pkg/mom_vecinv/mom_vecinv.F

C $Header: /u/gcmpack/MITgcm/pkg/mom_vecinv/mom_vecinv.F,v 1.4 2003/02/08 02:10:57 jmc Exp $
C $Name:  $

#include "CPP_OPTIONS.h"

      SUBROUTINE MOM_VECINV( 
     I        bi,bj,iMin,iMax,jMin,jMax,k,kUp,kDown,
     I        dPhiHydX,dPhiHydY,KappaRU,KappaRV,
     U        fVerU, fVerV,
     I        myCurrentTime, myIter, myThid)
C     /==========================================================\
C     | S/R MOM_VECINV                                           |
C     | o Form the right hand-side of the momentum equation.     |
C     |==========================================================|
C     | Terms are evaluated one layer at a time working from     |
C     | the bottom to the top. The vertically integrated         |
C     | barotropic flow tendency term is evluated by summing the |
C     | tendencies.                                              |
C     | Notes:                                                   |
C     | We have not sorted out an entirely satisfactory formula  |
C     | for the diffusion equation bc with lopping. The present  |
C     | form produces a diffusive flux that does not scale with  |
C     | open-area. Need to do something to solidfy this and to   |
C     | deal "properly" with thin walls.                         |
C     \==========================================================/
      IMPLICIT NONE

C     == Global variables ==
#include "SIZE.h"
#include "DYNVARS.h"
#include "EEPARAMS.h"
#include "PARAMS.h"
#include "GRID.h"

C     == Routine arguments ==
C     fVerU   - Flux of momentum in the vertical
C     fVerV     direction out of the upper face of a cell K
C               ( flux into the cell above ).
C     dPhiHydX,Y :: Gradient (X & Y dir.) of Hydrostatic Potential
C     bi, bj, iMin, iMax, jMin, jMax - Range of points for which calculation
C                                      results will be set.
C     kUp, kDown                     - Index for upper and lower layers.
C     myThid - Instance number for this innvocation of CALC_MOM_RHS
      _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)
      INTEGER kUp,kDown
      _RL     myCurrentTime
      INTEGER myIter
      INTEGER myThid
      INTEGER bi,bj,iMin,iMax,jMin,jMax

C     == Functions ==
      LOGICAL  DIFFERENT_MULTIPLE
      EXTERNAL DIFFERENT_MULTIPLE

C     == Local variables ==
      _RL      aF (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL      vF (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL      vrF (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL      uCf (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL      vCf (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 del2u(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL del2v(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL tension(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL strain(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _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 dStar(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL zStar(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL uDiss(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL vDiss(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
C     I,J,K - Loop counters
      INTEGER i,j,k
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)
      _RL omega3(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)

      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.
        vrF(i,j)  = 0.
        uCf(i,j)   = 0.
        vCf(i,j)   = 0.
        mT(i,j)   = 0.
        pF(i,j)   = 0.
        del2u(i,j) = 0.
        del2v(i,j) = 0.
        dStar(i,j) = 0.
        zStar(i,j) = 0.
        uDiss(i,j) = 0.
        vDiss(i,j) = 0.
        vort3(i,j) = 0.
        omega3(i,j) = 0.
        ke(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_VI_CALC_KE(bi,bj,k,uFld,vFld,KE,myThid)

      CALL MOM_VI_CALC_HDIV(bi,bj,k,uFld,vFld,hDiv,myThid)

      CALL MOM_VI_CALC_RELVORT3(bi,bj,k,uFld,vFld,hFacZ,vort3,myThid)

c     CALL MOM_VI_CALC_ABSVORT3(bi,bj,k,vort3,omega3,myThid)

