pkg/mom_fluxform/mom_fluxform.F

C $Header: /u/gcmpack/MITgcm/pkg/mom_fluxform/mom_fluxform.F,v 1.8 2003/01/26 21:18:50 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 "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,dPhihydX,dPhiHydY,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  dPhiHydX,Y           :: Gradient (X & Y dir.) of Hydrostatic Potential 
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 dPhiHydX(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL dPhiHydY(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _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--   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
     &   )
     &  - phxFac*dPhiHydX(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--   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
     &   )
     &  - phyFac*dPhiHydY(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,dPhiHydX,dPhiHydY,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	1.9	C $Header: /u/gcmpack/MITgcm/pkg/mom_fluxform/mom_fluxform.F,v 1.8 2003/01/26 21:18:50 jmc 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	jmc	1.9	I phi_hyd,dPhihydX,dPhiHydY,KappaRU,KappaRV,
37	adcroft	1.1	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	jmc	1.9	C dPhiHydX,Y :: Gradient (X & Y dir.) of Hydrostatic Potential
63	adcroft	1.3	C KappaRU :: vertical viscosity
64			C KappaRV :: vertical viscosity
65			C fVerU :: vertical flux of U, 2 1/2 dim for pipe-lining
66			C fVerV :: vertical flux of V, 2 1/2 dim for pipe-lining
67	jmc	1.8	C myTime :: current time
68	adcroft	1.3	C myIter :: current time-step number
69			C myThid :: thread number
70			INTEGER bi,bj,iMin,iMax,jMin,jMax
71			INTEGER k,kUp,kDown
72	adcroft	1.1	_RL phi_hyd(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
73	jmc	1.9	_RL dPhiHydX(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
74			_RL dPhiHydY(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
75	adcroft	1.1	_RL KappaRU(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
76			_RL KappaRV(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
77			_RL fVerU(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2)
78			_RL fVerV(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2)
79	jmc	1.8	_RL myTime
80	adcroft	1.2	INTEGER myIter
81	adcroft	1.1	INTEGER myThid
82
83	adcroft	1.3	C !OUTPUT PARAMETERS: ==================================================
84			C None - updates gU() and gV() in common blocks
85
86			C !LOCAL VARIABLES: ====================================================
87			C i,j :: loop indices
88			C aF :: advective flux
89			C vF :: viscous flux
90			C v4F :: bi-harmonic viscous flux
91			C vrF :: vertical viscous flux
92			C cF :: Coriolis acceleration
93			C mT :: Metric terms
94			C pF :: Pressure gradient
95			C fZon :: zonal fluxes
96			C fMer :: meridional fluxes
97			INTEGER i,j
98			_RL aF(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
99			_RL vF(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
100			_RL v4F(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
101			_RL vrF(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
102			_RL cF(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
103			_RL mT(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
104			_RL pF(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
105			_RL fZon(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
106			_RL fMer(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
107	adcroft	1.1	C wMaskOverride - Land sea flag override for top layer.
