C $Header: /u/gcmpack/MITgcm/pkg/mom_fluxform/mom_fluxform.F,v 1.42 2010/03/16 00:16:50 jmc Exp $
C $Name: $
CBOI
C !TITLE: pkg/mom\_advdiff
C !AUTHORS: adcroft@mit.edu
C !INTRODUCTION: Flux-form Momentum Equations Package
C
C Package "mom\_fluxform" provides methods for calculating explicit terms
C in the momentum equation cast in flux-form:
C \begin{eqnarray*}
C G^u & = & -\frac{1}{\rho} \partial_x \phi_h
C -\nabla \cdot {\bf v} u
C -fv
C +\frac{1}{\rho} \nabla \cdot {\bf \tau}^x
C + \mbox{metrics}
C \\
C G^v & = & -\frac{1}{\rho} \partial_y \phi_h
C -\nabla \cdot {\bf v} v
C +fu
C +\frac{1}{\rho} \nabla \cdot {\bf \tau}^y
C + \mbox{metrics}
C \end{eqnarray*}
C where ${\bf v}=(u,v,w)$ and $\tau$, the stress tensor, includes surface
C stresses as well as internal viscous stresses.
CEOI
#include "MOM_FLUXFORM_OPTIONS.h"
CBOP
C !ROUTINE: MOM_FLUXFORM
C !INTERFACE: ==========================================================
SUBROUTINE MOM_FLUXFORM(
I bi,bj,iMin,iMax,jMin,jMax,k,kUp,kDown,
I KappaRU, KappaRV,
U fVerU, fVerV,
O guDiss, gvDiss,
I myTime, myIter, myThid)
C !DESCRIPTION:
C Calculates all the horizontal accelerations except for the implicit surface
C pressure gradient and implicit vertical viscosity.
C !USES: ===============================================================
C == Global variables ==
IMPLICIT NONE
#include "SIZE.h"
#include "DYNVARS.h"
#include "FFIELDS.h"
#include "EEPARAMS.h"
#include "PARAMS.h"
#include "GRID.h"
#include "SURFACE.h"
#ifdef ALLOW_AUTODIFF_TAMC
# include "tamc.h"
# include "tamc_keys.h"
# include "MOM_FLUXFORM.h"
#endif
C !INPUT PARAMETERS: ===================================================
C bi,bj :: tile indices
C iMin,iMax,jMin,jMAx :: loop ranges
C k :: vertical level
C kUp :: =1 or 2 for consecutive k
C kDown :: =2 or 1 for consecutive k
C KappaRU :: vertical viscosity
C KappaRV :: vertical viscosity
C fVerU :: vertical flux of U, 2 1/2 dim for pipe-lining
C fVerV :: vertical flux of V, 2 1/2 dim for pipe-lining
C guDiss :: dissipation tendency (all explicit terms), u component
C gvDiss :: dissipation tendency (all explicit terms), v component
C myTime :: current time
C myIter :: current time-step number
C myThid :: thread number
INTEGER bi,bj,iMin,iMax,jMin,jMax
INTEGER k,kUp,kDown
_RL KappaRU(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
_RL KappaRV(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
_RL fVerU(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2)
_RL fVerV(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2)
_RL guDiss(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL gvDiss(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL myTime
INTEGER myIter
INTEGER myThid
C !OUTPUT PARAMETERS: ==================================================
C None - updates gU() and gV() in common blocks
C !LOCAL VARIABLES: ====================================================
C i,j :: loop indices
C vF :: viscous flux
C v4F :: bi-harmonic viscous flux
C cF :: Coriolis acceleration
C mT :: Metric terms
C fZon :: zonal fluxes
C fMer :: meridional fluxes
C fVrUp,fVrDw :: vertical viscous fluxes at interface k-1 & k
INTEGER i,j
#ifdef ALLOW_AUTODIFF_TAMC
INTEGER imomkey
#endif
_RL vF(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL v4F(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL cF(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL mT(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL fZon(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL fMer(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL fVrUp(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL fVrDw(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
C afFacMom :: Tracer parameters for turning terms on and off.