      IF (momViscosity) THEN
C      Calculate del^2 u and del^2 v for bi-harmonic term
       IF (viscA4.NE.0.) THEN
         CALL MOM_VI_DEL2UV(bi,bj,k,hDiv,vort3,hFacZ,
     O                      del2u,del2v,
     &                      myThid)
         CALL MOM_VI_CALC_HDIV(bi,bj,k,del2u,del2v,dStar,myThid)
         CALL MOM_VI_CALC_RELVORT3(
     &                         bi,bj,k,del2u,del2v,hFacZ,zStar,myThid)
       ENDIF
C      Calculate dissipation terms for U and V equations
C      in terms of vorticity and divergence
       IF (viscAh.NE.0. .OR. viscA4.NE.0.) THEN
         CALL MOM_VI_HDISSIP(bi,bj,k,hDiv,vort3,hFacZ,dStar,zStar,
     O                       uDiss,vDiss,
     &                       myThid)
       ENDIF
C      or in terms of tension and strain
       IF (viscAstrain.NE.0. .OR. viscAtension.NE.0.) THEN
         CALL MOM_CALC_TENSION(bi,bj,k,uFld,vFld,
     O                         tension,
     I                         myThid)
         CALL MOM_CALC_STRAIN(bi,bj,k,uFld,vFld,hFacZ,
     O                        strain,
     I                        myThid)
         CALL MOM_HDISSIP(bi,bj,k,
     I                    tension,strain,hFacZ,viscAtension,viscAstrain,
     O                    uDiss,vDiss,
     I                    myThid)
       ENDIF
      ENDIF

C---- Zonal momentum equation starts here

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

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) = ArDudrFac*vrF(i,j)
       ENDDO
      ENDDO

C--   Tendency is minus divergence of the fluxes + coriolis + pressure term
      DO j=2-Oly,sNy+Oly-1
       DO i=2-Olx,sNx+Olx-1
        gU(i,j,k,bi,bj) = uDiss(i,j)
     &   -_recip_hFacW(i,j,k,bi,bj)*recip_drF(k)
     &   *recip_rAw(i,j,bi,bj)
     &  *(
     &   +fVerU(i,j,kUp)*rkFac - fVerU(i,j,kDown)*rkFac
     &   )
     &  - phxFac*dPhiHydX(i,j)
       ENDDO
      ENDDO

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,del2u,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     myCurrentTime,myThid)

C--   Metric terms for curvilinear grid systems
c     IF (usingSphericalPolarMTerms) THEN
C      o Spherical polar grid metric terms
c      CALL MOM_U_METRIC_NH(bi,bj,k,uFld,wVel,mT,myThid)
c      DO j=jMin,jMax
c       DO i=iMin,iMax
c        gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+mTFacU*mT(i,j)
c       ENDDO
c      ENDDO
c     ENDIF


C---- Meridional momentum equation starts here

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

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) = 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) = vDiss(i,j)
     &   -_recip_hFacS(i,j,k,bi,bj)*recip_drF(k)
     &    *recip_rAs(i,j,bi,bj)
     &  *(
     &   +fVerV(i,j,kUp)*rkFac - fVerV(i,j,kDown)*rkFac
     &   )
     &  - phyFac*dPhiHydY(i,j)
       ENDDO
      ENDDO

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,del2v,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     myCurrentTime,myThid)

C--   Metric terms for curvilinear grid systems
c     IF (usingSphericalPolarMTerms) THEN
C      o Spherical polar grid metric terms
c      CALL MOM_V_METRIC_NH(bi,bj,k,vFld,wVel,mT,myThid)
c      DO j=jMin,jMax
c       DO i=iMin,iMax
c        gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+mTFacV*mT(i,j)
c       ENDDO
c      ENDDO
c     ENDIF

C--   Horizontal Coriolis terms
      IF (useCoriolis) THEN
       CALL MOM_VI_CORIOLIS(bi,bj,K,uFld,vFld,omega3,r_hFacZ,
     &                      uCf,vCf,myThid)
       DO j=jMin,jMax
        DO i=iMin,iMax
         gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+uCf(i,j)
         gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+vCf(i,j)
        ENDDO
       ENDDO
      ENDIF

