C $Header: /home/ubuntu/mnt/e9_copy/MITgcm/pkg/mom_common/mom_calc_visc.F,v 1.44 2011/05/03 19:32:35 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/pi)**6*grad(Vort3)**2 C +(viscC2leithD/pi)**6*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/pi)**6*grad(Vort3)**2 C +(viscC4leithD/pi)**6*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*viscAhgridmin*L**2/deltaT C biharmonic viscosity>viscA4gridmin*L**4/32/deltaT (approx) C C RECOMMENDED VALUES C viscC2Leith=1-3 C viscC2LeithD=1-3 C viscC4Leith=1-3 C viscC4LeithD=1.5-3 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" #ifdef ALLOW_NONHYDROSTATIC #include "NH_VARS.h" #endif #ifdef ALLOW_AUTODIFF_TAMC #include "tamc.h" #include "tamc_keys.h" #endif /* ALLOW_AUTODIFF_TAMC */ #include "MOM_VISC.h" #if defined (ALLOW_3D_VISCAH) || defined (ALLOW_3D_VISCA4) #include "DYNVARS.h" #endif 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 #ifdef ALLOW_NONHYDROSTATIC INTEGER kp1 #endif #ifdef ALLOW_AUTODIFF_TAMC INTEGER lockey_1, lockey_2 #endif _RL smag2fac, smag4fac _RL leith2fac, leith4fac _RL leithD2fac, leithD4fac _RL viscAhRe_max, viscA4Re_max _RL Alin,grdVrt,grdDiv, keZpt _RL L2,L3,L5,L2rdt,L4rdt _RL Uscl,U4scl _RL divDx(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL divDy(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL vrtDx(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL vrtDy(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _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 #ifdef ALLOW_AUTODIFF_TAMC act1 = bi - myBxLo(myThid) max1 = myBxHi(myThid) - myBxLo(myThid) + 1 act2 = bj - myByLo(myThid) max2 = myByHi(myThid) - myByLo(myThid) + 1 act3 = myThid - 1 max3 = nTx*nTy act4 = ikey_dynamics - 1 ikey = (act1 + 1) + act2*max1 & + act3*max1*max2 & + act4*max1*max2*max3 lockey_1 = (ikey-1)*Nr + k #endif /* ALLOW_AUTODIFF_TAMC */ C-- Set flags which are used in this S/R and elsewhere : 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.) #ifdef ALLOW_3D_VISCAH & .OR.( viscAhDfile .NE. ' ' ) & .OR.( viscAhZfile .NE. ' ' ) #endif #ifdef ALLOW_3D_VISCA4 & .OR.( viscA4Dfile .NE. ' ' ) & .OR.( viscA4Zfile .NE. ' ' ) #endif 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.) #ifdef ALLOW_3D_VISCAH & .OR.( viscAhDfile .NE. ' ' ) & .OR.( viscAhZfile .NE. ' ' ) #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.) #ifdef ALLOW_3D_VISCA4 & .OR.( viscA4Dfile .NE. ' ' ) & .OR.( viscA4Zfile .NE. ' ' ) #endif IF (useVariableViscosity) THEN C---- variable viscosity : IF ((harmonic).AND.