pkg/mom_fluxform/mom_fluxform.F

C $Header: /u/gcmpack/MITgcm/pkg/mom_fluxform/mom_fluxform.F,v 1.7 2002/11/07 21:51:15 adcroft 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 "CPP_OPTIONS.h"

CBOP
C !ROUTINE: MOM_FLUXFORM

C !INTERFACE: ==========================================================
      SUBROUTINE MOM_FLUXFORM( 
     I        bi,bj,iMin,iMax,jMin,jMax,k,kUp,kDown,
     I        phi_hyd,KappaRU,KappaRV,
     U        fVerU, fVerV,
     I        myTime,myIter,myThid)

C !DESCRIPTION:
C Calculates all the horizontal accelerations except for the implicit surface
C pressure gradient and implciit 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"

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  phi_hyd              :: hydrostatic pressure (perturbation)
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  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 phi_hyd(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
      _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     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  aF                   :: advective flux
C  vF                   :: viscous flux
C  v4F                  :: bi-harmonic viscous flux
C  vrF                  :: vertical viscous flux
C  cF                   :: Coriolis acceleration
C  mT                   :: Metric terms
C  pF                   :: Pressure gradient
C  fZon                 :: zonal fluxes
C  fMer                 :: meridional fluxes
      INTEGER i,j
      _RL aF(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL vF(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL v4F(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL vrF(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 pF(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)
C     wMaskOverride - Land sea flag override for top layer.
C     afFacMom      - Tracer parameters for turning terms
C     vfFacMom        on and off.
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 tracer parameters
      _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)
C     I,J,K - Loop counters
C     rVelMaskOverride - Factor for imposing special surface boundary conditions
C                        ( set according to free-surface condition ).
C     hFacROpen        - Lopped cell factos used tohold fraction of open
C     hFacRClosed        and closed cell wall.
      _RL  rVelMaskOverride
C     xxxFac - On-off tracer parameters used for switching terms off.
      _RL  uDudxFac
      _RL  AhDudxFac
      _RL  A4DuxxdxFac
      _RL  vDudyFac
      _RL  AhDudyFac
      _RL  A4DuyydyFac
      _RL  rVelDudrFac
      _RL  ArDudrFac
      _RL  fuFac
      _RL  phxFac
      _RL  mtFacU
      _RL  uDvdxFac
      _RL  AhDvdxFac
      _RL  A4DvxxdxFac
      _RL  vDvdyFac
      _RL  AhDvdyFac
      _RL  A4DvyydyFac
      _RL  rVelDvdrFac
      _RL  ArDvdrFac
      _RL  fvFac
      _RL  phyFac
      _RL  vForcFac
      _RL  mtFacV
      INTEGER km1,kp1
      _RL wVelBottomOverride
      LOGICAL bottomDragTerms
      _RL KE(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
CEOP

      km1=MAX(1,k-1)
      kp1=MIN(Nr,k+1)
      rVelMaskOverride=1.
      IF ( k .EQ. 1 ) rVelMaskOverride=freeSurfFac
      wVelBottomOverride=1.
      IF (k.EQ.Nr) wVelBottomOverride=0.

C     Initialise intermediate terms
      DO J=1-OLy,sNy+OLy
       DO I=1-OLx,sNx+OLx
        aF(i,j)   = 0.
        vF(i,j)   = 0.
        v4F(i,j)  = 0.
        vrF(i,j)  = 0.
        cF(i,j)   = 0.
        mT(i,j)   = 0.
        pF(i,j)   = 0.
        fZon(i,j) = 0.
        fMer(i,j) = 0.
        rTransU(i,j) = 0.
        rTransV(i,j) = 0.
       ENDDO
      ENDDO

C--   Term by term tracer parmeters
C     o U momentum equation
      uDudxFac     = afFacMom*1.
      AhDudxFac    = vfFacMom*1.
      A4DuxxdxFac  = vfFacMom*1.
      vDudyFac     = afFacMom*1.
      AhDudyFac    = vfFacMom*1.
      A4DuyydyFac  = vfFacMom*1.
      rVelDudrFac  = afFacMom*1.
      ArDudrFac    = vfFacMom*1.
      mTFacU       = mtFacMom*1.
      fuFac        = cfFacMom*1.
      phxFac       = pfFacMom*1.
C     o V momentum equation
      uDvdxFac     = afFacMom*1.
      AhDvdxFac    = vfFacMom*1.
      A4DvxxdxFac  = vfFacMom*1.
      vDvdyFac     = afFacMom*1.
      AhDvdyFac    = vfFacMom*1.
      A4DvyydyFac  = vfFacMom*1.
      rVelDvdrFac  = afFacMom*1.
      ArDvdrFac    = vfFacMom*1.
      mTFacV       = mtFacMom*1.
      fvFac        = cfFacMom*1.
      phyFac       = pfFacMom*1.
      vForcFac     = foFacMom*1.