      IF (momAdvection) THEN
C--   Horizontal advection of relative vorticity
c      CALL MOM_VI_U_CORIOLIS(bi,bj,K,vFld,omega3,r_hFacZ,uCf,myThid)
       CALL MOM_VI_U_CORIOLIS(bi,bj,K,vFld,vort3,r_hFacZ,uCf,myThid)
c      CALL MOM_VI_U_CORIOLIS_C4(bi,bj,K,vFld,vort3,r_hFacZ,uCf,myThid)
       DO j=jMin,jMax
        DO i=iMin,iMax
         gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+uCf(i,j)
        ENDDO
       ENDDO
c      CALL MOM_VI_V_CORIOLIS(bi,bj,K,uFld,omega3,r_hFacZ,vCf,myThid)
       CALL MOM_VI_V_CORIOLIS(bi,bj,K,uFld,vort3,r_hFacZ,vCf,myThid)
c      CALL MOM_VI_V_CORIOLIS_C4(bi,bj,K,uFld,vort3,r_hFacZ,vCf,myThid)
       DO j=jMin,jMax
        DO i=iMin,iMax
         gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+vCf(i,j)
        ENDDO
       ENDDO

C--   Vertical shear terms (-w*du/dr & -w*dv/dr)
       CALL MOM_VI_U_VERTSHEAR(bi,bj,K,uVel,wVel,uCf,myThid)
       DO j=jMin,jMax
        DO i=iMin,iMax
         gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+uCf(i,j)
        ENDDO
       ENDDO
       CALL MOM_VI_V_VERTSHEAR(bi,bj,K,vVel,wVel,vCf,myThid)
       DO j=jMin,jMax
        DO i=iMin,iMax
         gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+vCf(i,j)
        ENDDO
       ENDDO

C--   Bernoulli term
       CALL MOM_VI_U_GRAD_KE(bi,bj,K,KE,uCf,myThid)
       DO j=jMin,jMax
        DO i=iMin,iMax
         gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+uCf(i,j)
        ENDDO
       ENDDO
       CALL MOM_VI_V_GRAD_KE(bi,bj,K,KE,vCf,myThid)
       DO j=jMin,jMax
        DO i=iMin,iMax
         gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+vCf(i,j)
        ENDDO
       ENDDO
C--   end if momAdvection
      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)
        gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)*_maskS(i,j,k,bi,bj)
       ENDDO
      ENDDO


      IF (
     &  DIFFERENT_MULTIPLE(diagFreq,myCurrentTime,
     &                     myCurrentTime-deltaTClock)
     & ) THEN
       CALL WRITE_LOCAL_RL('Ds','I10',1,strain,bi,bj,k,myIter,myThid)
       CALL WRITE_LOCAL_RL('Dt','I10',1,tension,bi,bj,k,myIter,myThid)
       CALL WRITE_LOCAL_RL('fV','I10',1,uCf,bi,bj,k,myIter,myThid)
       CALL WRITE_LOCAL_RL('fU','I10',1,vCf,bi,bj,k,myIter,myThid)
       CALL WRITE_LOCAL_RL('Du','I10',1,uDiss,bi,bj,k,myIter,myThid)
       CALL WRITE_LOCAL_RL('Dv','I10',1,vDiss,bi,bj,k,myIter,myThid)
       CALL WRITE_LOCAL_RL('Z3','I10',1,vort3,bi,bj,k,myIter,myThid)
c      CALL WRITE_LOCAL_RL('W3','I10',1,omega3,bi,bj,k,myIter,myThid)
       CALL WRITE_LOCAL_RL('KE','I10',1,KE,bi,bj,k,myIter,myThid)
       CALL WRITE_LOCAL_RL('D','I10',1,hdiv,bi,bj,k,myIter,myThid)
      ENDIF