108			C afFacMom - Tracer parameters for turning terms
109			C vfFacMom on and off.
110			C pfFacMom afFacMom - Advective terms
111			C cfFacMom vfFacMom - Eddy viscosity terms
112			C mTFacMom pfFacMom - Pressure terms
113			C cfFacMom - Coriolis terms
114			C foFacMom - Forcing
115			C mTFacMom - Metric term
116			C uDudxFac, AhDudxFac, etc ... individual term tracer parameters
117			_RS hFacZ(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
118			_RS r_hFacZ(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
119			_RS xA(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
120			_RS yA(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
121			_RL uTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
122			_RL vTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
123			_RL uFld(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
124			_RL vFld(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
125	jmc	1.8	_RL rTransU(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
126			_RL rTransV(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
127	adcroft	1.1	C I,J,K - Loop counters
128			C rVelMaskOverride - Factor for imposing special surface boundary conditions
129			C ( set according to free-surface condition ).
130			C hFacROpen - Lopped cell factos used tohold fraction of open
131			C hFacRClosed and closed cell wall.
132			_RL rVelMaskOverride
133			C xxxFac - On-off tracer parameters used for switching terms off.
134			_RL uDudxFac
135			_RL AhDudxFac
136			_RL A4DuxxdxFac
137			_RL vDudyFac
138			_RL AhDudyFac
139			_RL A4DuyydyFac
140			_RL rVelDudrFac
141			_RL ArDudrFac
142			_RL fuFac
143			_RL phxFac
144			_RL mtFacU
145			_RL uDvdxFac
146			_RL AhDvdxFac
147			_RL A4DvxxdxFac
148			_RL vDvdyFac
149			_RL AhDvdyFac
150			_RL A4DvyydyFac
151			_RL rVelDvdrFac
152			_RL ArDvdrFac
153			_RL fvFac
154			_RL phyFac
155			_RL vForcFac
156			_RL mtFacV
157			INTEGER km1,kp1
158			_RL wVelBottomOverride
159			LOGICAL bottomDragTerms
160			_RL KE(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
161	adcroft	1.3	CEOP
162	adcroft	1.1
163			km1=MAX(1,k-1)
164			kp1=MIN(Nr,k+1)
165			rVelMaskOverride=1.
166			IF ( k .EQ. 1 ) rVelMaskOverride=freeSurfFac
167			wVelBottomOverride=1.
168			IF (k.EQ.Nr) wVelBottomOverride=0.
169
170			C Initialise intermediate terms
171			DO J=1-OLy,sNy+OLy
172			DO I=1-OLx,sNx+OLx
173			aF(i,j) = 0.
174			vF(i,j) = 0.
175			v4F(i,j) = 0.
176			vrF(i,j) = 0.
177			cF(i,j) = 0.
178			mT(i,j) = 0.
179			pF(i,j) = 0.
180			fZon(i,j) = 0.
181			fMer(i,j) = 0.
182	jmc	1.8	rTransU(i,j) = 0.
183			rTransV(i,j) = 0.
184	adcroft	1.1	ENDDO
185			ENDDO
186
187			C-- Term by term tracer parmeters
188			C o U momentum equation
189			uDudxFac = afFacMom*1.
190			AhDudxFac = vfFacMom*1.
191			A4DuxxdxFac = vfFacMom*1.
192			vDudyFac = afFacMom*1.
193			AhDudyFac = vfFacMom*1.
194			A4DuyydyFac = vfFacMom*1.
195			rVelDudrFac = afFacMom*1.
196			ArDudrFac = vfFacMom*1.
197			mTFacU = mtFacMom*1.
198			fuFac = cfFacMom*1.
199			phxFac = pfFacMom*1.
200			C o V momentum equation
201			uDvdxFac = afFacMom*1.
202			AhDvdxFac = vfFacMom*1.
203			A4DvxxdxFac = vfFacMom*1.
204			vDvdyFac = afFacMom*1.
205			AhDvdyFac = vfFacMom*1.
206			A4DvyydyFac = vfFacMom*1.
207			rVelDvdrFac = afFacMom*1.
208			ArDvdrFac = vfFacMom*1.
209			mTFacV = mtFacMom*1.
210			fvFac = cfFacMom*1.
211			phyFac = pfFacMom*1.
212			vForcFac = foFacMom*1.
213
214			IF ( no_slip_bottom
215			& .OR. bottomDragQuadratic.NE.0.
216			& .OR. bottomDragLinear.NE.0.) THEN
217			bottomDragTerms=.TRUE.
218			ELSE
219			bottomDragTerms=.FALSE.
220			ENDIF
221
222			C-- with stagger time stepping, grad Phi_Hyp is directly incoporated in TIMESTEP
223			IF (staggerTimeStep) THEN
224			phxFac = 0.
225			phyFac = 0.
226			ENDIF
227
228			C-- Calculate open water fraction at vorticity points
229			CALL MOM_CALC_HFACZ(bi,bj,k,hFacZ,r_hFacZ,myThid)
230
231			C---- Calculate common quantities used in both U and V equations
232			C Calculate tracer cell face open areas
233			DO j=1-OLy,sNy+OLy
234			DO i=1-OLx,sNx+OLx
235			xA(i,j) = _dyG(i,j,bi,bj)
236			& drF(k)_hFacW(i,j,k,bi,bj)
237			yA(i,j) = _dxG(i,j,bi,bj)
238			& drF(k)_hFacS(i,j,k,bi,bj)
239			ENDDO
240			ENDDO
241
242			C Make local copies of horizontal flow field
243			DO j=1-OLy,sNy+OLy
244			DO i=1-OLx,sNx+OLx
245			uFld(i,j) = uVel(i,j,k,bi,bj)
246			vFld(i,j) = vVel(i,j,k,bi,bj)