      IF (     no_slip_bottom
     &    .OR. bottomDragQuadratic.NE.0.
     &    .OR. bottomDragLinear.NE.0.) THEN
       bottomDragTerms=.TRUE.
      ELSE
       bottomDragTerms=.FALSE.
      ENDIF

C-- with stagger time stepping, grad Phi_Hyp is directly incoporated in TIMESTEP
      IF (staggerTimeStep) THEN
        phxFac = 0.
        phyFac = 0.
      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)
     &   *drF(k)*_hFacW(i,j,k,bi,bj)
        yA(i,j) = _dxG(i,j,bi,bj)
     &   *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.
      DO j=1-OLy,sNy+OLy
       DO i=1-OLx,sNx+OLx
        uTrans(i,j) = uFld(i,j)*xA(i,j)
        vTrans(i,j) = vFld(i,j)*yA(i,j)
       ENDDO
      ENDDO

      CALL MOM_CALC_KE(bi,bj,k,uFld,vFld,KE,myThid)

C---  First call (k=1): compute vertical adv. flux fVerU(kUp) & fVerV(kUp)
      IF (momAdvection.AND.k.EQ.1) THEN

C-    Calculate vertical transports above U & V points (West & South face):
       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,af,myThid)
       DO j=jMin,jMax
        DO i=iMin,iMax
         fVerU(i,j,kUp) = af(i,j)
        ENDDO
       ENDDO

       CALL MOM_V_ADV_WV(bi,bj,k,vVel,wVel,rTransV,af,myThid)
       DO j=jMin,jMax
        DO i=iMin,iMax
         fVerV(i,j,kUp) = af(i,j)
        ENDDO
       ENDDO

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


C---- Zonal momentum equation starts here

C     Bi-harmonic term del^2 U -> v4F
      IF (momViscosity)
     & CALL MOM_U_DEL2U(bi,bj,k,uFld,hFacZ,v4f,myThid)

C---  Calculate mean and eddy fluxes between cells for zonal flow.

C--   Zonal flux (fZon is at east face of "u" cell)

C     Mean flow component of zonal flux -> aF
      IF (momAdvection)
     & CALL MOM_U_ADV_UU(bi,bj,k,uTrans,uFld,aF,myThid)

C     Laplacian and bi-harmonic terms -> vF
      IF (momViscosity)
     & CALL MOM_U_XVISCFLUX(bi,bj,k,uFld,v4F,vF,myThid)

C     Combine fluxes -> fZon
      DO j=jMin,jMax
       DO i=iMin,iMax
        fZon(i,j) = uDudxFac*aF(i,j) + AhDudxFac*vF(i,j)
       ENDDO
      ENDDO

C--   Meridional flux (fMer is at south face of "u" cell)

C     Mean flow component of meridional flux
      IF (momAdvection)
     & CALL MOM_U_ADV_VU(bi,bj,k,vTrans,uFld,aF,myThid)

C     Laplacian and bi-harmonic term
      IF (momViscosity)
     & CALL MOM_U_YVISCFLUX(bi,bj,k,uFld,v4F,hFacZ,vF,myThid)

C     Combine fluxes -> fMer
      DO j=jMin,jMax
       DO i=iMin,iMax
        fMer(i,j) = vDudyFac*aF(i,j) + AhDudyFac*vF(i,j)
       ENDDO
      ENDDO

C--   Vertical flux (fVer is at upper face of "u" cell)

C     Mean flow component of vertical flux (at k+1) -> aF
      IF (momAdvection)
     & CALL MOM_U_ADV_WU(bi,bj,k+1,uVel,wVel,rTransU,af,myThid)

C     Eddy component of vertical flux (interior component only) -> vrF
      IF (momViscosity.AND..NOT.implicitViscosity)
     & CALL MOM_U_RVISCFLUX(bi,bj,k,uVel,KappaRU,vrF,myThid)

C     Combine fluxes
      DO j=jMin,jMax
       DO i=iMin,iMax
        fVerU(i,j,kDown) = rVelDudrFac*aF(i,j) + ArDudrFac*vrF(i,j)
       ENDDO
      ENDDO

C---  Hydrostatic term ( -1/rhoConst . dphi/dx )
      IF (momPressureForcing) THEN
       DO j=jMin,jMax
        DO i=iMin,iMax
         pf(i,j) = - _recip_dxC(i,j,bi,bj)
     &    *(phi_hyd(i,j,k)-phi_hyd(i-1,j,k))
        ENDDO
       ENDDO
      ENDIF

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)
#endif
     &  *(fZon(i,j  )          - fZon(i-1,j)
     &   +fMer(i,j+1)          - fMer(i  ,j)
     &   +fVerU(i,j,kUp)*rkFac - fVerU(i,j,kDown)*rkFac
     &   )
     & _PHM( +phxFac * pf(i,j) )
       ENDDO
      ENDDO

#ifdef NONLIN_FRSURF
C-- account for 3.D divergence of the flow in rStar coordinate:
      IF ( momAdvection .AND. 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 ( momAdvection .AND. 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 /* NONLIN_FRSURF */

C-- No-slip and drag BCs appear as body forces in cell abutting topography 
      IF (momViscosity.AND.no_slip_sides) THEN
C-     No-slip BCs impose a drag at walls...
       CALL MOM_U_SIDEDRAG(bi,bj,k,uFld,v4F,hFacZ,vF,myThid)
       DO j=jMin,jMax
        DO i=iMin,iMax
         gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+vF(i,j)
        ENDDO
       ENDDO
      ENDIF
C-    No-slip BCs impose a drag at bottom
      IF (momViscosity.AND.bottomDragTerms) THEN
       CALL MOM_U_BOTTOMDRAG(bi,bj,k,uFld,KE,KappaRU,vF,myThid)
       DO j=jMin,jMax
        DO i=iMin,iMax
         gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+vF(i,j)
        ENDDO
       ENDDO
      ENDIF

C--   Forcing term
      IF (momForcing)
     &  CALL EXTERNAL_FORCING_U(
     I     iMin,iMax,jMin,jMax,bi,bj,k,
     I     myTime,myThid)

C--   Metric terms for curvilinear grid systems
      IF (useNHMTerms) THEN
C      o Non-hydrosatic 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)+mTFacU*mT(i,j)
        ENDDO
       ENDDO
      ENDIF
      IF (usingSphericalPolarMTerms) THEN
       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

C--   Set du/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)
       ENDDO
      ENDDO


C---- Meridional momentum equation starts here

C     Bi-harmonic term del^2 V -> v4F
      IF (momViscosity)
     & CALL MOM_V_DEL2V(bi,bj,k,vFld,hFacZ,v4f,myThid)

C---  Calculate mean and eddy fluxes between cells for meridional flow.

