C $Header: /home/ubuntu/mnt/e9_copy/MITgcm/pkg/mom_common/mom_calc_visc.F,v 1.10 2005/09/22 00:21:23 jmc Exp $ C $Name: $ #include "MOM_COMMON_OPTIONS.h" SUBROUTINE MOM_CALC_VISC( I bi,bj,k, O viscAh_Z,viscAh_D,viscA4_Z,viscA4_D, O harmonic,biharmonic,useVariableViscosity, I hDiv,vort3,tension,strain,KE,hfacZ, I myThid) IMPLICIT NONE C C Calculate horizontal viscosities (L is typical grid width) C harmonic viscosity= C viscAh (or viscAhD on div pts and viscAhZ on zeta pts) C +0.25*L**2*viscAhGrid/deltaT C +sqrt(viscC2leith**2*grad(Vort3)**2 C +viscC2leithD**2*grad(hDiv)**2)*L**3 C +(viscC2smag/pi)**2*L**2*sqrt(Tension**2+Strain**2) C C biharmonic viscosity= C viscA4 (or viscA4D on div pts and viscA4Z on zeta pts) C +0.25*0.125*L**4*viscA4Grid/deltaT (approx) C +0.125*L**5*sqrt(viscC4leith**2*grad(Vort3)**2 C +viscC4leithD**2*grad(hDiv)**2) C +0.125*L**4*(viscC4smag/pi)**2*sqrt(Tension**2+Strain**2) C C Note that often 0.125*L**2 is the scale between harmonic and C biharmonic (see Griffies and Hallberg (2000)) C This allows the same value of the coefficient to be used C for roughly similar results with biharmonic and harmonic C C LIMITERS -- limit min and max values of viscosities C viscAhRemax is min value for grid point harmonic Reynolds num C harmonic viscosity>sqrt(2*KE)*L/viscAhRemax C C viscA4Remax is min value for grid point biharmonic Reynolds num C biharmonic viscosity>sqrt(2*KE)*L**3/8/viscA4Remax C C viscAhgridmax is CFL stability limiter for harmonic viscosity C harmonic viscosity<0.25*viscAhgridmax*L**2/deltaT C C viscA4gridmax is CFL stability limiter for biharmonic viscosity C biharmonic viscosity0.25*viscAhgridmax*L**2/deltaT C biharmonic viscosity>viscA4gridmax*L**4/32/deltaT (approx) C C RECOMMENDED VALUES C viscC2Leith=? C viscC2LeithD=? C viscC4Leith=? C viscC4LeithD=? C viscC2smag=2.2-4 (Griffies and Hallberg,2000) C 0.2-0.9 (Smagorinsky,1993) C viscC4smag=2.2-4 (Griffies and Hallberg,2000) C viscAhRemax>=1, (<2 suppresses a computational mode) C viscA4Remax>=1, (<2 suppresses a computational mode) C viscAhgridmax=1 C viscA4gridmax=1 C viscAhgrid<1 C viscA4grid<1 C viscAhgridmin<<1 C viscA4gridmin<<1 C == Global variables == #include "SIZE.h" #include "GRID.h" #include "EEPARAMS.h" #include "PARAMS.h" C == Routine arguments == INTEGER bi,bj,k _RL viscAh_Z(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL viscAh_D(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL viscA4_Z(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL viscA4_D(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL hDiv(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL vort3(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL tension(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL strain(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL KE(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RS hFacZ(1-OLx:sNx+OLx,1-OLy:sNy+OLy) INTEGER myThid LOGICAL