C vfFacMom
C pfFacMom afFacMom - Advective terms
C cfFacMom vfFacMom - Eddy viscosity terms
C mtFacMom pfFacMom - Pressure terms
C cfFacMom - Coriolis terms
C foFacMom - Forcing
C mtFacMom - Metric term
C uDudxFac, AhDudxFac, etc ... individual term parameters for switching terms off
_RS hFacZ(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RS r_hFacZ(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RS xA(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RS yA(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL uTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL vTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL uFld(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL vFld(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL rTransU(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL rTransV(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL KE(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL viscAh_D(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL viscAh_Z(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL viscA4_D(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL viscA4_Z(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL vort3(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL hDiv(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL strain(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL tension(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL uDudxFac
_RL AhDudxFac
_RL vDudyFac
_RL AhDudyFac
_RL rVelDudrFac
_RL ArDudrFac
_RL fuFac
_RL mtFacU
_RL mtNHFacU
_RL uDvdxFac
_RL AhDvdxFac
_RL vDvdyFac
_RL AhDvdyFac
_RL rVelDvdrFac
_RL ArDvdrFac
_RL fvFac
_RL mtFacV
_RL mtNHFacV
_RL sideMaskFac
LOGICAL bottomDragTerms,harmonic,biharmonic,useVariableViscosity
CEOP
#ifdef MOM_BOUNDARY_CONSERVE
COMMON / MOM_FLUXFORM_LOCAL / uBnd, vBnd
_RL uBnd(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
_RL vBnd(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy)
#endif /* MOM_BOUNDARY_CONSERVE */
#ifdef ALLOW_AUTODIFF_TAMC
act0 = k - 1
max0 = Nr
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
imomkey = (act0 + 1)
& + act1*max0
& + act2*max0*max1
& + act3*max0*max1*max2
& + act4*max0*max1*max2*max3
#endif /* ALLOW_AUTODIFF_TAMC */
C Initialise intermediate terms
DO j=1-OLy,sNy+OLy
DO i=1-OLx,sNx+OLx
vF(i,j) = 0.
v4F(i,j) = 0.
cF(i,j) = 0.
mT(i,j) = 0.
fZon(i,j) = 0.
fMer(i,j) = 0.
fVrUp(i,j)= 0.
fVrDw(i,j)= 0.
rTransU(i,j)= 0.
rTransV(i,j)= 0.
c KE(i,j) = 0.
hDiv(i,j) = 0.
vort3(i,j) = 0.
strain(i,j) = 0.
tension(i,j)= 0.
guDiss(i,j) = 0.
gvDiss(i,j) = 0.
ENDDO
ENDDO
C-- Term by term tracer parmeters
C o U momentum equation
uDudxFac = afFacMom*1.
AhDudxFac = vfFacMom*1.
vDudyFac = afFacMom*1.
AhDudyFac = vfFacMom*1.
rVelDudrFac = afFacMom*1.
ArDudrFac = vfFacMom*1.
mtFacU = mtFacMom*1.
mtNHFacU = 1.
fuFac = cfFacMom*1.
C o V momentum equation
uDvdxFac = afFacMom*1.
AhDvdxFac = vfFacMom*1.
vDvdyFac = afFacMom*1.
AhDvdyFac = vfFacMom*1.
rVelDvdrFac = afFacMom*1.
ArDvdrFac = vfFacMom*1.
mtFacV = mtFacMom*1.
mtNHFacV = 1.
fvFac = cfFacMom*1.
IF (implicitViscosity) THEN
ArDudrFac = 0.
ArDvdrFac = 0.
ENDIF
C note: using standard stencil (no mask) results in under-estimating
C vorticity at a no-slip boundary by a factor of 2 = sideDragFactor
IF ( no_slip_sides ) THEN
sideMaskFac = sideDragFactor
ELSE
sideMaskFac = 0. _d 0
ENDIF
IF ( no_slip_bottom
& .OR. bottomDragQuadratic.NE.0.
& .OR. bottomDragLinear.NE.0.) THEN
bottomDragTerms=.TRUE.
ELSE
bottomDragTerms=.FALSE.
ENDIF
C-- Calculate open water fraction at vorticity points
CALL MOM_CALC_HFACZ(bi,bj,k,hFacZ,r_hFacZ,myThid)
C---- Calculate common quantities used in both U and V equations
C Calculate tracer cell face open areas
DO j=1-OLy,sNy+OLy
DO i=1-OLx,sNx+OLx
xA(i,j) = _dyG(i,j,bi,bj)*deepFacC(k)
& *drF(k)*_hFacW(i,j,k,bi,bj)
yA(i,j) = _dxG(i,j,bi,bj)*deepFacC(k)
& *drF(k)*_hFacS(i,j,k,bi,bj)
ENDDO
ENDDO
C Make local copies of horizontal flow field
DO j=1-OLy,sNy+OLy
DO i=1-OLx,sNx+OLx
uFld(i,j) = uVel(i,j,k,bi,bj)
vFld(i,j) = vVel(i,j,k,bi,bj)
ENDDO
ENDDO
C Calculate velocity field "volume transports" through tracer cell faces.