      RETURN
      END
1	jmc	1.5	C $Header: /u/gcmpack/MITgcm/pkg/mom_vecinv/mom_vecinv.F,v 1.4 2003/02/08 02:10:57 jmc Exp $
2	adcroft	1.2	C $Name: $
3	adcroft	1.1
4			#include "CPP_OPTIONS.h"
5
6			SUBROUTINE MOM_VECINV(
7			I bi,bj,iMin,iMax,jMin,jMax,k,kUp,kDown,
8	jmc	1.4	I dPhiHydX,dPhiHydY,KappaRU,KappaRV,
9	adcroft	1.1	U fVerU, fVerV,
10	adcroft	1.2	I myCurrentTime, myIter, myThid)
11	adcroft	1.1	C /==========================================================\
12			C \| S/R MOM_VECINV \|
13			C \| o Form the right hand-side of the momentum equation. \|
14			C \|==========================================================\|
15			C \| Terms are evaluated one layer at a time working from \|
16			C \| the bottom to the top. The vertically integrated \|
17			C \| barotropic flow tendency term is evluated by summing the \|
18			C \| tendencies. \|
19			C \| Notes: \|
20			C \| We have not sorted out an entirely satisfactory formula \|
21			C \| for the diffusion equation bc with lopping. The present \|
22			C \| form produces a diffusive flux that does not scale with \|
23			C \| open-area. Need to do something to solidfy this and to \|
24			C \| deal "properly" with thin walls. \|
25			C \==========================================================/
26			IMPLICIT NONE
27
28			C == Global variables ==
29			#include "SIZE.h"
30			#include "DYNVARS.h"
31			#include "EEPARAMS.h"
32			#include "PARAMS.h"
33			#include "GRID.h"
34
35			C == Routine arguments ==
36			C fVerU - Flux of momentum in the vertical
37			C fVerV direction out of the upper face of a cell K
38			C ( flux into the cell above ).
39	jmc	1.4	C dPhiHydX,Y :: Gradient (X & Y dir.) of Hydrostatic Potential
40	adcroft	1.1	C bi, bj, iMin, iMax, jMin, jMax - Range of points for which calculation
41			C results will be set.
42			C kUp, kDown - Index for upper and lower layers.
43			C myThid - Instance number for this innvocation of CALC_MOM_RHS
44	jmc	1.4	_RL dPhiHydX(1-Olx:sNx+Olx,1-Oly:sNy+Oly)
45			_RL dPhiHydY(1-Olx:sNx+Olx,1-Oly:sNy+Oly)
46	adcroft	1.1	_RL KappaRU(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
47			_RL KappaRV(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
48			_RL fVerU(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2)
49			_RL fVerV(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2)
50			INTEGER kUp,kDown
51	adcroft	1.2	_RL myCurrentTime
52			INTEGER myIter
53	adcroft	1.1	INTEGER myThid
54			INTEGER bi,bj,iMin,iMax,jMin,jMax
55
56	adcroft	1.2	C == Functions ==
57			LOGICAL DIFFERENT_MULTIPLE
58			EXTERNAL DIFFERENT_MULTIPLE
59
60	adcroft	1.1	C == Local variables ==
61			_RL aF (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
62			_RL vF (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
63			_RL vrF (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
64			_RL uCf (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
65			_RL vCf (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
66			_RL mT (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
67			_RL pF (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
68			_RL del2u(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
69			_RL del2v(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