(viscAhReMax.NE.0.)) THEN viscAhRe_max=SQRT(2. _d 0)/viscAhReMax ELSE viscAhRe_max=0. _d 0 ENDIF 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 (calcSmag) THEN smag2fac=(viscC2smag/pi)**2 smag4fac=0.125 _d 0*(viscC4smag/pi)**2 ELSE smag2fac=0. _d 0 smag4fac=0. _d 0 ENDIF IF (calcLeith) THEN IF (useFullLeith) THEN leith2fac =(viscC2leith /pi)**6 leithD2fac=(viscC2leithD/pi)**6 leith4fac =0.015625 _d 0*(viscC4leith /pi)**6 leithD4fac=0.015625 _d 0*(viscC4leithD/pi)**6 ELSE leith2fac =(viscC2leith /pi)**3 leithD2fac=(viscC2leithD/pi)**3 leith4fac =0.125 _d 0*(viscC4leith /pi)**3 leithD4fac=0.125 _d 0*(viscC4leithD/pi)**3 ENDIF ELSE leith2fac=0. _d 0 leith4fac=0. _d 0 leithD2fac=0. _d 0 leithD4fac=0. _d 0 ENDIF #ifdef ALLOW_AUTODIFF_TAMC cphtest IF ( calcLeith .OR. calcSmag ) THEN cphtest STOP 'calcLeith or calcSmag not implemented for ADJOINT' cphtest ENDIF #endif 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 c visca4_zsmg(i,j) = 0. _d 0 viscah_zsmg(i,j) = 0. _d 0 c 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 c viscAh_DSmg(i,j) = 0. _d 0 viscA4_DSmg(i,j) = 0. _d 0 c 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 ENDDO ENDDO C- Initialise to zero gradient of vorticity & divergence: DO j=1-Oly,sNy+Oly DO i=1-Olx,sNx+Olx divDx(i,j) = 0. divDy(i,j) = 0. vrtDx(i,j) = 0. vrtDy(i,j) = 0. ENDDO ENDDO IF (calcLeith) THEN C horizontal gradient of horizontal divergence: C- gradient in x direction: cph-exch2#ifndef ALLOW_AUTODIFF_TAMC IF (useCubedSphereExchange) THEN C to compute d/dx(hDiv), fill corners with appropriate values: CALL FILL_CS_CORNER_TR_RL( 1, .FALSE., & hDiv, bi,bj, myThid ) ENDIF cph-exch2#endif DO j=2-Oly,sNy+Oly-1 DO i=2-Olx,sNx+Olx-1 divDx(i,j) = (hDiv(i,j)-hDiv(i-1,j))*recip_dxC(i,j,bi,bj) ENDDO ENDDO C- gradient in y direction: cph-exch2#ifndef ALLOW_AUTODIFF_TAMC IF (useCubedSphereExchange) THEN C to compute d/dy(hDiv), fill corners with appropriate values: CALL FILL_CS_CORNER_TR_RL( 2, .FALSE., & hDiv, bi,bj, myThid ) ENDIF cph-exch2#endif DO j=2-Oly,sNy+Oly-1 DO i=2-Olx,sNx+Olx-1 divDy(i,j) = (hDiv(i,j)-hDiv(i,j-1))*recip_dyC(i,j,bi,bj) ENDDO ENDDO C horizontal gradient of vertical vorticity: C- gradient in x direction: DO j=2-Oly,sNy+Oly DO i=2-Olx,sNx+Olx-1 vrtDx(i,j) = (vort3(i+1,j)-vort3(i,j)) & *recip_dxG(i,j,bi,bj) & *maskS(i,j,k,bi,bj) #ifdef ALLOW_OBCS & *maskInS(i,j,bi,bj) #endif ENDDO ENDDO C- gradient in y direction: DO j=2-Oly,sNy+Oly-1 DO i=2-Olx,sNx+Olx vrtDy(i,j) = (vort3(i,j+1)-vort3(i,j)) & *recip_dyG(i,j,bi,bj) & *maskW(i,j,k,bi,bj) #ifdef ALLOW_OBCS & *maskInW(i,j,bi,bj) #endif ENDDO ENDDO ENDIF DO j=2-Oly,sNy+Oly-1 DO i=2-Olx,sNx+Olx-1 CCCCCCCCCCCCCCC Divergence Point CalculationsCCCCCCCCCCCCCCCCCCCC #ifdef ALLOW_AUTODIFF_TAMC # ifndef AUTODIFF_DISABLE_LEITH lockey_2 = i+olx + (sNx+2*olx)*(j+oly-1) & + (sNx+2*olx)*(sNy+2*oly)*(lockey_1-1) CADJ STORE viscA4_ZSmg(i,j) CADJ & = comlev1_mom_ijk_loop , key=lockey_2, byte=isbyte CADJ STORE viscAh_ZSmg(i,j) CADJ & = comlev1_mom_ijk_loop , key=lockey_2, byte=isbyte # endif #endif /* ALLOW_AUTODIFF_TAMC */ C These are (powers of) length scales L2 = L2_D(i,j,bi,bj) L2rdt = 0.25 _d 0*recip_dt*L2 L3 = L3_D(i,j,bi,bj) L4rdt = L4rdt_D(i,j,bi,bj) L5 = (L2*L3) #ifndef AUTODIFF_DISABLE_REYNOLDS_SCALE C Velocity Reynolds Scale IF ( viscAhRe_max.GT.0. .AND. KE(i,j).GT.0. ) THEN Uscl=SQRT(KE(i,j)*L2)*viscAhRe_max ELSE Uscl=0. ENDIF IF ( viscA4Re_max.GT.0. .AND. KE(i,j).GT.0. ) THEN U4scl=SQRT(KE(i,j))*L3*viscA4Re_max ELSE U4scl=0. ENDIF #endif /* ndef AUTODIFF_DISABLE_REYNOLDS_SCALE */ cph-leith#ifndef ALLOW_AUTODIFF_TAMC #ifndef AUTODIFF_DISABLE_LEITH IF (useFullLeith.AND.calcLeith) THEN C This is the vector magnitude of the vorticity gradient squared grdVrt=0.25 _d 0*( (vrtDx(i,j+1)*vrtDx(i,j+1) & + vrtDx(i,j)*vrtDx(i,j) ) & + (vrtDy(i+1,j)*vrtDy(i+1,j) & + vrtDy(i,j)*vrtDy(i,j) ) ) 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*( (divDx(i+1,j)*divDx(i+1,j) & + divDx(i,j)*divDx(i,j) ) & + (divDy(i,j+1)*divDy(i,j+1) & + divDy(i,j)*divDy(i,j) ) ) viscAh_DLth(i,j)= & SQRT(leith2fac*grdVrt+leithD2fac*grdDiv)*L3 viscA4_DLth(i,j)= & SQRT(leith4fac*grdVrt+leithD4fac*grdDiv)*L5 viscAh_DLthd(i,j)= & SQRT(leithD2fac*grdDiv)*L3 viscA4_DLthd(i,j)= & SQRT(leithD4fac*grdDiv)*L5 ELSEIF (calcLeith) THEN C but this approximation will work on cube c (and differs by as much as 4X) grdVrt=MAX( ABS(vrtDx(i,j+1)), ABS(vrtDx(i,j)) ) grdVrt=MAX( grdVrt, ABS(vrtDy(i+1,j)) ) grdVrt=MAX( grdVrt, ABS(vrtDy(i,j)) ) c This approximation is good to the same order as above... grdDiv=MAX( ABS(divDx(i+1,j)), ABS(divDx(i,j)) ) grdDiv=MAX( grdDiv, ABS(divDy(i,j+1)) ) grdDiv=MAX( grdDiv, ABS(divDy(i,j)) ) viscAh_Dlth(i,j)=(leith2fac*grdVrt+(leithD2fac*grdDiv))*L3 viscA4_Dlth(i,j)=(leith4fac*grdVrt+(leithD4fac*grdDiv))*L5 viscAh_DlthD(i,j)=((leithD2fac*grdDiv))*L3 viscA4_DlthD(i,j)=((leithD4fac*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 #endif /* AUTODIFF_DISABLE_LEITH */ C Harmonic on Div.u points Alin=viscAhD+viscAhGrid*L2rdt & +viscAh_DLth(i,j)+viscAh_DSmg(i,j) #ifdef ALLOW_3D_VISCAH & +viscAhDfld(i,j,k,bi,bj) #endif 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) #ifdef ALLOW_3D_VISCA4 & +viscA4Dfld(i,j,k,bi,bj) #endif 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)) #ifdef ALLOW_NONHYDROSTATIC C-- Pass Viscosities to calc_gw, if constant, not necessary kp1 = MIN(k+1,Nr) IF ( k.EQ.1 ) THEN C Prepare for next level (next call) viscAh_W(i,j,kp1,bi,bj)=0.5*viscAh_D(i,j) viscA4_W(i,j,kp1,bi,bj)=0.5*viscA4_D(i,j) C These values dont get used viscAh_W(i,j,k,bi,bj)=viscAh_D(i,j) viscA4_W(i,j,k,bi,bj)=viscA4_D(i,j) ELSEIF ( k.EQ.Nr ) THEN viscAh_W(i,j,k,bi,bj)=viscAh_W(i,j,k,bi,bj)+0.5*viscAh_D(i,j) viscA4_W(i,j,k,bi,bj)=viscA4_W(i,j,k,bi,bj)+0.5*viscA4_D(i,j) ELSE C Prepare for next level (next