C anelastic: transports are scaled by rhoFacC (~ mass transport)
DO j=1-OLy,sNy+OLy
DO i=1-OLx,sNx+OLx
uTrans(i,j) = uFld(i,j)*xA(i,j)*rhoFacC(k)
vTrans(i,j) = vFld(i,j)*yA(i,j)*rhoFacC(k)
ENDDO
ENDDO
CALL MOM_CALC_KE(bi,bj,k,2,uFld,vFld,KE,myThid)
IF ( momViscosity) THEN
CALL MOM_CALC_HDIV(bi,bj,k,2,uFld,vFld,hDiv,myThid)
CALL MOM_CALC_RELVORT3(bi,bj,k,uFld,vFld,hFacZ,vort3,myThid)
CALL MOM_CALC_TENSION(bi,bj,k,uFld,vFld,tension,myThid)
CALL MOM_CALC_STRAIN(bi,bj,k,uFld,vFld,hFacZ,strain,myThid)
DO j=1-Oly,sNy+Oly
DO i=1-Olx,sNx+Olx
IF ( hFacZ(i,j).EQ.0. ) THEN
vort3(i,j) = sideMaskFac*vort3(i,j)
strain(i,j) = sideMaskFac*strain(i,j)
ENDIF
ENDDO
ENDDO
#ifdef ALLOW_DIAGNOSTICS
IF ( useDiagnostics ) THEN
CALL DIAGNOSTICS_FILL(hDiv, 'momHDiv ',k,1,2,bi,bj,myThid)
CALL DIAGNOSTICS_FILL(vort3, 'momVort3',k,1,2,bi,bj,myThid)
CALL DIAGNOSTICS_FILL(tension,'Tension ',k,1,2,bi,bj,myThid)
CALL DIAGNOSTICS_FILL(strain, 'Strain ',k,1,2,bi,bj,myThid)
ENDIF
#endif
ENDIF
C--- First call (k=1): compute vertical adv. flux fVerU(kUp) & fVerV(kUp)
IF (momAdvection.AND.k.EQ.1) THEN
#ifdef MOM_BOUNDARY_CONSERVE
CALL MOM_UV_BOUNDARY( bi, bj, k,
I uVel, vVel,
O uBnd(1-OLx,1-OLy,k,bi,bj),
O vBnd(1-OLx,1-OLy,k,bi,bj),
I myTime, myIter, myThid )
#endif /* MOM_BOUNDARY_CONSERVE */
C- Calculate vertical transports above U & V points (West & South face):
#ifdef ALLOW_AUTODIFF_TAMC
# ifdef NONLIN_FRSURF
# ifndef DISABLE_RSTAR_CODE
CADJ STORE dwtransc(:,:,bi,bj) =
CADJ & comlev1_bibj_k, key = imomkey, byte = isbyte
CADJ STORE dwtransu(:,:,bi,bj) =
CADJ & comlev1_bibj_k, key = imomkey, byte = isbyte
CADJ STORE dwtransv(:,:,bi,bj) =
CADJ & comlev1_bibj_k, key = imomkey, byte = isbyte
# endif
# endif /* NONLIN_FRSURF */
#endif /* ALLOW_AUTODIFF_TAMC */
CALL MOM_CALC_RTRANS( k, bi, bj,
O rTransU, rTransV,
I myTime, myIter, myThid)
C- Free surface correction term (flux at k=1)
CALL MOM_U_ADV_WU( bi,bj,k,uVel,wVel,rTransU,
O fVerU(1-OLx,1-OLy,kUp), myThid )
CALL MOM_V_ADV_WV( bi,bj,k,vVel,wVel,rTransV,
O fVerV(1-OLx,1-OLy,kUp), myThid )
C--- endif momAdvection & k=1
ENDIF
C--- Calculate vertical transports (at k+1) below U & V points :
IF (momAdvection) THEN
CALL MOM_CALC_RTRANS( k+1, bi, bj,
O rTransU, rTransV,
I myTime, myIter, myThid)
ENDIF
#ifdef MOM_BOUNDARY_CONSERVE
IF ( momAdvection .AND. k.LT.Nr ) THEN
CALL MOM_UV_BOUNDARY( bi, bj, k+1,
I uVel, vVel,
O uBnd(1-OLx,1-OLy,k+1,bi,bj),
O vBnd(1-OLx,1-OLy,k+1,bi,bj),
I myTime, myIter, myThid )
ENDIF
#endif /* MOM_BOUNDARY_CONSERVE */
IF (momViscosity) THEN
CALL 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)
ENDIF
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|
C---- Zonal momentum equation starts here
IF (momAdvection) THEN
C--- Calculate mean fluxes (advection) between cells for zonal flow.