70	adcroft	1.3	_RL tension(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
71			_RL strain(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
72	adcroft	1.1	_RS hFacZ(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
73			_RS r_hFacZ(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
74			_RS xA(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
75			_RS yA(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
76			_RL uTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
77			_RL vTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
78			_RL uFld(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
79			_RL vFld(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
80			_RL dStar(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
81			_RL zStar(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
82			_RL uDiss(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
83			_RL vDiss(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
84			C I,J,K - Loop counters
85			INTEGER i,j,k
86			C rVelMaskOverride - Factor for imposing special surface boundary conditions
87			C ( set according to free-surface condition ).
88			C hFacROpen - Lopped cell factos used tohold fraction of open
89			C hFacRClosed and closed cell wall.
90			_RL rVelMaskOverride
91			C xxxFac - On-off tracer parameters used for switching terms off.
92			_RL uDudxFac
93			_RL AhDudxFac
94			_RL A4DuxxdxFac
95			_RL vDudyFac
96			_RL AhDudyFac
97			_RL A4DuyydyFac
98			_RL rVelDudrFac
99			_RL ArDudrFac
100			_RL fuFac
101			_RL phxFac
102			_RL mtFacU
103			_RL uDvdxFac
104			_RL AhDvdxFac
105			_RL A4DvxxdxFac
106			_RL vDvdyFac
107			_RL AhDvdyFac
108			_RL A4DvyydyFac
109			_RL rVelDvdrFac
110			_RL ArDvdrFac
111			_RL fvFac
112			_RL phyFac
113			_RL vForcFac
114			_RL mtFacV
115			INTEGER km1,kp1
116			_RL wVelBottomOverride
117			LOGICAL bottomDragTerms
118			_RL KE(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
119			_RL omega3(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
120			_RL vort3(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
121			_RL hDiv(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
122
123			km1=MAX(1,k-1)
124			kp1=MIN(Nr,k+1)
125			rVelMaskOverride=1.
126			IF ( k .EQ. 1 ) rVelMaskOverride=freeSurfFac
127			wVelBottomOverride=1.
128			IF (k.EQ.Nr) wVelBottomOverride=0.
129
130			C Initialise intermediate terms
131			DO J=1-OLy,sNy+OLy
132			DO I=1-OLx,sNx+OLx
133			aF(i,j) = 0.
134			vF(i,j) = 0.
135			vrF(i,j) = 0.
136			uCf(i,j) = 0.
137			vCf(i,j) = 0.
138			mT(i,j) = 0.
139			pF(i,j) = 0.
140			del2u(i,j) = 0.
141			del2v(i,j) = 0.
142			dStar(i,j) = 0.
143			zStar(i,j) = 0.
144			uDiss(i,j) = 0.
145			vDiss(i,j) = 0.
146			vort3(i,j) = 0.
147			omega3(i,j) = 0.
148			ke(i,j) = 0.
149			ENDDO
150			ENDDO
151
152			C-- Term by term tracer parmeters
153			C o U momentum equation
154			uDudxFac = afFacMom*1.
155			AhDudxFac = vfFacMom*1.
156			A4DuxxdxFac = vfFacMom*1.
157			vDudyFac = afFacMom*1.
158			AhDudyFac = vfFacMom*1.
159			A4DuyydyFac = vfFacMom*1.
160			rVelDudrFac = afFacMom*1.
161			ArDudrFac = vfFacMom*1.
162			mTFacU = mtFacMom*1.
163			fuFac = cfFacMom*1.
164			phxFac = pfFacMom*1.
165			C o V momentum equation
166			uDvdxFac = afFacMom*1.
167			AhDvdxFac = vfFacMom*1.