call) viscAh_W(i,j,kp1,bi,bj)=0.5*viscAh_D(i,j) viscA4_W(i,j,kp1,bi,bj)=0.5*viscA4_D(i,j) C Note that previous call of this function has already added half. viscAh_W(i,j,k,bi,bj)=viscAh_W(i,j,k,bi,bj)+0.5*viscAh_D(i,j) viscA4_W(i,j,k,bi,bj)=viscA4_W(i,j,k,bi,bj)+0.5*viscA4_D(i,j) ENDIF #endif /* ALLOW_NONHYDROSTATIC */ CCCCCCCCCCCCC Vorticity Point CalculationsCCCCCCCCCCCCCCCCCC C These are (powers of) length scales L2 = L2_Z(i,j,bi,bj) L2rdt = 0.25 _d 0*recip_dt*L2 L3 = L3_Z(i,j,bi,bj) L4rdt = L4rdt_Z(i,j,bi,bj) L5 = (L2*L3) #ifndef AUTODIFF_DISABLE_REYNOLDS_SCALE C Velocity Reynolds Scale (Pb here at CS-grid corners !) IF ( viscAhRe_max.GT.0. .OR. viscA4Re_max.GT.0. ) THEN keZpt=0.25 _d 0*( (KE(i,j)+KE(i-1,j-1)) & +(KE(i-1,j)+KE(i,j-1)) ) IF ( keZpt.GT.0. ) THEN Uscl = SQRT(keZpt*L2)*viscAhRe_max U4scl= SQRT(keZpt)*L3*viscA4Re_max ELSE Uscl =0. U4scl=0. ENDIF ELSE Uscl =0. U4scl=0. ENDIF #endif /* ndef AUTODIFF_DISABLE_REYNOLDS_SCALE */ #ifndef AUTODIFF_DISABLE_LEITH C This is the vector magnitude of the vorticity gradient squared IF (useFullLeith.AND.calcLeith) THEN grdVrt=0.25 _d 0*( (vrtDx(i-1,j)*vrtDx(i-1,j) & + vrtDx(i,j)*vrtDx(i,j) ) & + (vrtDy(i,j-1)*vrtDy(i,j-1) & + vrtDy(i,j)*vrtDy(i,j) ) ) C This is the vector magnitude of grad(div.v) squared grdDiv=0.25 _d 0*( (divDx(i,j-1)*divDx(i,j-1) & + divDx(i,j)*divDx(i,j) ) & + (divDy(i-1,j)*divDy(i-1,j) & + divDy(i,j)*divDy(i,j) ) ) viscAh_ZLth(i,j)= & SQRT(leith2fac*grdVrt+leithD2fac*grdDiv)*L3 viscA4_ZLth(i,j)= & SQRT(leith4fac*grdVrt+leithD4fac*grdDiv)*L5 viscAh_ZLthD(i,j)= & SQRT(leithD2fac*grdDiv)*L3 viscA4_ZLthD(i,j)= & SQRT(leithD4fac*grdDiv)*L5 ELSEIF (calcLeith) THEN C but this approximation will work on cube (and differs by 4X) grdVrt=MAX( ABS(vrtDx(i-1,j)), ABS(vrtDx(i,j)) ) grdVrt=MAX( grdVrt, ABS(vrtDy(i,j-1)) ) grdVrt=MAX( grdVrt, ABS(vrtDy(i,j)) ) grdDiv=MAX( ABS(divDx(i,j)), ABS(divDx(i,j-1)) ) grdDiv=MAX( grdDiv, ABS(divDy(i,j)) ) grdDiv=MAX( grdDiv, ABS(divDy(i-1,j)) ) viscAh_ZLth(i,j)=(leith2fac*grdVrt+(leithD2fac*grdDiv))*L3 viscA4_ZLth(i,j)=(leith4fac*grdVrt+(leithD4fac*grdDiv))*L5 viscAh_ZLthD(i,j)=(leithD2fac*grdDiv)*L3 viscA4_ZLthD(i,j)=(leithD4fac*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 #endif /* AUTODIFF_DISABLE_LEITH */ C Harmonic on Zeta points Alin=viscAhZ+viscAhGrid*L2rdt & +viscAh_ZLth(i,j)+viscAh_ZSmg(i,j) #ifdef ALLOW_3D_VISCAH & +viscAhZfld(i,j,k,bi,bj) #endif 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) #ifdef ALLOW_3D_VISCA4 & +viscA4Zfld(i,j,k,bi,bj) #endif 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 C---- use constant viscosity (useVariableViscosity=F): 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 C---- variable/constant viscosity : end if/else block 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