harmonic,biharmonic,useVariableViscosity C == Local variables == INTEGER I,J _RL smag2fac, smag4fac _RL viscAhRe_max, viscA4Re_max _RL Alin,Alinmin,grdVrt,grdDiv _RL recip_dt,L2,L3,L4,L5,L2rdt,L4rdt _RL Uscl,U4scl _RL viscAh_ZMax(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL viscAh_DMax(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL viscA4_ZMax(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL viscA4_DMax(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL viscAh_ZMin(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL viscAh_DMin(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL viscA4_ZMin(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL viscA4_DMin(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL viscAh_ZLth(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL viscAh_DLth(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL viscA4_ZLth(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL viscA4_DLth(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL viscAh_ZLthD(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL viscAh_DLthD(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL viscA4_ZLthD(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL viscA4_DLthD(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL viscAh_ZSmg(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL viscAh_DSmg(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL viscA4_ZSmg(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL viscA4_DSmg(1-OLx:sNx+OLx,1-OLy:sNy+OLy) LOGICAL calcLeith,calcSmag useVariableViscosity= & (viscAhGrid.NE.0.) & .OR.(viscA4Grid.NE.0.) & .OR.(viscC2leith.NE.0.) & .OR.(viscC2leithD.NE.0.) & .OR.(viscC4leith.NE.0.) & .OR.(viscC4leithD.NE.0.) & .OR.(viscC2smag.NE.0.) & .OR.(viscC4smag.NE.0.) harmonic= & (viscAh.NE.0.) & .OR.(viscAhD.NE.0.) & .OR.(viscAhZ.NE.0.) & .OR.(viscAhGrid.NE.0.) & .OR.(viscC2leith.NE.0.) & .OR.(viscC2leithD.NE.0.) & .OR.(viscC2smag.NE.0.) IF ((harmonic).and.(viscAhremax.ne.0.)) THEN viscAhre_max=sqrt(2. _d 0)/viscAhRemax ELSE viscAhre_max=0. _d 0 ENDIF biharmonic= & (viscA4.NE.0.) & .OR.(viscA4D.NE.0.) & .OR.(viscA4Z.NE.0.) & .OR.(viscA4Grid.NE.0.) & .OR.(viscC4leith.NE.0.) & .OR.(viscC4leithD.NE.0.) & .OR.(viscC4smag.NE.0.) IF ((biharmonic).and.(viscA4remax.ne.0.)) THEN viscA4re_max=0.125 _d 0*sqrt(2. _d 0)/viscA4Remax ELSE viscA4re_max=0. _d 0 ENDIF calcleith= & (viscC2leith.NE.0.) & .OR.(viscC2leithD.NE.0.) & .OR.(viscC4leith.NE.0.) & .OR.(viscC4leithD.NE.0.) calcsmag= & (viscC2smag.NE.0.) & .OR.