosFacU(j,bi,bj)*( Dij-Dmj )*recip_DXC(i,j,bi,bj) |
313 |
& - viscAhZ*recip_hFacW(i,j,k,bi,bj)* |
314 |
& ( Zip-Zij )*recip_DYG(i,j,bi,bj) |
315 |
vD2 = viscAhZ*recip_hFacS(i,j,k,bi,bj)* |
316 |
& cosFacV(j,bi,bj)*( Zpj-Zij )*recip_DXG(i,j,bi,bj) |
317 |
& + viscAhD* ( Dij-Dim )*recip_DYC(i,j,bi,bj) |
318 |
ENDIF |
319 |
|
320 |
uDissip(i,j) = uD2 |
321 |
vDissip(i,j) = vD2 |
322 |
|
323 |
ENDDO |
324 |
ENDDO |
325 |
ELSE |
326 |
DO j=2-Oly,sNy+Oly-1 |
327 |
DO i=2-Olx,sNx+Olx-1 |
328 |
uDissip(i,j) = 0. |
329 |
vDissip(i,j) = 0. |
330 |
ENDDO |
331 |
ENDDO |
332 |
ENDIF |
333 |
|
334 |
C - Bi-harmonic terms |
335 |
IF ( viscC4leith.NE.0. .OR. viscA4Grid.NE.0. |
336 |
& .OR. viscA4D.NE.0. .OR. viscA4Z.NE.0. ) THEN |
337 |
DO j=2-Oly,sNy+Oly-1 |
338 |
DO i=2-Olx,sNx+Olx-1 |
339 |
|
340 |
#ifdef MOM_VI_ORIGINAL_VISCA4 |
341 |
Dim=dyF( i ,j-1,bi,bj)*dStar( i ,j-1) |
342 |
Dij=dyF( i , j ,bi,bj)*dStar( i , j ) |
343 |
Dmj=dyF(i-1, j ,bi,bj)*dStar(i-1, j ) |
344 |
|
345 |
Zip=dxV( i ,j+1,bi,bj)*hFacZ( i ,j+1)*zStar( i ,j+1) |
346 |
Zij=dxV( i , j ,bi,bj)*hFacZ( i , j )*zStar( i , j ) |
347 |
Zpj=dxV(i+1, j ,bi,bj)*hFacZ(i+1, j )*zStar(i+1, j ) |
348 |
#else |
349 |
Dim=dStar( i ,j-1) |
350 |
Dij=dStar( i , j ) |
351 |
Dmj=dStar(i-1, j ) |
352 |
|
353 |
Zip=hFacZ( i ,j+1)*zStar( i ,j+1) |
354 |
Zij=hFacZ( i , j )*zStar( i , j ) |
355 |
Zpj=hFacZ(i+1, j )*zStar(i+1, j ) |
356 |
#endif |
357 |
|
358 |
C This bit scales the harmonic dissipation operator to be proportional |
359 |
C to the grid-cell area over the time-step. viscAh is then non-dimensional |
360 |
C and should be less than 1/8, for example viscAh=0.01 |
361 |
IF (useVariableViscosity) THEN |
362 |
Dij=Dij*viscA4_D(i,j) |
363 |
Dim=Dim*viscA4_D(i,j-1) |
364 |
Dmj=Dmj*viscA4_D(i-1,j) |
365 |
Zij=Zij*viscA4_Z(i,j) |
366 |
Zip=Zip*viscA4_Z(i,j+1) |
367 |
Zpj=Zpj*viscA4_Z(i+1,j) |
368 |
|
369 |
#ifdef MOM_VI_ORIGINAL_VISCA4 |
370 |
uD4 = recip_rAw(i,j,bi,bj)*( |
371 |
& ( (Dij-Dmj)*cosFacU(j,bi,bj) ) |
372 |
& -recip_hFacW(i,j,k,bi,bj)*( Zip-Zij ) ) |
373 |
vD4 = recip_rAs(i,j,bi,bj)*( |
374 |
& recip_hFacS(i,j,k,bi,bj)*( (Zpj-Zij)*cosFacV(j,bi,bj) ) |
375 |
& + ( Dij-Dim ) ) |
376 |
ELSE |
377 |
uD4 = recip_rAw(i,j,bi,bj)*( |
378 |
& viscA4*( (Dij-Dmj)*cosFacU(j,bi,bj) ) |
379 |
& -recip_hFacW(i,j,k,bi,bj)*viscA4*( Zip-Zij ) ) |
380 |
vD4 = recip_rAs(i,j,bi,bj)*( |
381 |
& recip_hFacS(i,j,k,bi,bj)*viscA4*( (Zpj-Zij)*cosFacV(j,bi,bj) ) |
382 |
& + viscA4*( Dij-Dim ) ) |
383 |
#else /* MOM_VI_ORIGINAL_VISCA4 */ |
384 |
uD4 = ( |
385 |
& cosFacU(j,bi,bj)*( Dij-Dmj )*recip_DXC(i,j,bi,bj) |
386 |
& -recip_hFacW(i,j,k,bi,bj)*( Zip-Zij )*recip_DYG(i,j,bi,bj) ) |
387 |
vD4 = ( |
388 |
& recip_hFacS(i,j,k,bi,bj)*( Zpj-Zij )*recip_DXG(i,j,bi,bj) |
389 |
& *cosFacV(j,bi,bj) |
390 |
& +( Dij-Dim )*recip_DYC(i,j,bi,bj) ) |
391 |
ELSE |
392 |
uD4 = viscA4D* |
393 |
& cosFacU(j,bi,bj)*( Dij-Dmj )*recip_DXC(i,j,bi,bj) |
394 |
& - viscA4Z*recip_hFacW(i,j,k,bi,bj)* |
395 |
& ( Zip-Zij )*recip_DYG(i,j,bi,bj) |
396 |
vD4 = viscA4Z*recip_hFacS(i,j,k,bi,bj)* |
397 |
& cosFacV(j,bi,bj)*( Zpj-Zij )*recip_DXG(i,j,bi,bj) |
398 |
& + viscA4D* ( Dij-Dim )*recip_DYC(i,j,bi,bj) |
399 |
#endif /* MOM_VI_ORIGINAL_VISCA4 */ |
400 |
ENDIF |
401 |
|
402 |
uDissip(i,j) = uDissip(i,j) - uD4 |
403 |
vDissip(i,j) = vDissip(i,j) - vD4 |
404 |
|
405 |
ENDDO |
406 |
ENDDO |
407 |
ENDIF |
408 |
|
409 |
#ifdef ALLOW_DIAGNOSTICS |
410 |
IF (useDiagnostics) THEN |
411 |
CALL DIAGNOSTICS_FILL(viscAh_D,'VISCAH ',k,1,2,bi,bj,myThid) |
412 |
CALL DIAGNOSTICS_FILL(viscA4_D,'VISCA4 ',k,1,2,bi,bj,myThid) |
413 |
ENDIF |
414 |
#endif |
415 |
|
416 |
RETURN |
417 |
END |