#ifdef MOM_BOUNDARY_CONSERVE
CALL MOM_U_ADV_UU( bi,bj,k,uTrans,uBnd(1-OLx,1-OLy,k,bi,bj),
O fZon,myThid )
CALL MOM_U_ADV_VU( bi,bj,k,vTrans,uBnd(1-OLx,1-OLy,k,bi,bj),
O fMer,myThid )
CALL MOM_U_ADV_WU(
I bi,bj,k+1,uBnd,wVel,rTransU,
O fVerU(1-OLx,1-OLy,kDown), myThid )
#else /* MOM_BOUNDARY_CONSERVE */
C-- Zonal flux (fZon is at east face of "u" cell)
C Mean flow component of zonal flux -> fZon
CALL MOM_U_ADV_UU(bi,bj,k,uTrans,uFld,fZon,myThid)
C-- Meridional flux (fMer is at south face of "u" cell)
C Mean flow component of meridional flux -> fMer
CALL MOM_U_ADV_VU(bi,bj,k,vTrans,uFld,fMer,myThid)
C-- Vertical flux (fVer is at upper face of "u" cell)
C Mean flow component of vertical flux (at k+1) -> fVer
CALL MOM_U_ADV_WU(
I bi,bj,k+1,uVel,wVel,rTransU,
O fVerU(1-OLx,1-OLy,kDown), myThid )
#endif /* MOM_BOUNDARY_CONSERVE */
C-- Tendency is minus divergence of the fluxes + coriolis + pressure term
DO j=jMin,jMax
DO i=iMin,iMax
gU(i,j,k,bi,bj) =
#ifdef OLD_UV_GEOM
& -_recip_hFacW(i,j,k,bi,bj)*recip_drF(k)/
& ( 0.5 _d 0*(rA(i,j,bi,bj)+rA(i-1,j,bi,bj)) )
#else
& -_recip_hFacW(i,j,k,bi,bj)*recip_drF(k)
& *recip_rAw(i,j,bi,bj)*recip_deepFac2C(k)*recip_rhoFacC(k)
#endif
& *( ( fZon(i,j ) - fZon(i-1,j) )*uDudxFac
& +( fMer(i,j+1) - fMer(i, j) )*vDudyFac
& +(fVerU(i,j,kDown) - fVerU(i,j,kUp))*rkSign*rVelDudrFac
& )
ENDDO
ENDDO
#ifdef ALLOW_DIAGNOSTICS
IF ( useDiagnostics ) THEN
CALL DIAGNOSTICS_FILL(fZon,'ADVx_Um ',k,1,2,bi,bj,myThid)
CALL DIAGNOSTICS_FILL(fMer,'ADVy_Um ',k,1,2,bi,bj,myThid)
CALL DIAGNOSTICS_FILL(fVerU(1-Olx,1-Oly,kUp),
& 'ADVrE_Um',k,1,2,bi,bj,myThid)
ENDIF
#endif
#ifdef NONLIN_FRSURF
C-- account for 3.D divergence of the flow in rStar coordinate:
# ifndef DISABLE_RSTAR_CODE
IF ( select_rStar.GT.0 ) THEN
DO j=jMin,jMax
DO i=iMin,iMax
gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)
& - (rStarExpW(i,j,bi,bj) - 1. _d 0)/deltaTfreesurf
& *uVel(i,j,k,bi,bj)
ENDDO
ENDDO
ENDIF
IF ( select_rStar.LT.0 ) THEN
DO j=jMin,jMax
DO i=iMin,iMax
gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)
& - rStarDhWDt(i,j,bi,bj)*uVel(i,j,k,bi,bj)
ENDDO
ENDDO
ENDIF
# endif /* DISABLE_RSTAR_CODE */
#endif /* NONLIN_FRSURF */
ELSE
C- if momAdvection / else
DO j=1-OLy,sNy+OLy
DO i=1-OLx,sNx+OLx
gU(i,j,k,bi,bj) = 0. _d 0
ENDDO
ENDDO
C- endif momAdvection.
ENDIF
IF (momViscosity) THEN
C--- Calculate eddy fluxes (dissipation) between cells for zonal flow.