C--   Zonal flux (fZon is at west face of "v" cell)

C     Mean flow component of zonal flux -> aF
      IF (momAdvection)
     & CALL MOM_V_ADV_UV(bi,bj,k,uTrans,vFld,af,myThid)

C     Laplacian and bi-harmonic terms -> vF
      IF (momViscosity)
     & CALL MOM_V_XVISCFLUX(bi,bj,k,vFld,v4f,hFacZ,vf,myThid)

C     Combine fluxes -> fZon
      DO j=jMin,jMax
       DO i=iMin,iMax
        fZon(i,j) = uDvdxFac*aF(i,j) + AhDvdxFac*vF(i,j)
       ENDDO
      ENDDO

C--   Meridional flux (fMer is at north face of "v" cell)

C     Mean flow component of meridional flux
      IF (momAdvection)
     & CALL MOM_V_ADV_VV(bi,bj,k,vTrans,vFld,af,myThid)

C     Laplacian and bi-harmonic term
      IF (momViscosity)
     & CALL MOM_V_YVISCFLUX(bi,bj,k,vFld,v4f,vf,myThid)

C     Combine fluxes -> fMer
      DO j=jMin,jMax
       DO i=iMin,iMax
        fMer(i,j) = vDvdyFac*aF(i,j) + AhDvdyFac*vF(i,j)
       ENDDO
      ENDDO

C--   Vertical flux (fVer is at upper face of "v" cell)

C     o Mean flow component of vertical flux
      IF (momAdvection)
     & CALL MOM_V_ADV_WV(bi,bj,k+1,vVel,wVel,rTransV,af,myThid)

C     Eddy component of vertical flux (interior component only) -> vrF
      IF (momViscosity.AND..NOT.implicitViscosity)
     & CALL MOM_V_RVISCFLUX(bi,bj,k,vVel,KappaRV,vrf,myThid)

C     Combine fluxes -> fVerV
      DO j=jMin,jMax
       DO i=iMin,iMax
        fVerV(i,j,kDown) = rVelDvdrFac*aF(i,j) + ArDvdrFac*vrF(i,j)
       ENDDO
      ENDDO

C---  Hydorstatic term (-1/rhoConst . dphi/dy )
      IF (momPressureForcing) THEN
       DO j=jMin,jMax
        DO i=iMin,iMax
         pF(i,j) = -_recip_dyC(i,j,bi,bj)
     &    *(phi_hyd(i,j,k)-phi_hyd(i,j-1,k))
        ENDDO
       ENDDO
      ENDIF

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)
#endif
     &  *(fZon(i+1,j)          - fZon(i,j  )
     &   +fMer(i,j  )          - fMer(i,j-1)
     &   +fVerV(i,j,kUp)*rkFac - fVerV(i,j,kDown)*rkFac
     &   )
     & _PHM( +phyFac*pf(i,j) )
       ENDDO
      ENDDO

#ifdef NONLIN_FRSURF
C-- account for 3.D divergence of the flow in rStar coordinate:
      IF ( momAdvection .AND. 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 ( momAdvection .AND. 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 /* NONLIN_FRSURF */

C-- No-slip and drag BCs appear as body forces in cell abutting topography 
      IF (momViscosity.AND.no_slip_sides) THEN
C-     No-slip BCs impose a drag at walls...
       CALL MOM_V_SIDEDRAG(bi,bj,k,vFld,v4F,hFacZ,vF,myThid)
       DO j=jMin,jMax
        DO i=iMin,iMax
         gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+vF(i,j)
        ENDDO
       ENDDO
      ENDIF
C-    No-slip BCs impose a drag at bottom
      IF (momViscosity.AND.bottomDragTerms) THEN
       CALL MOM_V_BOTTOMDRAG(bi,bj,k,vFld,KE,KappaRV,vF,myThid)
       DO j=jMin,jMax
        DO i=iMin,iMax
         gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+vF(i,j)
        ENDDO
       ENDDO
      ENDIF

C--   Forcing term
      IF (momForcing)
     & CALL EXTERNAL_FORCING_V(
     I     iMin,iMax,jMin,jMax,bi,bj,k,
     I     myTime,myThid)

C--   Metric terms for curvilinear grid systems
      IF (useNHMTerms) THEN
C      o Spherical polar grid 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)+mTFacV*mT(i,j)
        ENDDO
       ENDDO
      ENDIF
      IF (usingSphericalPolarMTerms) THEN
       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

C--   Set dv/dt on boundaries to zero
      DO j=jMin,jMax
       DO i=iMin,iMax
        gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)*_maskS(i,j,k,bi,bj)
       ENDDO
      ENDDO

C--   Coriolis term
C     Note. As coded here, coriolis will not work with "thin walls"
#ifdef INCLUDE_CD_CODE
      CALL MOM_CDSCHEME(bi,bj,k,phi_hyd,myThid)
#else
      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
      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
#endif /* INCLUDE_CD_CODE */
      IF (nonHydrostatic.OR.quasiHydrostatic) 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
      ENDIF