168			A4DvxxdxFac = vfFacMom*1.
169			vDvdyFac = afFacMom*1.
170			AhDvdyFac = vfFacMom*1.
171			A4DvyydyFac = vfFacMom*1.
172			rVelDvdrFac = afFacMom*1.
173			ArDvdrFac = vfFacMom*1.
174			mTFacV = mtFacMom*1.
175			fvFac = cfFacMom*1.
176			phyFac = pfFacMom*1.
177			vForcFac = foFacMom*1.
178
179			IF ( no_slip_bottom
180			& .OR. bottomDragQuadratic.NE.0.
181			& .OR. bottomDragLinear.NE.0.) THEN
182			bottomDragTerms=.TRUE.
183			ELSE
184			bottomDragTerms=.FALSE.
185			ENDIF
186
187			C-- with stagger time stepping, grad Phi_Hyp is directly incoporated in TIMESTEP
188			IF (staggerTimeStep) THEN
189			phxFac = 0.
190			phyFac = 0.
191			ENDIF
192
193			C-- Calculate open water fraction at vorticity points
194			CALL MOM_CALC_HFACZ(bi,bj,k,hFacZ,r_hFacZ,myThid)
195
196			C---- Calculate common quantities used in both U and V equations
197			C Calculate tracer cell face open areas
198			DO j=1-OLy,sNy+OLy
199			DO i=1-OLx,sNx+OLx
200			xA(i,j) = _dyG(i,j,bi,bj)
201			& drF(k)_hFacW(i,j,k,bi,bj)
202			yA(i,j) = _dxG(i,j,bi,bj)
203			& drF(k)_hFacS(i,j,k,bi,bj)
204			ENDDO
205			ENDDO
206
207			C Make local copies of horizontal flow field
208			DO j=1-OLy,sNy+OLy
209			DO i=1-OLx,sNx+OLx
210			uFld(i,j) = uVel(i,j,k,bi,bj)
211			vFld(i,j) = vVel(i,j,k,bi,bj)
212			ENDDO
213			ENDDO
214
215			C Calculate velocity field "volume transports" through tracer cell faces.
216			DO j=1-OLy,sNy+OLy
217			DO i=1-OLx,sNx+OLx
218			uTrans(i,j) = uFld(i,j)*xA(i,j)
219			vTrans(i,j) = vFld(i,j)*yA(i,j)
220			ENDDO
221			ENDDO
222
223			CALL MOM_VI_CALC_KE(bi,bj,k,uFld,vFld,KE,myThid)
224
225			CALL MOM_VI_CALC_HDIV(bi,bj,k,uFld,vFld,hDiv,myThid)
226
227			CALL MOM_VI_CALC_RELVORT3(bi,bj,k,uFld,vFld,hFacZ,vort3,myThid)
228
229	jmc	1.5	c CALL MOM_VI_CALC_ABSVORT3(bi,bj,k,vort3,omega3,myThid)
230	adcroft	1.1
231			IF (momViscosity) THEN
232			C Calculate del^2 u and del^2 v for bi-harmonic term
233	adcroft	1.2	IF (viscA4.NE.0.) THEN
234			CALL MOM_VI_DEL2UV(bi,bj,k,hDiv,vort3,hFacZ,
235			O del2u,del2v,
236			& myThid)
237			CALL MOM_VI_CALC_HDIV(bi,bj,k,del2u,del2v,dStar,myThid)
238			CALL MOM_VI_CALC_RELVORT3(
239			& bi,bj,k,del2u,del2v,hFacZ,zStar,myThid)
240			ENDIF
241	adcroft	1.1	C Calculate dissipation terms for U and V equations
242	adcroft	1.2	C in terms of vorticity and divergence
243			IF (viscAh.NE.0. .OR. viscA4.NE.0.) THEN
244			CALL MOM_VI_HDISSIP(bi,bj,k,hDiv,vort3,hFacZ,dStar,zStar,
245			O uDiss,vDiss,
246			& myThid)
247			ENDIF
248	adcroft	1.3	C or in terms of tension and strain
249			IF (viscAstrain.NE.0. .OR. viscAtension.NE.0.) THEN
250			CALL MOM_CALC_TENSION(bi,bj,k,uFld,vFld,
251			O tension,
252			I myThid)
253			CALL MOM_CALC_STRAIN(bi,bj,k,uFld,vFld,hFacZ,
254			O strain,
255			I myThid)
256			CALL MOM_HDISSIP(bi,bj,k,
257			I tension,strain,hFacZ,viscAtension,viscAstrain,
258			O uDiss,vDiss,
259			I myThid)
260			ENDIF
261	adcroft	1.1	ENDIF
262
263			C---- Zonal momentum equation starts here
264
265			C-- Vertical flux (fVer is at upper face of "u" cell)
266
267			C Eddy component of vertical flux (interior component only) -> vrF
268			IF (momViscosity.AND..NOT.implicitViscosity)
269			& CALL MOM_U_RVISCFLUX(bi,bj,k,uVel,KappaRU,vrF,myThid)
270
271			C Combine fluxes