C Bi-harmonic term del^2 U -> v4F
IF (biharmonic)
& CALL MOM_U_DEL2U(bi,bj,k,uFld,hFacZ,v4f,myThid)
C Laplacian and bi-harmonic terms, Zonal Fluxes -> fZon
CALL MOM_U_XVISCFLUX(bi,bj,k,uFld,v4F,fZon,
I viscAh_D,viscA4_D,myThid)
C Laplacian and bi-harmonic termis, Merid Fluxes -> fMer
CALL MOM_U_YVISCFLUX(bi,bj,k,uFld,v4F,hFacZ,fMer,
I viscAh_Z,viscA4_Z,myThid)
C Eddy component of vertical flux (interior component only) -> fVrUp & fVrDw
IF (.NOT.implicitViscosity) THEN
CALL MOM_U_RVISCFLUX(bi,bj, k, uVel,KappaRU,fVrUp,myThid)
CALL MOM_U_RVISCFLUX(bi,bj,k+1,uVel,KappaRU,fVrDw,myThid)
ENDIF
C-- Tendency is minus divergence of the fluxes
C anelastic: hor.visc.fluxes are not scaled by rhoFac (by vert.visc.flx is)
DO j=jMin,jMax
DO i=iMin,iMax
guDiss(i,j) =
#ifdef OLD_UV_GEOM
& -_recip_hFacW(i,j,k,bi,bj)*recip_drF(k)/
& ( 0.5 _d 0*(rA(i,j,bi,bj)+rA(i-1,j,bi,bj)) )
#else
& -_recip_hFacW(i,j,k,bi,bj)*recip_drF(k)
& *recip_rAw(i,j,bi,bj)*recip_deepFac2C(k)
#endif
& *( ( fZon(i,j ) - fZon(i-1,j) )*AhDudxFac
& +( fMer(i,j+1) - fMer(i, j) )*AhDudyFac
& +( fVrDw(i,j) - fVrUp(i,j) )*rkSign*ArDudrFac
& *recip_rhoFacC(k)
& )
ENDDO
ENDDO
#ifdef ALLOW_DIAGNOSTICS
IF ( useDiagnostics ) THEN
CALL DIAGNOSTICS_FILL(fZon, 'VISCx_Um',k,1,2,bi,bj,myThid)
CALL DIAGNOSTICS_FILL(fMer, 'VISCy_Um',k,1,2,bi,bj,myThid)
IF (.NOT.implicitViscosity)
& CALL DIAGNOSTICS_FILL(fVrUp,'VISrE_Um',k,1,2,bi,bj,myThid)
ENDIF
#endif
C-- No-slip and drag BCs appear as body forces in cell abutting topography
IF (no_slip_sides) THEN
C- No-slip BCs impose a drag at walls...
CALL MOM_U_SIDEDRAG(
I bi,bj,k,
I uFld, v4f, hFacZ,
I viscAh_Z,viscA4_Z,
I harmonic,biharmonic,useVariableViscosity,
O vF,
I myThid)
DO j=jMin,jMax
DO i=iMin,iMax
gUdiss(i,j) = gUdiss(i,j) + vF(i,j)
ENDDO
ENDDO
ENDIF
C- No-slip BCs impose a drag at bottom
IF (bottomDragTerms) THEN
CALL MOM_U_BOTTOMDRAG(bi,bj,k,uFld,KE,KappaRU,vF,myThid)
DO j=jMin,jMax
DO i=iMin,iMax
gUdiss(i,j) = gUdiss(i,j) + vF(i,j)
ENDDO
ENDDO
ENDIF
#ifdef ALLOW_SHELFICE
IF (useShelfIce) THEN
CALL SHELFICE_U_DRAG(bi,bj,k,uFld,KE,KappaRU,vF,myThid)
DO j=jMin,jMax
DO i=iMin,iMax
gUdiss(i,j) = gUdiss(i,j) + vF(i,j)
ENDDO
ENDDO
ENDIF
#endif /* ALLOW_SHELFICE */
C- endif momViscosity
ENDIF
C-- Forcing term (moved to timestep.F)
c IF (momForcing)
c & CALL EXTERNAL_FORCING_U(
c I iMin,iMax,jMin,jMax,bi,bj,k,
c I myTime,myThid)
C-- Metric terms for curvilinear grid systems
IF (useNHMTerms) THEN
C o Non-Hydrostatic (spherical) metric terms
CALL MOM_U_METRIC_NH(bi,bj,k,uFld,wVel,mT,myThid)
DO j=jMin,jMax
DO i=iMin,iMax
gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+mtNHFacU*mT(i,j)
ENDDO
ENDDO
ENDIF
IF ( usingSphericalPolarGrid .AND. metricTerms ) THEN
C o Spherical polar grid metric terms
CALL MOM_U_METRIC_SPHERE(bi,bj,k,uFld,vFld,mT,myThid)
DO j=jMin,jMax