247			ENDDO
248			ENDDO
249
250			C Calculate velocity field "volume transports" through tracer cell faces.
251			DO j=1-OLy,sNy+OLy
252			DO i=1-OLx,sNx+OLx
253			uTrans(i,j) = uFld(i,j)*xA(i,j)
254			vTrans(i,j) = vFld(i,j)*yA(i,j)
255			ENDDO
256			ENDDO
257
258			CALL MOM_CALC_KE(bi,bj,k,uFld,vFld,KE,myThid)
259
260	jmc	1.8	C--- First call (k=1): compute vertical adv. flux fVerU(kUp) & fVerV(kUp)
261			IF (momAdvection.AND.k.EQ.1) THEN
262
263			C- Calculate vertical transports above U & V points (West & South face):
264			CALL MOM_CALC_RTRANS( k, bi, bj,
265			O rTransU, rTransV,
266			I myTime, myIter, myThid)
267
268			C- Free surface correction term (flux at k=1)
269			CALL MOM_U_ADV_WU(bi,bj,k,uVel,wVel,rTransU,af,myThid)
270			DO j=jMin,jMax
271			DO i=iMin,iMax
272			fVerU(i,j,kUp) = af(i,j)
273			ENDDO
274			ENDDO
275
276			CALL MOM_V_ADV_WV(bi,bj,k,vVel,wVel,rTransV,af,myThid)
277			DO j=jMin,jMax
278			DO i=iMin,iMax
279			fVerV(i,j,kUp) = af(i,j)
280			ENDDO
281			ENDDO
282
283			C--- endif momAdvection & k=1
284			ENDIF
285
286
287			C--- Calculate vertical transports (at k+1) below U & V points :
288			IF (momAdvection) THEN
289			CALL MOM_CALC_RTRANS( k+1, bi, bj,
290			O rTransU, rTransV,
291			I myTime, myIter, myThid)
292			ENDIF
293
294
295	adcroft	1.1	C---- Zonal momentum equation starts here
296
297			C Bi-harmonic term del^2 U -> v4F
298			IF (momViscosity)
299			& CALL MOM_U_DEL2U(bi,bj,k,uFld,hFacZ,v4f,myThid)
300
301			C--- Calculate mean and eddy fluxes between cells for zonal flow.
302
303			C-- Zonal flux (fZon is at east face of "u" cell)
304
305			C Mean flow component of zonal flux -> aF
306			IF (momAdvection)
307			& CALL MOM_U_ADV_UU(bi,bj,k,uTrans,uFld,aF,myThid)
308
309			C Laplacian and bi-harmonic terms -> vF
310			IF (momViscosity)
311			& CALL MOM_U_XVISCFLUX(bi,bj,k,uFld,v4F,vF,myThid)
312
313			C Combine fluxes -> fZon
314			DO j=jMin,jMax
315			DO i=iMin,iMax
316			fZon(i,j) = uDudxFacaF(i,j) + AhDudxFacvF(i,j)
317			ENDDO
318			ENDDO
319
320			C-- Meridional flux (fMer is at south face of "u" cell)
321
322			C Mean flow component of meridional flux
323			IF (momAdvection)
324			& CALL MOM_U_ADV_VU(bi,bj,k,vTrans,uFld,aF,myThid)
325
326			C Laplacian and bi-harmonic term
327			IF (momViscosity)
328			& CALL MOM_U_YVISCFLUX(bi,bj,k,uFld,v4F,hFacZ,vF,myThid)
329
330			C Combine fluxes -> fMer
331			DO j=jMin,jMax
332			DO i=iMin,iMax
333			fMer(i,j) = vDudyFacaF(i,j) + AhDudyFacvF(i,j)
334			ENDDO
335			ENDDO
336
337			C-- Vertical flux (fVer is at upper face of "u" cell)
338
339			C Mean flow component of vertical flux (at k+1) -> aF
340			IF (momAdvection)
341	jmc	1.8	& CALL MOM_U_ADV_WU(bi,bj,k+1,uVel,wVel,rTransU,af,myThid)
342	adcroft	1.1
343			C Eddy component of vertical flux (interior component only) -> vrF
344			IF (momViscosity.AND..NOT.implicitViscosity)
345			& CALL MOM_U_RVISCFLUX(bi,bj,k,uVel,KappaRU,vrF,myThid)
346
347			C Combine fluxes
348			DO j=jMin,jMax
349			DO i=iMin,iMax
350			fVerU(i,j,kDown) = rVelDudrFacaF(i,j) + ArDudrFacvrF(i,j)
351			ENDDO
352			ENDDO
353