      RETURN
      END
1	jmc	1.8	C $Header: /u/gcmpack/MITgcm/pkg/mom_fluxform/mom_fluxform.F,v 1.7 2002/11/07 21:51:15 adcroft Exp $
2	adcroft	1.2	C $Name: $
3	adcroft	1.1
4	adcroft	1.3	CBOI
5			C !TITLE: pkg/mom\_advdiff
6			C !AUTHORS: adcroft@mit.edu
7	adcroft	1.4	C !INTRODUCTION: Flux-form Momentum Equations Package
8	adcroft	1.3	C
9			C Package "mom\_fluxform" provides methods for calculating explicit terms
10			C in the momentum equation cast in flux-form:
11			C \begin{eqnarray*}
12			C G^u & = & -\frac{1}{\rho} \partial_x \phi_h
13			C -\nabla \cdot {\bf v} u
14			C -fv
15			C +\frac{1}{\rho} \nabla \cdot {\bf \tau}^x
16			C + \mbox{metrics}
17			C \\
18			C G^v & = & -\frac{1}{\rho} \partial_y \phi_h
19			C -\nabla \cdot {\bf v} v
20			C +fu
21			C +\frac{1}{\rho} \nabla \cdot {\bf \tau}^y
22			C + \mbox{metrics}
23			C \end{eqnarray*}
24			C where ${\bf v}=(u,v,w)$ and $\tau$, the stress tensor, includes surface
25			C stresses as well as internal viscous stresses.
26			CEOI
27
28	adcroft	1.1	#include "CPP_OPTIONS.h"
29
30	adcroft	1.3	CBOP
31			C !ROUTINE: MOM_FLUXFORM
32
33			C !INTERFACE: ==========================================================
34	adcroft	1.1	SUBROUTINE MOM_FLUXFORM(
35			I bi,bj,iMin,iMax,jMin,jMax,k,kUp,kDown,
36			I phi_hyd,KappaRU,KappaRV,
37			U fVerU, fVerV,
38	jmc	1.8	I myTime,myIter,myThid)
39	adcroft	1.3
40			C !DESCRIPTION:
41			C Calculates all the horizontal accelerations except for the implicit surface
42			C pressure gradient and implciit vertical viscosity.
43	adcroft	1.1
44	adcroft	1.3	C !USES: ===============================================================
45	adcroft	1.1	C == Global variables ==
46	adcroft	1.3	IMPLICIT NONE
47	adcroft	1.1	#include "SIZE.h"
48			#include "DYNVARS.h"
49			#include "FFIELDS.h"
50			#include "EEPARAMS.h"
51			#include "PARAMS.h"
52			#include "GRID.h"
53			#include "SURFACE.h"
54
55	adcroft	1.3	C !INPUT PARAMETERS: ===================================================
56			C bi,bj :: tile indices
57			C iMin,iMax,jMin,jMAx :: loop ranges
58			C k :: vertical level
59			C kUp :: =1 or 2 for consecutive k
60			C kDown :: =2 or 1 for consecutive k
61			C phi_hyd :: hydrostatic pressure (perturbation)
62			C KappaRU :: vertical viscosity
63			C KappaRV :: vertical viscosity
64			C fVerU :: vertical flux of U, 2 1/2 dim for pipe-lining
65			C fVerV :: vertical flux of V, 2 1/2 dim for pipe-lining
66	jmc	1.8	C myTime :: current time
67	adcroft	1.3	C myIter :: current time-step number
68			C myThid :: thread number
69			INTEGER bi,bj,iMin,iMax,jMin,jMax
70			INTEGER k,kUp,kDown
71	adcroft	1.1	_RL phi_hyd(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
72			_RL KappaRU(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
73			_RL KappaRV(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
74			_RL fVerU(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2)
75			_RL fVerV(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2)
76	jmc	1.8	_RL myTime
77	adcroft	1.2	INTEGER myIter
78	adcroft	1.1	INTEGER myThid
79
80	adcroft	1.3	C !OUTPUT PARAMETERS: ==================================================
81			C None - updates gU() and gV() in common blocks
82
83			C !LOCAL VARIABLES: ====================================================
84			C i,j :: loop indices
85			C aF :: advective flux
86			C vF :: viscous flux
87			C v4F :: bi-harmonic viscous flux
88			C vrF :: vertical viscous flux
89			C cF :: Coriolis acceleration
90			C mT :: Metric terms
91			C pF :: Pressure gradient
92			C fZon :: zonal fluxes
93			C fMer :: meridional fluxes
94			INTEGER i,j
95			_RL aF(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
96			_RL vF(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
97			_RL v4F(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
98			_RL vrF(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
99			_RL cF(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
100			_RL mT(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
101			_RL pF(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
102			_RL fZon(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
103			_RL fMer(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