DO i=iMin,iMax
gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+mtFacU*mT(i,j)
ENDDO
ENDDO
ENDIF
IF ( usingCylindricalGrid .AND. metricTerms ) THEN
C o Cylindrical grid metric terms
CALL MOM_U_METRIC_CYLINDER(bi,bj,k,uFld,vFld,mT,myThid)
DO j=jMin,jMax
DO i=iMin,iMax
gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+mtFacU*mT(i,j)
ENDDO
ENDDO
ENDIF
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|
C---- Meridional momentum equation starts here
IF (momAdvection) THEN
#ifdef MOM_BOUNDARY_CONSERVE
CALL MOM_V_ADV_UV( bi,bj,k,uTrans,vBnd(1-OLx,1-OLy,k,bi,bj),
O fZon,myThid )
CALL MOM_V_ADV_VV( bi,bj,k,vTrans,vBnd(1-OLx,1-OLy,k,bi,bj),
O fMer,myThid )
CALL MOM_V_ADV_WV(
I bi,bj,k+1,vBnd,wVel,rTransV,
O fVerV(1-OLx,1-OLy,kDown), myThid )
#else /* MOM_BOUNDARY_CONSERVE */
C--- Calculate mean fluxes (advection) between cells for meridional flow.
C Mean flow component of zonal flux -> fZon
CALL MOM_V_ADV_UV(bi,bj,k,uTrans,vFld,fZon,myThid)
C-- Meridional flux (fMer is at north face of "v" cell)
C Mean flow component of meridional flux -> fMer
CALL MOM_V_ADV_VV(bi,bj,k,vTrans,vFld,fMer,myThid)
C-- Vertical flux (fVer is at upper face of "v" cell)
C Mean flow component of vertical flux (at k+1) -> fVerV
CALL MOM_V_ADV_WV(
I bi,bj,k+1,vVel,wVel,rTransV,
O fVerV(1-OLx,1-OLy,kDown), myThid )
#endif /* MOM_BOUNDARY_CONSERVE */
C-- Tendency is minus divergence of the fluxes + coriolis + pressure term
DO j=jMin,jMax
DO i=iMin,iMax
gV(i,j,k,bi,bj) =
#ifdef OLD_UV_GEOM
& -_recip_hFacS(i,j,k,bi,bj)*recip_drF(k)/
& ( 0.5 _d 0*(_rA(i,j,bi,bj)+_rA(i,j-1,bi,bj)) )
#else
& -_recip_hFacS(i,j,k,bi,bj)*recip_drF(k)
& *recip_rAs(i,j,bi,bj)*recip_deepFac2C(k)*recip_rhoFacC(k)
#endif
& *( ( fZon(i+1,j) - fZon(i,j ) )*uDvdxFac
& +( fMer(i, j) - fMer(i,j-1) )*vDvdyFac
& +(fVerV(i,j,kDown) - fVerV(i,j,kUp))*rkSign*rVelDvdrFac
& )
ENDDO
ENDDO
#ifdef ALLOW_DIAGNOSTICS
IF ( useDiagnostics ) THEN
CALL DIAGNOSTICS_FILL(fZon,'ADVx_Vm ',k,1,2,bi,bj,myThid)
CALL DIAGNOSTICS_FILL(fMer,'ADVy_Vm ',k,1,2,bi,bj,myThid)
CALL DIAGNOSTICS_FILL(fVerV(1-Olx,1-Oly,kUp),
& 'ADVrE_Vm',k,1,2,bi,bj,myThid)
ENDIF
#endif
#ifdef NONLIN_FRSURF
C-- account for 3.D divergence of the flow in rStar coordinate:
# ifndef DISABLE_RSTAR_CODE
IF ( select_rStar.GT.0 ) THEN
DO j=jMin,jMax
DO i=iMin,iMax
gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)
& - (rStarExpS(i,j,bi,bj) - 1. _d 0)/deltaTfreesurf
& *vVel(i,j,k,bi,bj)
ENDDO
ENDDO
ENDIF
IF ( select_rStar.LT.0 ) THEN
DO j=jMin,jMax
DO i=iMin,iMax
gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)
& - rStarDhSDt(i,j,bi,bj)*vVel(i,j,k,bi,bj)
ENDDO
ENDDO
ENDIF
# endif /* DISABLE_RSTAR_CODE */
#endif /* NONLIN_FRSURF */
ELSE
C- if momAdvection / else
DO j=1-OLy,sNy+OLy
DO i=1-OLx,sNx+OLx
gV(i,j,k,bi,bj) = 0. _d 0
ENDDO
ENDDO
C- endif momAdvection.