(viscC4smag.NE.0.) IF (deltaTmom.NE.0.) THEN recip_dt=1. _d 0/deltaTmom ELSE recip_dt=0. _d 0 ENDIF IF (calcsmag) THEN smag2fac=(viscC2smag/pi)**2 smag4fac=0.125 _d 0*(viscC4smag/pi)**2 ELSE smag2fac=0. _d 0 smag4fac=0. _d 0 ENDIF C - Viscosity IF (useVariableViscosity) THEN DO j=2-Oly,sNy+Oly-1 DO i=2-Olx,sNx+Olx-1 CCCCCCCCCCCCCCC Divergence Point CalculationsCCCCCCCCCCCCCCCCCCCC C These are (powers of) length scales L2=2. _d 0/((recip_DXF(I,J,bi,bj)**2+recip_DYF(I,J,bi,bj)**2)) L3=(L2**1.5) L4=(L2**2) L5=(L2**2.5) L2rdt=0.25 _d 0*recip_dt*L2 L4rdt=recip_dt/( 6. _d 0*(recip_DXF(I,J,bi,bj)**4 & +recip_DYF(I,J,bi,bj)**4) & +8. _d 0*((recip_DXF(I,J,bi,bj) & *recip_DYF(I,J,bi,bj))**2) ) C Velocity Reynolds Scale Uscl=sqrt(KE(i,j)*L2)*viscAhRe_max U4scl=sqrt(KE(i,j))*L3*viscA4Re_max IF (useFullLeith.and.calcleith) THEN C This is the vector magnitude of the vorticity gradient squared grdVrt=0.25 _d 0*( & ((vort3(i+1,j)-vort3(i,j))*recip_DXG(i,j,bi,bj))**2 & +((vort3(i,j+1)-vort3(i,j))*recip_DYG(i,j,bi,bj))**2 & +((vort3(i+1,j+1)-vort3(i,j+1)) & *recip_DXG(i,j+1,bi,bj))**2 & +((vort3(i+1,j+1)-vort3(i+1,j)) & *recip_DYG(i+1,j,bi,bj))**2) C This is the vector magnitude of grad (div.v) squared C Using it in Leith serves to damp instabilities in w. grdDiv=0.25 _d 0*( & ((hDiv(i+1,j)-hDiv(i,j))*recip_DXC(i+1,j,bi,bj))**2 & +((hDiv(i,j+1)-hDiv(i,j))*recip_DYC(i,j+1,bi,bj))**2 & +((hDiv(i,j)-hDiv(i-1,j))*recip_DXC(i,j,bi,bj))**2 & +((hDiv(i,j)-hDiv(i,j-1))*recip_DYC(i,j,bi,bj))**2) viscAh_DLth(i,j)= & sqrt(viscC2leith**2*grdVrt+viscC2leithD**2*grdDiv)*L3 viscA4_DLth(i,j)=0.125 _d 0* & sqrt(viscC4leith**2*grdVrt+viscC4leithD**2*grdDiv)*L5 viscAh_DLthd(i,j)= & sqrt(viscC2leithD**2*grdDiv)*L3 viscA4_DLthd(i,j)=0.125 _d 0* & sqrt(viscC4leithD**2*grdDiv)*L5 ELSEIF (calcleith) THEN C but this approximation will work on cube c (and differs by as much as 4X) grdVrt=abs((vort3(i+1,j)-vort3(i,j))*recip_DXG(i,j,bi,bj)) grdVrt=max(grdVrt, & abs((vort3(i,j+1)-vort3(i,j))*recip_DYG(i,j,bi,bj))) grdVrt=max(grdVrt, & abs((vort3(i+1,j+1)-vort3(i,j+1))*recip_DXG(i,j+1,bi,bj))) grdVrt=max(grdVrt, & abs((vort3(i+1,j+1)-vort3(i+1,j))*recip_DYG(i+1,j,bi,bj))) grdDiv=abs((hDiv(i+1,j)-hDiv(i,j))*recip_DXC(i+1,j,bi,bj)) grdDiv=max(grdDiv, & abs((hDiv(i,j+1)-hDiv(i,j))*recip_DYC(i,j+1,bi,bj))) grdDiv=max(grdDiv, & abs((hDiv(i,j)-hDiv(i-1,j))*recip_DXC(i,j,bi,bj))) grdDiv=max(grdDiv, & abs((hDiv(i,j)-hDiv(i,j-1))*recip_DYC(i,j,bi,bj))) c This approximation is good to the same order as above... viscAh_Dlth(i,j)= & (viscC2leith*grdVrt+(viscC2leithD*grdDiv))*L3 viscA4_Dlth(i,j)=0.125 _d 0* & (viscC4leith*grdVrt+(viscC4leithD*grdDiv))*L5 viscAh_DlthD(i,j)= & ((viscC2leithD*grdDiv))*L3 viscA4_DlthD(i,j)=0.125 _d 0* & ((viscC4leithD*grdDiv))*L5 ELSE viscAh_Dlth(i,j)=0. _d 0 viscA4_Dlth(i,j)=0. _d 0 viscAh_DlthD(i,j)=0. _d 0 viscA4_DlthD(i,j)=0. _d 0 ENDIF IF (calcsmag) THEN viscAh_DSmg(i,j)=L2 & *sqrt(tension(i,j)**2 & +0.25 _d 0*(strain(i+1, j )**2+strain( i ,j+1)**2 & +strain(i , j )**2+strain(i+1,j+1)**2)) viscA4_DSmg(i,j)=smag4fac*L2*viscAh_DSmg(i,j) viscAh_DSmg(i,j)=smag2fac*viscAh_DSmg(i,j) ELSE viscAh_DSmg(i,j)=0. _d 0 viscA4_DSmg(i,j)=0. _d 0 ENDIF C Harmonic on Div.u points Alin=viscAhD+viscAhGrid*L2rdt & +viscAh_DLth(i,j)+viscAh_DSmg(i,j) viscAh_DMin(i,j)=max(viscAhGridMin*L2rdt,Uscl) viscAh_D(i,j)=max(viscAh_DMin(i,j),Alin) viscAh_DMax(i,j)=min(viscAhGridMax*L2rdt,viscAhMax) viscAh_D(i,j)=min(viscAh_DMax(i,j),viscAh_D(i,j)) C BiHarmonic on Div.u points Alin=viscA4D+viscA4Grid*L4rdt & +viscA4_DLth(i,j)+viscA4_DSmg(i,j) viscA4_DMin(i,j)=max(viscA4GridMin*L4rdt,U4scl) viscA4_D(i,j)=max(viscA4_DMin(i,j),Alin) viscA4_DMax(i,j)=min(viscA4GridMax*L4rdt,viscA4Max) viscA4_D(i,j)=min(viscA4_DMax(i,j),viscA4_D(i,j)) CCCCCCCCCCCCC Vorticity Point CalculationsCCCCCCCCCCCCCCCCCC C These are (powers of) length scales L2=2. _d 0/((recip_DXV(I,J,bi,bj)**2+recip_DYU(I,J,bi,bj)**2)) L3=(L2**1.5) L4=(L2**2) L5=(L2**2.5) L2rdt=0.25 _d 0*recip_dt*L2 L4rdt=recip_dt/ & ( 6. _d 0*(recip_DXF(I,J,bi,bj)**4+recip_DYF(I,J,bi,bj)**4) & +8. _d 0*((recip_DXF(I,J,bi,bj)*recip_DYF(I,J,bi,bj))**2)) C Velocity Reynolds Scale Uscl=sqrt(0.25 _d 0*(KE(i,j)+KE(i,j+1)+KE(i+1,j)+KE(i+1,j+1)) & *L2)*viscAhRe_max U4scl=sqrt(0.25 _d 0*(KE(i,j)+KE(i,j+1)+KE(i+1,j)+KE(i+1,j+1))) & *L3*viscA4Re_max C This is the vector magnitude of the vorticity gradient squared IF (useFullLeith.and.calcleith) THEN grdVrt=0.25 _d 0*( & ((vort3(i+1,j)-vort3(i,j))*recip_DXG(i,j,bi,bj))**2 & +((vort3(i,j+1)-vort3(i,j))*recip_DYG(i,j,bi,bj))**2 & +((vort3(i-1,j)-vort3(i,j))*recip_DXG(i-1,j,bi,bj))**2 & +((vort3(i,j-1)-vort3(i,j))*recip_DYG(i,j-1,bi,bj))**2) C This is the vector magnitude of grad(div.v) squared grdDiv=0.25 _d 0*( & ((hDiv(i,j)-hDiv(i-1,j))*recip_DXC(i,j,bi,bj))**2 & +((hDiv(i,j)-hDiv(i,j-1))*recip_DYC(i,j,bi,bj))**2 & +((hDiv(i,j-1)-hDiv(i-1,j-1))*recip_DXC(i,j-1,bi,bj))**2 & +((hDiv(i-1,j)-hDiv(i-1,j-1))*recip_DYC(i-1,j,bi,bj))**2) viscAh_ZLth(i,j)= & sqrt(viscC2leith**2*grdVrt+viscC2leithD**2*grdDiv)*L3 viscA4_ZLth(i,j)=0.125 _d 0* & sqrt(viscC4leith**2*grdVrt+viscC4leithD**2*grdDiv)*L5 viscAh_ZLthD(i,j)= & sqrt(viscC2leithD**2*grdDiv)*L3 viscA4_ZLthD(i,j)=0.125 _d 0* & sqrt(viscC4leithD**2*grdDiv)*L5 ELSEIF (calcleith) THEN C but this approximation will work on cube (and differs by 4X) grdVrt=abs((vort3(i+1,j)-vort3(i,j))*recip_DXG(i,j,bi,bj)) grdVrt=max(grdVrt, & abs((vort3(i,j+1)-vort3(i,j))*recip_DYG(i,j,bi,bj))) grdVrt=max(grdVrt, & abs((vort3(i-1,j)-vort3(i,j))*recip_DXG(i-1,j,bi,bj))) grdVrt=max(grdVrt, & abs((vort3(i,j-1)-vort3(i,j))*recip_DYG(i,j-1,bi,bj))) grdDiv=abs((hDiv(i,j)-hDiv(i-1,j))*recip_DXC(i,j,bi,bj)) grdDiv=max(grdDiv, & abs((hDiv(i,j)-hDiv(i,j-1))*recip_DYC(i,j,bi,bj))) grdDiv=max(grdDiv, & abs((hDiv(i,j-1)-hDiv(i-1,j-1))*recip_DXC(i,j-1,bi,bj))) grdDiv=max(grdDiv, & abs((hDiv(i-1,j)-hDiv(i-1,j-1))*recip_DYC(i-1,j,bi,bj))) viscAh_ZLth(i,j)=(viscC2leith*grdVrt & +(viscC2leithD*grdDiv))*L3 viscA4_ZLth(i,j)=0.125 _d 0*(viscC4leith*grdVrt & +(viscC4leithD*grdDiv))*L5 viscAh_ZLthD(i,j)=((viscC2leithD*grdDiv))*L3 viscA4_ZLthD(i,j)=0.125 _d 0*((viscC4leithD*grdDiv))*L5 ELSE viscAh_ZLth(i,j)=0. _d 0 viscA4_ZLth(i,j)=0. _d 0 viscAh_ZLthD(i,j)=0. _d 0 viscA4_ZLthD(i,j)=0. _d 0 ENDIF IF (calcsmag) THEN viscAh_ZSmg(i,j)=L2 & *sqrt(strain(i,j)**2 & +0.25 _d 0*(tension( i , j )**2+tension( i ,j-1)**2 & +tension(i-1, j )**2+tension(i-1,j-1)**2)) viscA4_ZSmg(i,j)=smag4fac*L2*viscAh_ZSmg(i,j) viscAh_ZSmg(i,j)=smag2fac*viscAh_ZSmg(i,j) ENDIF C Harmonic on Zeta points Alin=viscAhZ+viscAhGrid*L2rdt & +viscAh_ZLth(i,j)+viscAh_ZSmg(i,j) viscAh_ZMin(i,j)=max(viscAhGridMin*L2rdt,Uscl) viscAh_Z(i,j)=max(viscAh_ZMin(i,j),Alin) viscAh_ZMax(i,j)=min(viscAhGridMax*L2rdt,viscAhMax) viscAh_Z(i,j)=min(viscAh_ZMax(i,j),viscAh_Z(i,j)) C BiHarmonic on Zeta points Alin=viscA4Z+viscA4Grid*L4rdt & +viscA4_ZLth(i,j)+viscA4_ZSmg(i,j) viscA4_ZMin(i,j)=max(viscA4GridMin*L4rdt,U4scl) viscA4_Z(i,j)=max(viscA4_ZMin(i,j),Alin) viscA4_ZMax(i,j)=min(viscA4GridMax*L4rdt,viscA4Max) viscA4_Z(i,j)=min(viscA4_ZMax(i,j),viscA4_Z(i,j)) ENDDO ENDDO ELSE DO j=1-Oly,sNy+Oly DO i=1-Olx,sNx+Olx viscAh_D(i,j)=viscAhD viscAh_Z(i,j)=viscAhZ viscA4_D(i,j)=viscA4D viscA4_Z(i,j)=viscA4Z ENDDO ENDDO ENDIF #ifdef ALLOW_DIAGNOSTICS IF (useDiagnostics) THEN CALL DIAGNOSTICS_FILL(viscAh_D,'VISCAHD ',k,1,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(viscA4_D,'VISCA4D ',k,1,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(viscAh_Z,'VISCAHZ ',k,1,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(viscA4_Z,'VISCA4Z ',k,1,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(viscAh_DMax,'VAHDMAX ',k,1,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(viscA4_DMax,'VA4DMAX ',k,1,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(viscAh_ZMax,'VAHZMAX ',k,1,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(viscA4_ZMax,'VA4ZMAX ',k,1,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(viscAh_DMin,'VAHDMIN ',k,1,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(viscA4_DMin,'VA4DMIN ',k,1,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(viscAh_ZMin,'VAHZMIN ',k,1,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(viscA4_ZMin,'VA4ZMIN ',k,1,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(viscAh_DLth,'VAHDLTH ',k,1,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(viscA4_DLth,'VA4DLTH ',k,1,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(viscAh_ZLth,'VAHZLTH ',k,1,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(viscA4_ZLth,'VA4ZLTH ',k,1,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(viscAh_DLthD,'VAHDLTHD' & ,k,1,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(viscA4_DLthD,'VA4DLTHD' & ,k,1,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(viscAh_ZLthD,'VAHZLTHD' & ,k,1,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(viscA4_ZLthD,'VA4ZLTHD' & ,k,1,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(viscAh_DSmg,'VAHDSMAG',k,1,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(viscA4_DSmg,'VA4DSMAG',k,1,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(viscAh_ZSmg,'VAHZSMAG',k,1,2,bi,bj,myThid) CALL DIAGNOSTICS_FILL(viscA4_ZSmg,'VA4ZSMAG',k,1,2,bi,bj,myThid) ENDIF #endif RETURN END