104	adcroft	1.1	C wMaskOverride - Land sea flag override for top layer.
105			C afFacMom - Tracer parameters for turning terms
106			C vfFacMom on and off.
107			C pfFacMom afFacMom - Advective terms
108			C cfFacMom vfFacMom - Eddy viscosity terms
109			C mTFacMom pfFacMom - Pressure terms
110			C cfFacMom - Coriolis terms
111			C foFacMom - Forcing
112			C mTFacMom - Metric term
113			C uDudxFac, AhDudxFac, etc ... individual term tracer parameters
114			_RS hFacZ(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
115			_RS r_hFacZ(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
116			_RS xA(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
117			_RS yA(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
118			_RL uTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
119			_RL vTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
120			_RL uFld(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
121			_RL vFld(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
122	jmc	1.8	_RL rTransU(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
123			_RL rTransV(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
124	adcroft	1.1	C I,J,K - Loop counters
125			C rVelMaskOverride - Factor for imposing special surface boundary conditions
126			C ( set according to free-surface condition ).
127			C hFacROpen - Lopped cell factos used tohold fraction of open
128			C hFacRClosed and closed cell wall.
129			_RL rVelMaskOverride
130			C xxxFac - On-off tracer parameters used for switching terms off.
131			_RL uDudxFac
132			_RL AhDudxFac
133			_RL A4DuxxdxFac
134			_RL vDudyFac
135			_RL AhDudyFac
136			_RL A4DuyydyFac
137			_RL rVelDudrFac
138			_RL ArDudrFac
139			_RL fuFac
140			_RL phxFac
141			_RL mtFacU
142			_RL uDvdxFac
143			_RL AhDvdxFac
144			_RL A4DvxxdxFac
145			_RL vDvdyFac
146			_RL AhDvdyFac
147			_RL A4DvyydyFac
148			_RL rVelDvdrFac
149			_RL ArDvdrFac
150			_RL fvFac
151			_RL phyFac
152			_RL vForcFac
153			_RL mtFacV
154			INTEGER km1,kp1
155			_RL wVelBottomOverride
156			LOGICAL bottomDragTerms
157			_RL KE(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
158	adcroft	1.3	CEOP
159	adcroft	1.1
160			km1=MAX(1,k-1)
161			kp1=MIN(Nr,k+1)
162			rVelMaskOverride=1.
163			IF ( k .EQ. 1 ) rVelMaskOverride=freeSurfFac
164			wVelBottomOverride=1.
165			IF (k.EQ.Nr) wVelBottomOverride=0.
166
167			C Initialise intermediate terms
168			DO J=1-OLy,sNy+OLy
169			DO I=1-OLx,sNx+OLx
170			aF(i,j) = 0.
171			vF(i,j) = 0.
172			v4F(i,j) = 0.
173			vrF(i,j) = 0.
174			cF(i,j) = 0.
175			mT(i,j) = 0.
176			pF(i,j) = 0.
177			fZon(i,j) = 0.
178			fMer(i,j) = 0.
179	jmc	1.8	rTransU(i,j) = 0.
180			rTransV(i,j) = 0.
181	adcroft	1.1	ENDDO
182			ENDDO
183
184			C-- Term by term tracer parmeters
185			C o U momentum equation
186			uDudxFac = afFacMom*1.
187			AhDudxFac = vfFacMom*1.
188			A4DuxxdxFac = vfFacMom*1.
189			vDudyFac = afFacMom*1.
190			AhDudyFac = vfFacMom*1.
191			A4DuyydyFac = vfFacMom*1.
192			rVelDudrFac = afFacMom*1.
193			ArDudrFac = vfFacMom*1.
194			mTFacU = mtFacMom*1.
195			fuFac = cfFacMom*1.
196			phxFac = pfFacMom*1.
197			C o V momentum equation
198			uDvdxFac = afFacMom*1.
199			AhDvdxFac = vfFacMom*1.
200			A4DvxxdxFac = vfFacMom*1.
201			vDvdyFac = afFacMom*1.
202			AhDvdyFac = vfFacMom*1.
203			A4DvyydyFac = vfFacMom*1.
204			rVelDvdrFac = afFacMom*1.
205			ArDvdrFac = vfFacMom*1.
206			mTFacV = mtFacMom*1.
207			fvFac = cfFacMom*1.
208			phyFac = pfFacMom*1.
209			vForcFac = foFacMom*1.
210
211			IF ( no_slip_bottom
212			& .OR. bottomDragQuadratic.NE.0.
213			& .OR. bottomDragLinear.NE.0.) THEN
214			bottomDragTerms=.TRUE.
215			ELSE
216			bottomDragTerms=.FALSE.
217			ENDIF
218
219			C-- with stagger time stepping, grad Phi_Hyp is directly incoporated in TIMESTEP
220			IF (staggerTimeStep) THEN
221			phxFac = 0.
222			phyFac = 0.
223			ENDIF
224
225			C-- Calculate open water fraction at vorticity points
226			CALL MOM_CALC_HFACZ(bi,bj,k,hFacZ,r_hFacZ,myThid)
227
228			C---- Calculate common quantities used in both U and V equations
229			C Calculate tracer cell face open areas
230			DO j=1-OLy,sNy+OLy