ENDIF
IF (momViscosity) THEN
C--- Calculate eddy fluxes (dissipation) between cells for meridional flow.
C Bi-harmonic term del^2 V -> v4F
IF (biharmonic)
& CALL MOM_V_DEL2V(bi,bj,k,vFld,hFacZ,v4f,myThid)
C Laplacian and bi-harmonic terms, Zonal Fluxes -> fZon
CALL MOM_V_XVISCFLUX(bi,bj,k,vFld,v4f,hFacZ,fZon,
I viscAh_Z,viscA4_Z,myThid)
C Laplacian and bi-harmonic termis, Merid Fluxes -> fMer
CALL MOM_V_YVISCFLUX(bi,bj,k,vFld,v4f,fMer,
I viscAh_D,viscA4_D,myThid)
C Eddy component of vertical flux (interior component only) -> fVrUp & fVrDw
IF (.NOT.implicitViscosity) THEN
CALL MOM_V_RVISCFLUX(bi,bj, k, vVel,KappaRV,fVrUp,myThid)
CALL MOM_V_RVISCFLUX(bi,bj,k+1,vVel,KappaRV,fVrDw,myThid)
ENDIF
C-- Tendency is minus divergence of the fluxes + coriolis + pressure term
C anelastic: hor.visc.fluxes are not scaled by rhoFac (by vert.visc.flx is)
DO j=jMin,jMax
DO i=iMin,iMax
gvDiss(i,j) =
#ifdef OLD_UV_GEOM
& -_recip_hFacS(i,j,k,bi,bj)*recip_drF(k)/
& ( 0.5 _d 0*(_rA(i,j,bi,bj)+_rA(i,j-1,bi,bj)) )
#else
& -_recip_hFacS(i,j,k,bi,bj)*recip_drF(k)
& *recip_rAs(i,j,bi,bj)*recip_deepFac2C(k)
#endif
& *( ( fZon(i+1,j) - fZon(i,j ) )*AhDvdxFac
& +( fMer(i, j) - fMer(i,j-1) )*AhDvdyFac
& +( fVrDw(i,j) - fVrUp(i,j) )*rkSign*ArDvdrFac
& *recip_rhoFacC(k)
& )
ENDDO
ENDDO
#ifdef ALLOW_DIAGNOSTICS
IF ( useDiagnostics ) THEN
CALL DIAGNOSTICS_FILL(fZon, 'VISCx_Vm',k,1,2,bi,bj,myThid)
CALL DIAGNOSTICS_FILL(fMer, 'VISCy_Vm',k,1,2,bi,bj,myThid)
IF (.NOT.implicitViscosity)
& CALL DIAGNOSTICS_FILL(fVrUp,'VISrE_Vm',k,1,2,bi,bj,myThid)
ENDIF
#endif
C-- No-slip and drag BCs appear as body forces in cell abutting topography
IF (no_slip_sides) THEN
C- No-slip BCs impose a drag at walls...
CALL MOM_V_SIDEDRAG(
I bi,bj,k,
I vFld, v4f, hFacZ,
I viscAh_Z,viscA4_Z,
I harmonic,biharmonic,useVariableViscosity,
O vF,
I myThid)
DO j=jMin,jMax
DO i=iMin,iMax
gvDiss(i,j) = gvDiss(i,j) + vF(i,j)
ENDDO
ENDDO
ENDIF
C- No-slip BCs impose a drag at bottom
IF (bottomDragTerms) THEN
CALL MOM_V_BOTTOMDRAG(bi,bj,k,vFld,KE,KappaRV,vF,myThid)
DO j=jMin,jMax
DO i=iMin,iMax
gvDiss(i,j) = gvDiss(i,j) + vF(i,j)
ENDDO
ENDDO
ENDIF
#ifdef ALLOW_SHELFICE
IF (useShelfIce) THEN
CALL SHELFICE_V_DRAG(bi,bj,k,vFld,KE,KappaRU,vF,myThid)
DO j=jMin,jMax
DO i=iMin,iMax
gvDiss(i,j) = gvDiss(i,j) + vF(i,j)
ENDDO
ENDDO
ENDIF
#endif /* ALLOW_SHELFICE */
C- endif momViscosity
ENDIF
C-- Forcing term (moved to timestep.F)
c IF (momForcing)
c & CALL EXTERNAL_FORCING_V(
c I iMin,iMax,jMin,jMax,bi,bj,k,
c I myTime,myThid)
C-- Metric terms for curvilinear grid systems
IF (useNHMTerms) THEN
C o Non-Hydrostatic (spherical) metric terms
CALL MOM_V_METRIC_NH(bi,bj,k,vFld,wVel,mT,myThid)
DO j=jMin,jMax
DO i=iMin,iMax
gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+mtNHFacV*mT(i,j)
ENDDO
ENDDO
ENDIF
IF ( usingSphericalPolarGrid .AND. metricTerms ) THEN
C o Spherical polar grid metric terms
CALL MOM_V_METRIC_SPHERE(bi,bj,k,uFld,mT,myThid)
DO j=jMin,jMax
DO i=iMin,iMax
gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+mtFacV*mT(i,j)
ENDDO
ENDDO
ENDIF
IF ( usingCylindricalGrid .AND. metricTerms ) THEN
C o Cylindrical grid metric terms
CALL MOM_V_METRIC_CYLINDER(bi,bj,k,uFld,vFld,mT,myThid)
DO j=jMin,jMax
DO i=iMin,iMax
gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+mtFacV*mT(i,j)
ENDDO
ENDDO
ENDIF
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|
C-- Coriolis term
C Note. As coded here, coriolis will not work with "thin walls"
c IF (useCDscheme) THEN
c CALL MOM_CDSCHEME(bi,bj,k,dPhiHydX,dPhiHydY,myThid)
c ELSE
IF (.NOT.useCDscheme) THEN
CALL MOM_U_CORIOLIS(bi,bj,k,vFld,cf,myThid)
DO j=jMin,jMax
DO i=iMin,iMax
gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+fuFac*cf(i,j)
ENDDO
ENDDO
#ifdef ALLOW_DIAGNOSTICS
IF ( useDiagnostics )
& CALL DIAGNOSTICS_FILL(cf,'Um_Cori ',k,1,2,bi,bj,myThid)
#endif
CALL MOM_V_CORIOLIS(bi,bj,k,uFld,cf,myThid)
DO j=jMin,jMax
DO i=iMin,iMax
gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+fvFac*cf(i,j)
ENDDO
ENDDO
#ifdef ALLOW_DIAGNOSTICS
IF ( useDiagnostics )
& CALL DIAGNOSTICS_FILL(cf,'Vm_Cori ',k,1,2,bi,bj,myThid)
#endif
ENDIF
C-- 3.D Coriolis term (horizontal momentum, Eastward component: -fprime*w)
IF ( use3dCoriolis ) THEN
CALL MOM_U_CORIOLIS_NH(bi,bj,k,wVel,cf,myThid)
DO j=jMin,jMax
DO i=iMin,iMax
gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+fuFac*cf(i,j)
ENDDO
ENDDO
IF ( usingCurvilinearGrid ) THEN
C- presently, non zero angleSinC array only supported with Curvilinear-Grid
CALL MOM_V_CORIOLIS_NH(bi,bj,k,wVel,cf,myThid)
DO j=jMin,jMax
DO i=iMin,iMax
gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+fvFac*cf(i,j)
ENDDO
ENDDO
ENDIF
ENDIF
C-- Set du/dt & dv/dt on boundaries to zero
DO j=jMin,jMax
DO i=iMin,iMax
gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)*_maskW(i,j,k,bi,bj)
guDiss(i,j) = guDiss(i,j) *_maskW(i,j,k,bi,bj)
gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)*_maskS(i,j,k,bi,bj)
gvDiss(i,j) = gvDiss(i,j) *_maskS(i,j,k,bi,bj)
ENDDO
ENDDO
#ifdef ALLOW_DIAGNOSTICS
IF ( useDiagnostics ) THEN
CALL DIAGNOSTICS_FILL(KE, 'momKE ',k,1,2,bi,bj,myThid)
CALL DIAGNOSTICS_FILL(gU(1-Olx,1-Oly,k,bi,bj),
& 'Um_Advec',k,1,2,bi,bj,myThid)
CALL DIAGNOSTICS_FILL(gV(1-Olx,1-Oly,k,bi,bj),
& 'Vm_Advec',k,1,2,bi,bj,myThid)
IF (momViscosity) THEN
CALL DIAGNOSTICS_FILL(guDiss,'Um_Diss ',k,1,2,bi,bj,myThid)
CALL DIAGNOSTICS_FILL(gvDiss,'Vm_Diss ',k,1,2,bi,bj,myThid)
ENDIF
ENDIF
#endif /* ALLOW_DIAGNOSTICS */
RETURN
END