354			C-- Tendency is minus divergence of the fluxes + coriolis + pressure term
355			DO j=jMin,jMax
356			DO i=iMin,iMax
357			gU(i,j,k,bi,bj) =
358			#ifdef OLD_UV_GEOM
359			& -_recip_hFacW(i,j,k,bi,bj)*recip_drF(k)/
360			& ( 0.5 _d 0*(rA(i,j,bi,bj)+rA(i-1,j,bi,bj)) )
361			#else
362			& -_recip_hFacW(i,j,k,bi,bj)*recip_drF(k)
363			& *recip_rAw(i,j,bi,bj)
364			#endif
365			& *(fZon(i,j ) - fZon(i-1,j)
366			& +fMer(i,j+1) - fMer(i ,j)
367			& +fVerU(i,j,kUp)rkFac - fVerU(i,j,kDown)rkFac
368			& )
369	jmc	1.9	& - phxFac*dPhiHydX(i,j)
370	adcroft	1.1	ENDDO
371			ENDDO
372
373	jmc	1.8	#ifdef NONLIN_FRSURF
374			C-- account for 3.D divergence of the flow in rStar coordinate:
375			IF ( momAdvection .AND. select_rStar.GT.0 ) THEN
376			DO j=jMin,jMax
377			DO i=iMin,iMax
378			gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)
379			& - (rStarExpW(i,j,bi,bj) - 1. _d 0)/deltaTfreesurf
380			& *uVel(i,j,k,bi,bj)
381			ENDDO
382			ENDDO
383			ENDIF
384			IF ( momAdvection .AND. select_rStar.LT.0 ) THEN
385			DO j=jMin,jMax
386			DO i=iMin,iMax
387			gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)
388			& - rStarDhWDt(i,j,bi,bj)*uVel(i,j,k,bi,bj)
389			ENDDO
390			ENDDO
391			ENDIF
392			#endif /* NONLIN_FRSURF */
393
394	adcroft	1.1	C-- No-slip and drag BCs appear as body forces in cell abutting topography
395			IF (momViscosity.AND.no_slip_sides) THEN
396			C- No-slip BCs impose a drag at walls...
397			CALL MOM_U_SIDEDRAG(bi,bj,k,uFld,v4F,hFacZ,vF,myThid)
398			DO j=jMin,jMax
399			DO i=iMin,iMax
400			gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+vF(i,j)
401			ENDDO
402			ENDDO
403			ENDIF
404			C- No-slip BCs impose a drag at bottom
405			IF (momViscosity.AND.bottomDragTerms) THEN
406			CALL MOM_U_BOTTOMDRAG(bi,bj,k,uFld,KE,KappaRU,vF,myThid)
407			DO j=jMin,jMax
408			DO i=iMin,iMax
409			gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+vF(i,j)
410			ENDDO
411			ENDDO
412			ENDIF
413
414			C-- Forcing term
415			IF (momForcing)
416			& CALL EXTERNAL_FORCING_U(
417			I iMin,iMax,jMin,jMax,bi,bj,k,
418	jmc	1.8	I myTime,myThid)
419	adcroft	1.1
420			C-- Metric terms for curvilinear grid systems
421	adcroft	1.5	IF (useNHMTerms) THEN
422			C o Non-hydrosatic metric terms
423	adcroft	1.1	CALL MOM_U_METRIC_NH(bi,bj,k,uFld,wVel,mT,myThid)
424			DO j=jMin,jMax
425			DO i=iMin,iMax
426			gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+mTFacU*mT(i,j)
427			ENDDO
428			ENDDO
429	adcroft	1.5	ENDIF
430			IF (usingSphericalPolarMTerms) THEN
431	adcroft	1.1	CALL MOM_U_METRIC_SPHERE(bi,bj,k,uFld,vFld,mT,myThid)
432			DO j=jMin,jMax
433			DO i=iMin,iMax
434			gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+mTFacU*mT(i,j)
435			ENDDO
436			ENDDO
437			ENDIF
438
439			C-- Set du/dt on boundaries to zero
440			DO j=jMin,jMax
441			DO i=iMin,iMax
442			gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)*_maskW(i,j,k,bi,bj)
443			ENDDO
444			ENDDO
445
446
447			C---- Meridional momentum equation starts here
448
449			C Bi-harmonic term del^2 V -> v4F
450			IF (momViscosity)
451			& CALL MOM_V_DEL2V(bi,bj,k,vFld,hFacZ,v4f,myThid)
