C $Header: /home/ubuntu/mnt/e9_copy/MITgcm/pkg/mom_vecinv/mom_vi_hdissip.F,v 1.6 2004/05/26 14:50:10 adcroft Exp $ C $Name: $ #include "CPP_OPTIONS.h" SUBROUTINE MOM_VI_HDISSIP( I bi,bj,k, I hDiv,vort3,hFacZ,dStar,zStar, c I viscAh_Z,viscAh_D,viscA4_Z,viscA4_D, O uDissip,vDissip, I myThid) IMPLICIT NONE C C Calculate horizontal dissipation terms C [del^2 - del^4] (u,v) C C == Global variables == #include "SIZE.h" #include "GRID.h" #include "EEPARAMS.h" #include "PARAMS.h" C == Routine arguments == INTEGER bi,bj,k _RL hDiv(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL vort3(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RS hFacZ(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL dStar(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL zStar(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _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 uDissip(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL vDissip(1-OLx:sNx+OLx,1-OLy:sNy+OLy) INTEGER myThid C == Local variables == INTEGER I,J _RL Zip,Zij,Zpj,Dim,Dij,Dmj,uD2,vD2,uD4,vD4 _RL Alin,Alth,grdVrt,vg2,vg4 LOGICAL useVariableViscosity useVariableViscosity= & (viscAhGrid*deltaTmom.NE.0.) & .OR.(viscA4Grid*deltaTmom.NE.0.) & .OR.(viscC2leith.NE.0.) & .OR.(viscC4leith.NE.0.) IF (deltaTmom.NE.0.) THEN vg2=viscAhGrid/deltaTmom vg4=viscA4Grid/deltaTmom ELSE vg2=0. vg4=0. ENDIF C - Viscosity IF (useVariableViscosity) THEN DO j=2-Oly,sNy+Oly-1 DO i=2-Olx,sNx+Olx-1 C This is the vector magnitude of the vorticity gradient c grdVrt=sqrt(0.25*( c & ((vort3(i+1,j)-vort3(i,j))*recip_DXG(i,j,bi,bj))**2 c & +((vort3(i,j+1)-vort3(i,j))*recip_DYG(i,j,bi,bj))**2 c & +((vort3(i+1,j+1)-vort3(i,j+1))*recip_DXG(i,j+1,bi,bj))**2 c & +((vort3(i+1,j+1)-vort3(i+1,j))*recip_DYG(i+1,j,bi,bj))**2 )) C but this approximation will work on cube (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))) Alth=viscC2leith*grdVrt*(rA(i,j,bi,bj)**1.5) Alin=viscAh+vg2*rA ( i , j ,bi,bj) viscAh_D(i,j)=min(viscAhMax,Alin+Alth) Alth=viscC4leith*grdVrt*0.125*(rA(i,j,bi,bj)**2.5) Alin=viscA4+vg4*(rA ( i , j ,bi,bj)**2) viscA4_D(i,j)=min(viscA4Max,Alin+Alth) C This is the vector magnitude of the vorticity gradient c grdVrt=sqrt(0.25*( c & ((vort3(i+1,j)-vort3(i,j))*recip_DXG(i,j,bi,bj))**2 c & +((vort3(i,j+1)-vort3(i,j))*recip_DYG(i,j,bi,bj))**2 c & +((vort3(i-1,j)-vort3(i,j))*recip_DXG(i-1,j,bi,bj))**2 c & +((vort3(i,j-1)-vort3(i,j))*recip_DYG(i,j-1,bi,bj))**2 )) C but this approximation will work on cube (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)-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))) Alth=viscC2leith*grdVrt*(rAz(i,j,bi,bj)**1.5) Alin=viscAh+vg2*rAz( i , j ,bi,bj) viscAh_Z(i,j)=min(viscAhMax,Alin+Alth) Alth=viscC4leith*grdVrt*0.125*(rAz(i,j,bi,bj)**2.5) Alin=viscA4+vg4*(rAz( i , j ,bi,bj)**2) viscA4_Z(i,j)=min(viscA4Max,Alin+Alth) ENDDO ENDDO ELSE DO j=1-Oly,sNy+Oly DO i=1-Olx,sNx+Olx viscAh_D(i,j)=viscAh viscAh_Z(i,j)=viscAh viscA4_D(i,j)=viscA4 viscA4_Z(i,j)=viscA4 ENDDO ENDDO ENDIF C - Laplacian and bi-harmonic terms DO j=2-Oly,sNy+Oly-1 DO i=2-Olx,sNx+Olx-1 Dim=hDiv( i ,j-1) Dij=hDiv( i , j ) Dmj=hDiv(i-1, j ) Zip=hFacZ( i ,j+1)*vort3( i ,j+1) Zij=hFacZ( i , j )*vort3( i , j ) Zpj=hFacZ(i+1, j )*vort3(i+1, j ) C This bit scales the harmonic dissipation operator to be proportional C to the grid-cell area over the time-step. viscAh is then non-dimensional C and should be less than 1/8, for example viscAh=0.01 if (useVariableViscosity) then Dij=Dij*viscAh_D(i,j) Dim=Dim*viscAh_D(i,j-1) Dmj=Dmj*viscAh_D(i-1,j) Zij=Zij*viscAh_Z(i,j) Zip=Zip*viscAh_Z(i,j+1) Zpj=Zpj*viscAh_Z(i+1,j) uD2 = ( & cosFacU(j,bi,bj)*( Dij-Dmj )*recip_DXC(i,j,bi,bj) & -recip_hFacW(i,j,k,bi,bj)*( Zip-Zij )*recip_DYG(i,j,bi,bj) ) vD2 = ( & recip_hFacS(i,j,k,bi,bj)*( Zpj-Zij )*recip_DXG(i,j,bi,bj) & *cosFacV(j,bi,bj) & +( Dij-Dim )*recip_DYC(i,j,bi,bj) ) else uD2 = viscAh*( & cosFacU(j,bi,bj)*( Dij-Dmj )*recip_DXC(i,j,bi,bj) & -recip_hFacW(i,j,k,bi,bj)*( Zip-Zij )*recip_DYG(i,j,bi,bj) ) vD2 = viscAh*( & recip_hFacS(i,j,k,bi,bj)*( Zpj-Zij )*recip_DXG(i,j,bi,bj) & *cosFacV(j,bi,bj) & +( Dij-Dim )*recip_DYC(i,j,bi,bj) ) endif Dim=dyF( i ,j-1,bi,bj)*dStar( i ,j-1) Dij=dyF( i , j ,bi,bj)*dStar( i , j ) Dmj=dyF(i-1, j ,bi,bj)*dStar(i-1, j ) Zip=dxV( i ,j+1,bi,bj)*hFacZ( i ,j+1)*zStar( i ,j+1) Zij=dxV( i , j ,bi,bj)*hFacZ( i , j )*zStar( i , j ) Zpj=dxV(i+1, j ,bi,bj)*hFacZ(i+1, j )*zStar(i+1, j ) C This bit scales the harmonic dissipation operator to be proportional C to the grid-cell area over the time-step. viscAh is then non-dimensional C and should be less than 1/8, for example viscAh=0.01 if (useVariableViscosity) then Dij=Dij*viscA4_D(i,j) Dim=Dim*viscA4_D(i,j-1) Dmj=Dmj*viscA4_D(i-1,j) Zij=Zij*viscA4_Z(i,j) Zip=Zip*viscA4_Z(i,j+1) Zpj=Zpj*viscA4_Z(i+1,j) uD4 = recip_rAw(i,j,bi,bj)*( & ( (Dij-Dmj)*cosFacU(j,bi,bj) ) & -recip_hFacW(i,j,k,bi,bj)*( Zip-Zij ) ) vD4 = recip_rAs(i,j,bi,bj)*( & recip_hFacS(i,j,k,bi,bj)*( (Zpj-Zij)*cosFacV(j,bi,bj) ) & + ( Dij-Dim ) ) else uD4 = recip_rAw(i,j,bi,bj)*( & viscA4*( (Dij-Dmj)*cosFacU(j,bi,bj) ) & -recip_hFacW(i,j,k,bi,bj)*viscA4*( Zip-Zij ) ) vD4 = recip_rAs(i,j,bi,bj)*( & recip_hFacS(i,j,k,bi,bj)*viscA4*( (Zpj-Zij)*cosFacV(j,bi,bj) ) & + viscA4*( Dij-Dim ) ) endif uDissip(i,j) = uD2 - uD4 vDissip(i,j) = vD2 - vD4 ENDDO ENDDO RETURN END