231			DO i=1-OLx,sNx+OLx
232			xA(i,j) = _dyG(i,j,bi,bj)
233			& drF(k)_hFacW(i,j,k,bi,bj)
234			yA(i,j) = _dxG(i,j,bi,bj)
235			& drF(k)_hFacS(i,j,k,bi,bj)
236			ENDDO
237			ENDDO
238
239			C Make local copies of horizontal flow field
240			DO j=1-OLy,sNy+OLy
241			DO i=1-OLx,sNx+OLx
242			uFld(i,j) = uVel(i,j,k,bi,bj)
243			vFld(i,j) = vVel(i,j,k,bi,bj)
244			ENDDO
245			ENDDO
246
247			C Calculate velocity field "volume transports" through tracer cell faces.
248			DO j=1-OLy,sNy+OLy
249			DO i=1-OLx,sNx+OLx
250			uTrans(i,j) = uFld(i,j)*xA(i,j)
251			vTrans(i,j) = vFld(i,j)*yA(i,j)
252			ENDDO
253			ENDDO
254
255			CALL MOM_CALC_KE(bi,bj,k,uFld,vFld,KE,myThid)
256
257	jmc	1.8	C--- First call (k=1): compute vertical adv. flux fVerU(kUp) & fVerV(kUp)
258			IF (momAdvection.AND.k.EQ.1) THEN
259
260			C- Calculate vertical transports above U & V points (West & South face):
261			CALL MOM_CALC_RTRANS( k, bi, bj,
262			O rTransU, rTransV,
263			I myTime, myIter, myThid)
264
265			C- Free surface correction term (flux at k=1)
266			CALL MOM_U_ADV_WU(bi,bj,k,uVel,wVel,rTransU,af,myThid)
267			DO j=jMin,jMax
268			DO i=iMin,iMax
269			fVerU(i,j,kUp) = af(i,j)
270			ENDDO
271			ENDDO
272
273			CALL MOM_V_ADV_WV(bi,bj,k,vVel,wVel,rTransV,af,myThid)
274			DO j=jMin,jMax
275			DO i=iMin,iMax
276			fVerV(i,j,kUp) = af(i,j)
277			ENDDO
278			ENDDO
279
280			C--- endif momAdvection & k=1
281			ENDIF
282
283
284			C--- Calculate vertical transports (at k+1) below U & V points :
285			IF (momAdvection) THEN
286			CALL MOM_CALC_RTRANS( k+1, bi, bj,
287			O rTransU, rTransV,
288			I myTime, myIter, myThid)
289			ENDIF
290
291
292	adcroft	1.1	C---- Zonal momentum equation starts here
293
294			C Bi-harmonic term del^2 U -> v4F
295			IF (momViscosity)
296			& CALL MOM_U_DEL2U(bi,bj,k,uFld,hFacZ,v4f,myThid)
297
298			C--- Calculate mean and eddy fluxes between cells for zonal flow.
299
300			C-- Zonal flux (fZon is at east face of "u" cell)
301
302			C Mean flow component of zonal flux -> aF
303			IF (momAdvection)
304			& CALL MOM_U_ADV_UU(bi,bj,k,uTrans,uFld,aF,myThid)
305
306			C Laplacian and bi-harmonic terms -> vF
307			IF (momViscosity)
308			& CALL MOM_U_XVISCFLUX(bi,bj,k,uFld,v4F,vF,myThid)
309
310			C Combine fluxes -> fZon
311			DO j=jMin,jMax
312			DO i=iMin,iMax
313			fZon(i,j) = uDudxFacaF(i,j) + AhDudxFacvF(i,j)
314			ENDDO
315			ENDDO
316
317			C-- Meridional flux (fMer is at south face of "u" cell)
318
319			C Mean flow component of meridional flux
320			IF (momAdvection)
321			& CALL MOM_U_ADV_VU(bi,bj,k,vTrans,uFld,aF,myThid)
322
323			C Laplacian and bi-harmonic term
324			IF (momViscosity)
325			& CALL MOM_U_YVISCFLUX(bi,bj,k,uFld,v4F,hFacZ,vF,myThid)
326
327			C Combine fluxes -> fMer
328			DO j=jMin,jMax
329			DO i=iMin,iMax
330			fMer(i,j) = vDudyFacaF(i,j) + AhDudyFacvF(i,j)
331			ENDDO
332			ENDDO
333
334			C-- Vertical flux (fVer is at upper face of "u" cell)
335
336			C Mean flow component of vertical flux (at k+1) -> aF
337			IF (momAdvection)
338	jmc	1.8	& CALL MOM_U_ADV_WU(bi,bj,k+1,uVel,wVel,rTransU,af,myThid)
339	adcroft	1.1
340			C Eddy component of vertical flux (interior component only) -> vrF
341			IF (momViscosity.AND..NOT.implicitViscosity)
342			& CALL MOM_U_RVISCFLUX(bi,bj,k,uVel,KappaRU,vrF,myThid)
343
344			C Combine fluxes
345			DO j=jMin,jMax
346			DO i=iMin,iMax
347			fVerU(i,j,kDown) = rVelDudrFacaF(i,j) + ArDudrFacvrF(i,j)
348			ENDDO
349			ENDDO
350
351			C--- Hydrostatic term ( -1/rhoConst . dphi/dx )
352			IF (momPressureForcing) THEN
353			DO j=jMin,jMax
354			DO i=iMin,iMax
355			pf(i,j) = - _recip_dxC(i,j,bi,bj)
356			& *(phi_hyd(i,j,k)-phi_hyd(i-1,j,k))
357			ENDDO
358			ENDDO
359			ENDIF
360
361			C-- Tendency is minus divergence of the fluxes + coriolis + pressure term
362			DO j=jMin,jMax
363			DO i=iMin,iMax
364			gU(i,j,k,bi,bj) =
365			#ifdef OLD_UV_GEOM
366			& -_recip_hFacW(i,j,k,bi,bj)*recip_drF(k)/
367			& ( 0.5 _d 0*(rA(i,j,bi,bj)+rA(i-1,j,bi,bj)) )
368			#else
369			& -_recip_hFacW(i,j,k,bi,bj)*recip_drF(k)
370			& *recip_rAw(i,j,bi,bj)
371			#endif
372			& *(fZon(i,j ) - fZon(i-1,j)
373			& +fMer(i,j+1) - fMer(i ,j)
374			& +fVerU(i,j,kUp)rkFac - fVerU(i,j,kDown)rkFac