452
453			C--- Calculate mean and eddy fluxes between cells for meridional flow.
454
455			C-- Zonal flux (fZon is at west face of "v" cell)
456
457			C Mean flow component of zonal flux -> aF
458			IF (momAdvection)
459			& CALL MOM_V_ADV_UV(bi,bj,k,uTrans,vFld,af,myThid)
460
461			C Laplacian and bi-harmonic terms -> vF
462			IF (momViscosity)
463			& CALL MOM_V_XVISCFLUX(bi,bj,k,vFld,v4f,hFacZ,vf,myThid)
464
465			C Combine fluxes -> fZon
466			DO j=jMin,jMax
467			DO i=iMin,iMax
468			fZon(i,j) = uDvdxFacaF(i,j) + AhDvdxFacvF(i,j)
469			ENDDO
470			ENDDO
471
472			C-- Meridional flux (fMer is at north face of "v" cell)
473
474			C Mean flow component of meridional flux
475			IF (momAdvection)
476			& CALL MOM_V_ADV_VV(bi,bj,k,vTrans,vFld,af,myThid)
477
478			C Laplacian and bi-harmonic term
479			IF (momViscosity)
480			& CALL MOM_V_YVISCFLUX(bi,bj,k,vFld,v4f,vf,myThid)
481
482			C Combine fluxes -> fMer
483			DO j=jMin,jMax
484			DO i=iMin,iMax
485			fMer(i,j) = vDvdyFacaF(i,j) + AhDvdyFacvF(i,j)
486			ENDDO
487			ENDDO
488
489			C-- Vertical flux (fVer is at upper face of "v" cell)
490
491			C o Mean flow component of vertical flux
492			IF (momAdvection)
493	jmc	1.8	& CALL MOM_V_ADV_WV(bi,bj,k+1,vVel,wVel,rTransV,af,myThid)
494	adcroft	1.1
495			C Eddy component of vertical flux (interior component only) -> vrF
496			IF (momViscosity.AND..NOT.implicitViscosity)
497			& CALL MOM_V_RVISCFLUX(bi,bj,k,vVel,KappaRV,vrf,myThid)
498
499			C Combine fluxes -> fVerV
500			DO j=jMin,jMax
501			DO i=iMin,iMax
502			fVerV(i,j,kDown) = rVelDvdrFacaF(i,j) + ArDvdrFacvrF(i,j)
503			ENDDO
504			ENDDO
505
506			C-- Tendency is minus divergence of the fluxes + coriolis + pressure term
507			DO j=jMin,jMax
508			DO i=iMin,iMax
509			gV(i,j,k,bi,bj) =
510			#ifdef OLD_UV_GEOM
511			& -_recip_hFacS(i,j,k,bi,bj)*recip_drF(k)/
512			& ( 0.5 _d 0*(_rA(i,j,bi,bj)+_rA(i,j-1,bi,bj)) )
513			#else
514			& -_recip_hFacS(i,j,k,bi,bj)*recip_drF(k)
515			& *recip_rAs(i,j,bi,bj)
516			#endif
517			& *(fZon(i+1,j) - fZon(i,j )
518			& +fMer(i,j ) - fMer(i,j-1)
519			& +fVerV(i,j,kUp)rkFac - fVerV(i,j,kDown)rkFac
520			& )
521	jmc	1.9	& - phyFac*dPhiHydY(i,j)
522	adcroft	1.1	ENDDO
523			ENDDO
524
525	jmc	1.8	#ifdef NONLIN_FRSURF
526			C-- account for 3.D divergence of the flow in rStar coordinate:
527			IF ( momAdvection .AND. select_rStar.GT.0 ) THEN
528			DO j=jMin,jMax
529			DO i=iMin,iMax
530			gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)
531			& - (rStarExpS(i,j,bi,bj) - 1. _d 0)/deltaTfreesurf
532			& *vVel(i,j,k,bi,bj)
533			ENDDO
534			ENDDO
535			ENDIF
536			IF ( momAdvection .AND. select_rStar.LT.0 ) THEN
537			DO j=jMin,jMax
538			DO i=iMin,iMax
539			gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)
540			& - rStarDhSDt(i,j,bi,bj)*vVel(i,j,k,bi,bj)
541			ENDDO
542			ENDDO
543			ENDIF
544			#endif /* NONLIN_FRSURF */
545
546	adcroft	1.1	C-- No-slip and drag BCs appear as body forces in cell abutting topography
