--- MITgcm/pkg/mom_common/mom_calc_visc.F 2005/09/16 19:33:59 1.1 +++ MITgcm/pkg/mom_common/mom_calc_visc.F 2005/09/21 14:32:59 1.7 @@ -1,16 +1,71 @@ -C $Header: /home/ubuntu/mnt/e9_copy/MITgcm/pkg/mom_common/mom_calc_visc.F,v 1.1 2005/09/16 19:33:59 baylor Exp $ +C $Header: /home/ubuntu/mnt/e9_copy/MITgcm/pkg/mom_common/mom_calc_visc.F,v 1.7 2005/09/21 14:32:59 baylor 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, + 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/2/viscAhRemax +C +C viscA4Remax is min value for grid point biharmonic Reynolds num +C biharmonic viscosity>sqrt(2*KE)*L**3/16/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 +C viscA4Remax>=1 +C viscAhgridmax=1 +C viscA4gridmax=1 +C viscAhgrid<1 +C viscA4grid<1 +C viscAhgridmin<<1 +C viscA4gridmin<<1 C == Global variables == #include "SIZE.h" @@ -35,13 +90,32 @@ C == Local variables == INTEGER I,J - _RL ASmag2, ASmag4, smag2fac, smag4fac - _RL vg2Min, vg2Max, AlinMax, AlinMin - _RL lenA2, lenAz2 - _RL Alin,Alth2,Alth4,grdVrt,grdDiv - _RL vg2,vg4,vg4Min,vg4Max + _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.) @@ -62,6 +136,8 @@ & .OR.(viscC2leithD.NE.0.) & .OR.(viscC2smag.NE.0.) + IF (harmonic) viscAhre_max=viscAhremax + biharmonic= & (viscA4.NE.0.) & .OR.(viscA4D.NE.0.) @@ -71,42 +147,53 @@ & .OR.(viscC4leithD.NE.0.) & .OR.(viscC4smag.NE.0.) + IF (biharmonic) viscA4re_max=viscA4remax + + 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./deltaTmom ELSE recip_dt=0. ENDIF - vg2=viscAhGrid*recip_dt - vg2Min=viscAhGridMin*recip_dt - vg2Max=viscAhGridMax*recip_dt - vg4=viscA4Grid*recip_dt - vg4Min=viscA4GridMin*recip_dt - vg4Max=viscA4GridMax*recip_dt - - smag2fac=(viscC2smag/pi)**2 - smag4fac=0.125*(viscC4smag/pi)**2 + IF (calcsmag) THEN + smag2fac=(viscC2smag/pi)**2 + smag4fac=0.125*(viscC4smag/pi)**2 + 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=rA(i,j,bi,bj) + L2=2./((recip_DXF(I,J,bi,bj)**2+recip_DYF(I,J,bi,bj)**2)) L3=(L2**1.5) L4=(L2**2) - L5=0.125*(L2**2.5) - IF (useAnisotropicViscAGridMax) THEN - L2rdt=recip_dt/( 2.*(recip_DXF(I,J,bi,bj)**2 - & +recip_DYF(I,J,bi,bj)**2) ) - L4rdt=recip_dt/( 6.*(recip_DXF(I,J,bi,bj)**4 + L5=(L2**2.5) + + L2rdt=0.25*recip_dt*L2 + + L4rdt=recip_dt/( 6.*(recip_DXF(I,J,bi,bj)**4 & +recip_DYF(I,J,bi,bj)**4) & +8.