375			& )
376			& _PHM( +phxFac * pf(i,j) )
377			ENDDO
378			ENDDO
379
380	jmc	1.8	#ifdef NONLIN_FRSURF
381			C-- account for 3.D divergence of the flow in rStar coordinate:
382			IF ( momAdvection .AND. select_rStar.GT.0 ) THEN
383			DO j=jMin,jMax
384			DO i=iMin,iMax
385			gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)
386			& - (rStarExpW(i,j,bi,bj) - 1. _d 0)/deltaTfreesurf
387			& *uVel(i,j,k,bi,bj)
388			ENDDO
389			ENDDO
390			ENDIF
391			IF ( momAdvection .AND. select_rStar.LT.0 ) THEN
392			DO j=jMin,jMax
393			DO i=iMin,iMax
394			gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)
395			& - rStarDhWDt(i,j,bi,bj)*uVel(i,j,k,bi,bj)
396			ENDDO
397			ENDDO
398			ENDIF
399			#endif /* NONLIN_FRSURF */
400
401	adcroft	1.1	C-- No-slip and drag BCs appear as body forces in cell abutting topography
402			IF (momViscosity.AND.no_slip_sides) THEN
403			C- No-slip BCs impose a drag at walls...
404			CALL MOM_U_SIDEDRAG(bi,bj,k,uFld,v4F,hFacZ,vF,myThid)
405			DO j=jMin,jMax
406			DO i=iMin,iMax
407			gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+vF(i,j)
408			ENDDO
409			ENDDO
410			ENDIF
411			C- No-slip BCs impose a drag at bottom
412			IF (momViscosity.AND.bottomDragTerms) THEN
413			CALL MOM_U_BOTTOMDRAG(bi,bj,k,uFld,KE,KappaRU,vF,myThid)
414			DO j=jMin,jMax
415			DO i=iMin,iMax
416			gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+vF(i,j)
417			ENDDO
418			ENDDO
419			ENDIF
420
421			C-- Forcing term
422			IF (momForcing)
423			& CALL EXTERNAL_FORCING_U(
424			I iMin,iMax,jMin,jMax,bi,bj,k,
425	jmc	1.8	I myTime,myThid)
426	adcroft	1.1
427			C-- Metric terms for curvilinear grid systems
428	adcroft	1.5	IF (useNHMTerms) THEN
429			C o Non-hydrosatic metric terms
430	adcroft	1.1	CALL MOM_U_METRIC_NH(bi,bj,k,uFld,wVel,mT,myThid)
431			DO j=jMin,jMax
432			DO i=iMin,iMax
433			gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+mTFacU*mT(i,j)
434			ENDDO
435			ENDDO
436	adcroft	1.5	ENDIF
437			IF (usingSphericalPolarMTerms) THEN
438	adcroft	1.1	CALL MOM_U_METRIC_SPHERE(bi,bj,k,uFld,vFld,mT,myThid)
439			DO j=jMin,jMax
440			DO i=iMin,iMax
441			gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+mTFacU*mT(i,j)
442			ENDDO
443			ENDDO
444			ENDIF
445
446			C-- Set du/dt on boundaries to zero
447			DO j=jMin,jMax
448			DO i=iMin,iMax
449			gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)*_maskW(i,j,k,bi,bj)
450			ENDDO
451			ENDDO
452
453
454			C---- Meridional momentum equation starts here
455
456			C Bi-harmonic term del^2 V -> v4F
457			IF (momViscosity)
458			& CALL MOM_V_DEL2V(bi,bj,k,vFld,hFacZ,v4f,myThid)
459
460			C--- Calculate mean and eddy fluxes between cells for meridional flow.
461
462			C-- Zonal flux (fZon is at west face of "v" cell)
463
464			C Mean flow component of zonal flux -> aF
465			IF (momAdvection)
466			& CALL MOM_V_ADV_UV(bi,bj,k,uTrans,vFld,af,myThid)
467
468			C Laplacian and bi-harmonic terms -> vF
469			IF (momViscosity)
470			& CALL MOM_V_XVISCFLUX(bi,bj,k,vFld,v4f,hFacZ,vf,myThid)
471
472			C Combine fluxes -> fZon
473			DO j=jMin,jMax
474			DO i=iMin,iMax
475			fZon(i,j) = uDvdxFacaF(i,j) + AhDvdxFacvF(i,j)
476			ENDDO
477			ENDDO
478
479			C-- Meridional flux (fMer is at north face of "v" cell)
480
481			C Mean flow component of meridional flux
482			IF (momAdvection)
483			& CALL MOM_V_ADV_VV(bi,bj,k,vTrans,vFld,af,myThid)
484
485			C Laplacian and bi-harmonic term
486			IF (momViscosity)
487			& CALL MOM_V_YVISCFLUX(bi,bj,k,vFld,v4f,vf,myThid)
488
489			C Combine fluxes -> fMer
490			DO j=jMin,jMax
491			DO i=iMin,iMax
492			fMer(i,j) = vDvdyFacaF(i,j) + AhDvdyFacvF(i,j)
493			ENDDO
494			ENDDO
495
496			C-- Vertical flux (fVer is at upper face of "v" cell)
497
498			C o Mean flow component of vertical flux
499			IF (momAdvection)
500	jmc	1.8	& CALL MOM_V_ADV_WV(bi,bj,k+1,vVel,wVel,rTransV,af,myThid)
501	adcroft	1.1
502			C Eddy component of vertical flux (interior component only) -> vrF
503			IF (momViscosity.AND..NOT.implicitViscosity)
504			& CALL MOM_V_RVISCFLUX(bi,bj,k,vVel,KappaRV,vrf,myThid)
505
506			C Combine fluxes -> fVerV
507			DO j=jMin,jMax
508			DO i=iMin,iMax