547			IF (momViscosity.AND.no_slip_sides) THEN
548			C- No-slip BCs impose a drag at walls...
549			CALL MOM_V_SIDEDRAG(bi,bj,k,vFld,v4F,hFacZ,vF,myThid)
550			DO j=jMin,jMax
551			DO i=iMin,iMax
552			gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+vF(i,j)
553			ENDDO
554			ENDDO
555			ENDIF
556			C- No-slip BCs impose a drag at bottom
557			IF (momViscosity.AND.bottomDragTerms) THEN
558			CALL MOM_V_BOTTOMDRAG(bi,bj,k,vFld,KE,KappaRV,vF,myThid)
559			DO j=jMin,jMax
560			DO i=iMin,iMax
561			gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+vF(i,j)
562			ENDDO
563			ENDDO
564			ENDIF
565
566			C-- Forcing term
567			IF (momForcing)
568			& CALL EXTERNAL_FORCING_V(
569			I iMin,iMax,jMin,jMax,bi,bj,k,
570	jmc	1.8	I myTime,myThid)
571	adcroft	1.1
572			C-- Metric terms for curvilinear grid systems
573	adcroft	1.5	IF (useNHMTerms) THEN
574	adcroft	1.1	C o Spherical polar grid metric terms
575			CALL MOM_V_METRIC_NH(bi,bj,k,vFld,wVel,mT,myThid)
576			DO j=jMin,jMax
577			DO i=iMin,iMax
578			gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+mTFacV*mT(i,j)
579			ENDDO
580			ENDDO
581	adcroft	1.5	ENDIF
582			IF (usingSphericalPolarMTerms) THEN
583	adcroft	1.1	CALL MOM_V_METRIC_SPHERE(bi,bj,k,uFld,mT,myThid)
584			DO j=jMin,jMax
585			DO i=iMin,iMax
586			gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+mTFacV*mT(i,j)
587			ENDDO
588			ENDDO
589			ENDIF
590
591			C-- Set dv/dt on boundaries to zero
592			DO j=jMin,jMax
593			DO i=iMin,iMax
594			gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)*_maskS(i,j,k,bi,bj)
595			ENDDO
596			ENDDO
597
598			C-- Coriolis term
599			C Note. As coded here, coriolis will not work with "thin walls"
600			#ifdef INCLUDE_CD_CODE
601	jmc	1.9	CALL MOM_CDSCHEME(bi,bj,k,phi_hyd,dPhiHydX,dPhiHydY,myThid)
602	adcroft	1.1	#else
603			CALL MOM_U_CORIOLIS(bi,bj,k,vFld,cf,myThid)
604			DO j=jMin,jMax
605			DO i=iMin,iMax
606			gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+fuFac*cf(i,j)
607			ENDDO
608			ENDDO
609			CALL MOM_V_CORIOLIS(bi,bj,k,uFld,cf,myThid)
610			DO j=jMin,jMax
611			DO i=iMin,iMax
612			gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+fvFac*cf(i,j)
613			ENDDO
614			ENDDO
615			#endif /* INCLUDE_CD_CODE */
616	adcroft	1.7	IF (nonHydrostatic.OR.quasiHydrostatic) THEN
617	adcroft	1.6	CALL MOM_U_CORIOLIS_NH(bi,bj,k,wVel,cf,myThid)
618			DO j=jMin,jMax
619			DO i=iMin,iMax
620			gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+fuFac*cf(i,j)
621			ENDDO
622			ENDDO
623			ENDIF
624	adcroft	1.1
625			RETURN
626			END