272			DO j=jMin,jMax
273			DO i=iMin,iMax
274			fVerU(i,j,kDown) = ArDudrFac*vrF(i,j)
275			ENDDO
276			ENDDO
277
278			C-- Tendency is minus divergence of the fluxes + coriolis + pressure term
279			DO j=2-Oly,sNy+Oly-1
280			DO i=2-Olx,sNx+Olx-1
281			gU(i,j,k,bi,bj) = uDiss(i,j)
282			& -_recip_hFacW(i,j,k,bi,bj)*recip_drF(k)
283			& *recip_rAw(i,j,bi,bj)
284			& *(
285			& +fVerU(i,j,kUp)rkFac - fVerU(i,j,kDown)rkFac
286			& )
287	jmc	1.4	& - phxFac*dPhiHydX(i,j)
288	adcroft	1.1	ENDDO
289			ENDDO
290
291			C-- No-slip and drag BCs appear as body forces in cell abutting topography
292			IF (momViscosity.AND.no_slip_sides) THEN
293			C- No-slip BCs impose a drag at walls...
294			CALL MOM_U_SIDEDRAG(bi,bj,k,uFld,del2u,hFacZ,vF,myThid)
295			DO j=jMin,jMax
296			DO i=iMin,iMax
297			gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+vF(i,j)
298			ENDDO
299			ENDDO
300			ENDIF
301			C- No-slip BCs impose a drag at bottom
302			IF (momViscosity.AND.bottomDragTerms) THEN
303			CALL MOM_U_BOTTOMDRAG(bi,bj,k,uFld,KE,KappaRU,vF,myThid)
304			DO j=jMin,jMax
305			DO i=iMin,iMax
306			gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+vF(i,j)
307			ENDDO
308			ENDDO
309			ENDIF
310
311			C-- Forcing term
312			IF (momForcing)
313			& CALL EXTERNAL_FORCING_U(
314			I iMin,iMax,jMin,jMax,bi,bj,k,
315			I myCurrentTime,myThid)
316
317			C-- Metric terms for curvilinear grid systems
318			c IF (usingSphericalPolarMTerms) THEN
319			C o Spherical polar grid metric terms
320			c CALL MOM_U_METRIC_NH(bi,bj,k,uFld,wVel,mT,myThid)
321			c DO j=jMin,jMax
322			c DO i=iMin,iMax
323			c gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+mTFacU*mT(i,j)
324			c ENDDO
325			c ENDDO
326			c ENDIF
327
328
329			C---- Meridional momentum equation starts here
330
331			C-- Vertical flux (fVer is at upper face of "v" cell)
332
333			C Eddy component of vertical flux (interior component only) -> vrF
334			IF (momViscosity.AND..NOT.implicitViscosity)
335			& CALL MOM_V_RVISCFLUX(bi,bj,k,vVel,KappaRV,vrf,myThid)
336
337			C Combine fluxes -> fVerV
338			DO j=jMin,jMax
339			DO i=iMin,iMax
340			fVerV(i,j,kDown) = ArDvdrFac*vrF(i,j)
341			ENDDO
342			ENDDO
343
344			C-- Tendency is minus divergence of the fluxes + coriolis + pressure term
345			DO j=jMin,jMax
346			DO i=iMin,iMax
347			gV(i,j,k,bi,bj) = vDiss(i,j)
348			& -_recip_hFacS(i,j,k,bi,bj)*recip_drF(k)
349			& *recip_rAs(i,j,bi,bj)
350			& *(
351			& +fVerV(i,j,kUp)rkFac - fVerV(i,j,kDown)rkFac
352			& )
353	jmc	1.4	& - phyFac*dPhiHydY(i,j)
354	adcroft	1.1	ENDDO
355			ENDDO
356
357			C-- No-slip and drag BCs appear as body forces in cell abutting topography
358			IF (momViscosity.AND.no_slip_sides) THEN
359			C- No-slip BCs impose a drag at walls...
360			CALL MOM_V_SIDEDRAG(bi,bj,k,vFld,del2v,hFacZ,vF,myThid)
361			DO j=jMin,jMax
362			DO i=iMin,iMax
363			gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+vF(i,j)
364			ENDDO
365			ENDDO
366			ENDIF
367			C- No-slip BCs impose a drag at bottom
368			IF (momViscosity.AND.bottomDragTerms) THEN
369			CALL MOM_V_BOTTOMDRAG(bi,bj,k,vFld,KE,KappaRV,vF,myThid)
370			DO j=jMin,jMax
371			DO i=iMin,iMax
372			gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+vF(i,j)
373			ENDDO
374			ENDDO