509			fVerV(i,j,kDown) = rVelDvdrFacaF(i,j) + ArDvdrFacvrF(i,j)
510			ENDDO
511			ENDDO
512
513			C--- Hydorstatic term (-1/rhoConst . dphi/dy )
514			IF (momPressureForcing) THEN
515			DO j=jMin,jMax
516			DO i=iMin,iMax
517			pF(i,j) = -_recip_dyC(i,j,bi,bj)
518			& *(phi_hyd(i,j,k)-phi_hyd(i,j-1,k))
519			ENDDO
520			ENDDO
521			ENDIF
522
523			C-- Tendency is minus divergence of the fluxes + coriolis + pressure term
524			DO j=jMin,jMax
525			DO i=iMin,iMax
526			gV(i,j,k,bi,bj) =
527			#ifdef OLD_UV_GEOM
528			& -_recip_hFacS(i,j,k,bi,bj)*recip_drF(k)/
529			& ( 0.5 _d 0*(_rA(i,j,bi,bj)+_rA(i,j-1,bi,bj)) )
530			#else
531			& -_recip_hFacS(i,j,k,bi,bj)*recip_drF(k)
532			& *recip_rAs(i,j,bi,bj)
533			#endif
534			& *(fZon(i+1,j) - fZon(i,j )
535			& +fMer(i,j ) - fMer(i,j-1)
536			& +fVerV(i,j,kUp)rkFac - fVerV(i,j,kDown)rkFac
537			& )
538			& _PHM( +phyFac*pf(i,j) )
539			ENDDO
540			ENDDO
541
542	jmc	1.8	#ifdef NONLIN_FRSURF
543			C-- account for 3.D divergence of the flow in rStar coordinate:
544			IF ( momAdvection .AND. select_rStar.GT.0 ) THEN
545			DO j=jMin,jMax
546			DO i=iMin,iMax
547			gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)
548			& - (rStarExpS(i,j,bi,bj) - 1. _d 0)/deltaTfreesurf
549			& *vVel(i,j,k,bi,bj)
550			ENDDO
551			ENDDO
552			ENDIF
553			IF ( momAdvection .AND. select_rStar.LT.0 ) THEN
554			DO j=jMin,jMax
555			DO i=iMin,iMax
556			gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)
557			& - rStarDhSDt(i,j,bi,bj)*vVel(i,j,k,bi,bj)
558			ENDDO
559			ENDDO
560			ENDIF
561			#endif /* NONLIN_FRSURF */
562
563	adcroft	1.1	C-- No-slip and drag BCs appear as body forces in cell abutting topography
564			IF (momViscosity.AND.no_slip_sides) THEN
565			C- No-slip BCs impose a drag at walls...
566			CALL MOM_V_SIDEDRAG(bi,bj,k,vFld,v4F,hFacZ,vF,myThid)
567			DO j=jMin,jMax
568			DO i=iMin,iMax
569			gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+vF(i,j)
570			ENDDO
571			ENDDO
572			ENDIF
573			C- No-slip BCs impose a drag at bottom
574			IF (momViscosity.AND.bottomDragTerms) THEN
575			CALL MOM_V_BOTTOMDRAG(bi,bj,k,vFld,KE,KappaRV,vF,myThid)
576			DO j=jMin,jMax
577			DO i=iMin,iMax
578			gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+vF(i,j)
579			ENDDO
580			ENDDO
581			ENDIF
582
583			C-- Forcing term
584			IF (momForcing)
585			& CALL EXTERNAL_FORCING_V(
586			I iMin,iMax,jMin,jMax,bi,bj,k,
587	jmc	1.8	I myTime,myThid)
588	adcroft	1.1
589			C-- Metric terms for curvilinear grid systems
590	adcroft	1.5	IF (useNHMTerms) THEN
591	adcroft	1.1	C o Spherical polar grid metric terms
592			CALL MOM_V_METRIC_NH(bi,bj,k,vFld,wVel,mT,myThid)
593			DO j=jMin,jMax
594			DO i=iMin,iMax
595			gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+mTFacV*mT(i,j)
596			ENDDO
597			ENDDO
598	adcroft	1.5	ENDIF
599			IF (usingSphericalPolarMTerms) THEN
600	adcroft	1.1	CALL MOM_V_METRIC_SPHERE(bi,bj,k,uFld,mT,myThid)
601			DO j=jMin,jMax
602			DO i=iMin,iMax
603			gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+mTFacV*mT(i,j)
604			ENDDO
605			ENDDO
606			ENDIF
607
608			C-- Set dv/dt on boundaries to zero
609			DO j=jMin,jMax
610			DO i=iMin,iMax
611			gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)*_maskS(i,j,k,bi,bj)
612			ENDDO
613			ENDDO
614
615			C-- Coriolis term
616			C Note. As coded here, coriolis will not work with "thin walls"
617			#ifdef INCLUDE_CD_CODE
618			CALL MOM_CDSCHEME(bi,bj,k,phi_hyd,myThid)
619			#else
620			CALL MOM_U_CORIOLIS(bi,bj,k,vFld,cf,myThid)
621			DO j=jMin,jMax
622			DO i=iMin,iMax
623			gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+fuFac*cf(i,j)
624			ENDDO
625			ENDDO
626			CALL MOM_V_CORIOLIS(bi,bj,k,uFld,cf,myThid)
627			DO j=jMin,jMax
628			DO i=iMin,iMax
629			gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+fvFac*cf(i,j)
630			ENDDO
631			ENDDO
632			#endif /* INCLUDE_CD_CODE */
633	adcroft	1.7	IF (nonHydrostatic.OR.quasiHydrostatic) THEN
634	adcroft	1.6	CALL MOM_U_CORIOLIS_NH(bi,bj,k,wVel,cf,myThid)
635			DO j=jMin,jMax
636			DO i=iMin,iMax
637			gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+fuFac*cf(i,j)
638			ENDDO
639			ENDDO
640			ENDIF
641	adcroft	1.1
642			RETURN
643			END