*((recip_DXF(I,J,bi,bj) & *recip_DYF(I,J,bi,bj))**2) ) - ENDIF - IF (useFullLeith) THEN +C Velocity Reynolds Scale + Uscl=sqrt(KE(i,j)*L2*0.5)/viscAhRe_max + U4scl=0.125*L2*Uscl/viscA4Re_max + + IF (useFullLeith.and.calcleith) THEN C This is the vector magnitude of the vorticity gradient squared grdVrt=0.25*( & ((vort3(i+1,j)-vort3(i,j))*recip_DXG(i,j,bi,bj))**2 @@ -116,208 +203,179 @@ 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*( - & ((hDiv(i+1,j)-hDiv(i,j))*recip_DXG(i,j,bi,bj))**2 - & +((hDiv(i,j+1)-hDiv(i,j))*recip_DYG(i,j,bi,bj))**2 - & +((hDiv(i-1,j)-hDiv(i,j))*recip_DXG(i-1,j,bi,bj))**2 - & +((hDiv(i,j-1)-hDiv(i,j))*recip_DYG(i,j-1,bi,bj))**2) - - IF ( (viscC2leith**2*grdVrt+viscC2leithD**2*grdDiv) - & .NE. 0. ) THEN - Alth2=sqrt(viscC2leith**2*grdVrt+viscC2leithD**2*grdDiv)*L3 - ELSE - Alth2=0. _d 0 - ENDIF - IF ( (viscC4leith**2*grdVrt+viscC4leithD**2*grdDiv) - & .NE. 0. ) THEN - Alth4=sqrt(viscC4leith**2*grdVrt+viscC4leithD**2*grdDiv)*L5 - ELSE - Alth4=0. _d 0 - ENDIF - ELSE + grdDiv=0.25*( + & ((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)= + & sqrt(viscC4leith**2*grdVrt+viscC4leithD**2*grdDiv)*L5 + viscAh_DLthd(i,j)= + & sqrt(viscC2leithD**2*grdDiv)*L3 + viscA4_DLthd(i,j)= + & 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_DXG(i,j,bi,bj)) - grdDiv=max(grdDiv, - & abs((hDiv(i,j+1)-hDiv(i,j))*recip_DYG(i,j,bi,bj))) - grdDiv=max(grdDiv, - & abs((hDiv(i-1,j)-hDiv(i,j))*recip_DXG(i-1,j,bi,bj))) - grdDiv=max(grdDiv, - & abs((hDiv(i,j-1)-hDiv(i,j))*recip_DYG(i,j-1,bi,bj))) + 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... - Alth2=(viscC2leith*grdVrt+(viscC2leithD*grdDiv))*L3 - Alth4=(viscC4leith*grdVrt+(viscC4leithD*grdDiv))*L5 - ENDIF - - IF (smag2fac.NE.0.) THEN - Asmag2=smag2fac*L2 - & *sqrt(tension(i,j)**2 - & +0.25*(strain(i+1, j )**2+strain( i ,j+1)**2 - & +strain(i-1, j )**2+strain( i ,j-1)**2)) + viscAh_Dlth(i,j)= + & (viscC2leith*grdVrt+(viscC2leithD*grdDiv))*L3 + viscA4_Dlth(i,j)=0.125* + & (viscC4leith*grdVrt+(viscC4leithD*grdDiv))*L5 + viscAh_DlthD(i,j)= + & ((viscC2leithD*grdDiv))*L3 + viscA4_DlthD(i,j)=0.125* + & ((viscC4leithD*grdDiv))*L5 ELSE - Asmag2=0d0 + viscAh_Dlth(i,j)=0d0 + viscA4_Dlth(i,j)=0d0 + viscAh_DlthD(i,j)=0d0 + viscA4_DlthD(i,j)=0d0 ENDIF - IF (smag4fac.NE.0.) THEN - Asmag4=smag4fac*L4 - & *sqrt(tension(i,j)**2 - & +0.25*(strain(i+1, j )**2+strain( i ,j+1)**2 - & +strain(i-1, j )**2+strain( i ,j-1)**2)) + IF (calcsmag) THEN + viscAh_DSmg(i,j)=L2 + & *sqrt(tension(i,j)**2 + & +0.25*(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 - Asmag4=0d0 + viscAh_DSmg(i,j)=0d0 + viscA4_DSmg(i,j)=0d0 ENDIF C Harmonic on Div.u points - Alin=viscAhD+vg2*L2+Alth2+Asmag2 - viscAh_D(i,j)=min(viscAhMax,Alin) - IF (useAnisotropicViscAGridMax) THEN - AlinMax=viscAhGridMax*L2rdt - viscAh_D(i,j)=min(AlinMax,viscAh_D(i,j)) - ELSE - IF (vg2Max.GT.0.) THEN - AlinMax=vg2Max*L2 - viscAh_D(i,j)=min(AlinMax,viscAh_D(i,j)) - ENDIF - ENDIF - AlinMin=vg2Min*L2 - viscAh_D(i,j)=max(AlinMin,viscAh_D(i,j)) + 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+vg4*L4+Alth4+Asmag4 - viscA4_D(i,j)=min(viscA4Max,Alin) - IF (useAnisotropicViscAGridMax) THEN - AlinMax=viscA4GridMax*L4rdt - viscA4_D(i,j)=min(AlinMax,viscA4_D(i,j)) - ELSE - IF (vg4Max.GT.0.) THEN - AlinMax=vg4Max*L4 - viscA4_D(i,j)=min(AlinMax,viscA4_D(i,j)) - ENDIF - ENDIF - AlinMin=vg4Min*L4 - viscA4_D(i,j)=max(AlinMin,viscA4_D(i,j)) + 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=rAz(i,j,bi,bj) + L2=2./((recip_DXV(I,J,bi,bj)**2+recip_DYU(I,J,bi,bj)**2)) L3=(L2**1.5) L4=(L2**2) - L5=0.125*(L2**2.5) - IF (useAnisotropicViscAGridMax) THEN - L2rdt=recip_dt/( 2.*(recip_DXV(I,J,bi,bj)**2 - & +recip_DYU(I,J,bi,bj)**2) ) - L4rdt=recip_dt/( 6.*(recip_DXV(I,J,bi,bj)**4 - & +recip_DYU(I,J,bi,bj)**4) - & +8.*((recip_DXV(I,J,bi,bj) - & *recip_DYU(I,J,bi,bj))**2) ) - ENDIF + L5=(L2**2.5) + + L2rdt=0.25*recip_dt*L2 + L4rdt=recip_dt/ + & ( 6.*(recip_DXF(I,J,bi,bj)**4+recip_DYF(I,J,bi,bj)**4) + & +8.*((recip_DXF(I,J,bi,bj)*recip_DYF(I,J,bi,bj))**2)) + +C Velocity Reynolds Scale + Uscl=sqrt((KE(i,j)+KE(i,j+1)+KE(i+1,j)+KE(i+1,j+1))*L2*0.125)/ + & viscAhRe_max + U4scl=0.125*L2*Uscl/viscA4Re_max C This is the vector magnitude of the vorticity gradient squared - IF (useFullLeith) THEN - grdVrt=0.25*( - & ((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) + IF (useFullLeith.and.calcleith) THEN + grdVrt=0.25*( + & ((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*( - & ((hDiv(i+1,j)-hDiv(i,j))*recip_DXG(i,j,bi,bj))**2 - & +((hDiv(i,j+1)-hDiv(i,j))*recip_DYG(i,j,bi,bj))**2 - & +((hDiv(i+1,j+1)-hDiv(i,j+1))*recip_DXG(i,j+1,bi,bj))**2 - & +((hDiv(i+1,j+1)-hDiv(i+1,j))*recip_DYG(i+1,j,bi,bj))**2) - - IF ( (viscC2leith**2*grdVrt+viscC2leithD**2*grdDiv) - & .NE. 0. ) THEN - Alth2=sqrt(viscC2leith**2*grdVrt+viscC2leithD**2*grdDiv)*L3 - ELSE - Alth2=0. _d 0 - ENDIF - IF ( (viscC4leith**2*grdVrt+viscC4leithD**2*grdDiv) - & .NE. 0. ) THEN - Alth4=sqrt(viscC4leith**2*grdVrt+viscC4leithD**2*grdDiv)*L5 - ELSE - Alth4=0. _d 0 - ENDIF - ELSE -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+1,j)-hDiv(i,j))*recip_DXG(i,j,bi,bj)) - grdDiv=max(grdDiv, - & abs((hDiv(i,j+1)-hDiv(i,j))*recip_DYG(i,j,bi,bj))) - grdDiv=max(grdDiv, - & abs((hDiv(i+1,j+1)-hDiv(i,j+1))*recip_DXG(i-1,j,bi,bj))) - grdDiv=max(grdDiv, - & abs((hDiv(i+1,j+1)-hDiv(i+1,j))*recip_DYG(i,j-1,bi,bj))) - -C This if statement is just to prevent bitwise changes when leithd=0 - Alth2=(viscC2leith*grdVrt+(viscC2leithD*grdDiv))*L3 - Alth4=(viscC4leith*grdVrt+(viscC4leithD*grdDiv))*L5 - ENDIF + grdDiv=0.25*( + & ((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)= + & sqrt(viscC4leith**2*grdVrt+viscC4leithD**2*grdDiv)*L5 + viscAh_ZLthD(i,j)= + & sqrt(viscC2leithD**2*grdDiv)*L3 + viscA4_ZLthD(i,j)= + & sqrt(viscC4leithD**2*grdDiv)*L5 - IF (smag2fac.NE.0.) THEN - Asmag2=smag2fac*L2 - & *sqrt(strain(i,j)**2 - & +0.25*(tension( i , j )**2+tension( i ,j+1)**2 - & +tension(i+1, j )**2+tension(i+1,j+1)**2)) + 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_DXG(i,j-1,bi,bj))) + grdDiv=max(grdDiv, + & abs((hDiv(i-1,j)-hDiv(i-1,j-1))*recip_DYG(i-1,j,bi,bj))) + + viscAh_ZLth(i,j)=(viscC2leith*grdVrt + & +(viscC2leithD*grdDiv))*L3 + viscA4_ZLth(i,j)=(viscC4leith*grdVrt + & +(viscC4leithD*grdDiv))*L5 + viscAh_ZLthD(i,j)=((viscC2leithD*grdDiv))*L3 + viscA4_ZLthD(i,j)=((viscC4leithD*grdDiv))*L5 ELSE - Asmag2=0d0 + viscAh_ZLth(i,j)=0d0 + viscA4_ZLth(i,j)=0d0 + viscAh_ZLthD(i,j)=0d0 + viscA4_ZLthD(i,j)=0d0 ENDIF - IF (smag4fac.NE.0.) THEN - Asmag4=smag4fac*L4 - & *sqrt(strain(i,j)**2 - & +0.25*(tension( i , j )**2+tension( i ,j+1)**2 - & +tension(i+1, j )**2+tension(i+1,j+1)**2)) - ELSE - Asmag4=0d0 + IF (calcsmag) THEN + viscAh_ZSmg(i,j)=L2 + & *sqrt(strain(i,j)**2 + & +0.25*(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+vg2*L2+Alth2+Asmag2 - viscAh_Z(i,j)=min(viscAhMax,Alin) - IF (useAnisotropicViscAGridMax) THEN - AlinMax=viscAhGridMax*L2rdt - viscAh_Z(i,j)=min(AlinMax,viscAh_Z(i,j)) - ELSE - IF (vg2Max.GT.0.) THEN - AlinMax=vg2Max*L2 - viscAh_Z(i,j)=min(AlinMax,viscAh_Z(i,j)) - ENDIF - ENDIF - AlinMin=vg2Min*L2 - viscAh_Z(i,j)=max(AlinMin,viscAh_Z(i,j)) - -C BiHarmonic on Zeta Points - Alin=viscA4Z+vg4*L4+Alth4+Asmag4 - viscA4_Z(i,j)=min(viscA4Max,Alin) - IF (useAnisotropicViscAGridMax) THEN - AlinMax=viscA4GridMax*L4rdt - viscA4_Z(i,j)=min(AlinMax,viscA4_Z(i,j)) - ELSE - IF (vg4Max.GT.0.) THEN - AlinMax=vg4Max*L4 - viscA4_Z(i,j)=min(AlinMax,viscA4_Z(i,j)) - ENDIF - ENDIF - AlinMin=vg4Min*L4 - viscA4_Z(i,j)=max(AlinMin,viscA4_Z(i,j)) + 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 @@ -337,8 +395,38 @@ 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 +