375			ENDIF
376
377			C-- Forcing term
378			IF (momForcing)
379			& CALL EXTERNAL_FORCING_V(
380			I iMin,iMax,jMin,jMax,bi,bj,k,
381			I myCurrentTime,myThid)
382
383			C-- Metric terms for curvilinear grid systems
384			c IF (usingSphericalPolarMTerms) THEN
385			C o Spherical polar grid metric terms
386			c CALL MOM_V_METRIC_NH(bi,bj,k,vFld,wVel,mT,myThid)
387			c DO j=jMin,jMax
388			c DO i=iMin,iMax
389			c gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+mTFacV*mT(i,j)
390			c ENDDO
391			c ENDDO
392			c ENDIF
393
394	jmc	1.5	C-- Horizontal Coriolis terms
395			IF (useCoriolis) THEN
396			CALL MOM_VI_CORIOLIS(bi,bj,K,uFld,vFld,omega3,r_hFacZ,
397			& uCf,vCf,myThid)
398			DO j=jMin,jMax
399			DO i=iMin,iMax
400			gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+uCf(i,j)
401			gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+vCf(i,j)
402			ENDDO
403	adcroft	1.1	ENDDO
404	jmc	1.5	ENDIF
405	adcroft	1.1
406	jmc	1.5	IF (momAdvection) THEN
407			C-- Horizontal advection of relative vorticity
408			c CALL MOM_VI_U_CORIOLIS(bi,bj,K,vFld,omega3,r_hFacZ,uCf,myThid)
409			CALL MOM_VI_U_CORIOLIS(bi,bj,K,vFld,vort3,r_hFacZ,uCf,myThid)
410			c CALL MOM_VI_U_CORIOLIS_C4(bi,bj,K,vFld,vort3,r_hFacZ,uCf,myThid)
411			DO j=jMin,jMax
412			DO i=iMin,iMax
413			gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+uCf(i,j)
414			ENDDO
415	adcroft	1.1	ENDDO
416	jmc	1.5	c CALL MOM_VI_V_CORIOLIS(bi,bj,K,uFld,omega3,r_hFacZ,vCf,myThid)
417			CALL MOM_VI_V_CORIOLIS(bi,bj,K,uFld,vort3,r_hFacZ,vCf,myThid)
418			c CALL MOM_VI_V_CORIOLIS_C4(bi,bj,K,uFld,vort3,r_hFacZ,vCf,myThid)
419			DO j=jMin,jMax
420			DO i=iMin,iMax
421			gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+vCf(i,j)
422			ENDDO
423	adcroft	1.1	ENDDO
424
425	jmc	1.5	C-- Vertical shear terms (-wdu/dr & -wdv/dr)
426			CALL MOM_VI_U_VERTSHEAR(bi,bj,K,uVel,wVel,uCf,myThid)
427			DO j=jMin,jMax
428			DO i=iMin,iMax
429			gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+uCf(i,j)
430			ENDDO
431	adcroft	1.1	ENDDO
432	jmc	1.5	CALL MOM_VI_V_VERTSHEAR(bi,bj,K,vVel,wVel,vCf,myThid)
433			DO j=jMin,jMax
434			DO i=iMin,iMax
435			gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+vCf(i,j)
436			ENDDO
437	adcroft	1.1	ENDDO
438
439			C-- Bernoulli term
440	jmc	1.5	CALL MOM_VI_U_GRAD_KE(bi,bj,K,KE,uCf,myThid)
441			DO j=jMin,jMax
442			DO i=iMin,iMax
443			gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+uCf(i,j)
444			ENDDO
445			ENDDO
446			CALL MOM_VI_V_GRAD_KE(bi,bj,K,KE,vCf,myThid)
447			DO j=jMin,jMax
448			DO i=iMin,iMax
449			gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+vCf(i,j)
450			ENDDO
451	adcroft	1.1	ENDDO
452	jmc	1.5	C-- end if momAdvection
453			ENDIF
454
455			C-- Set du/dt & dv/dt on boundaries to zero
456	adcroft	1.1	DO j=jMin,jMax
457			DO i=iMin,iMax
458	jmc	1.5	gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)*_maskW(i,j,k,bi,bj)
459			gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)*_maskS(i,j,k,bi,bj)
460	adcroft	1.1	ENDDO
461			ENDDO
462	jmc	1.5
463	adcroft	1.2
464			IF (
465			& DIFFERENT_MULTIPLE(diagFreq,myCurrentTime,
466			& myCurrentTime-deltaTClock)
467			& ) THEN
468	adcroft	1.3	CALL WRITE_LOCAL_RL('Ds','I10',1,strain,bi,bj,k,myIter,myThid)
469			CALL WRITE_LOCAL_RL('Dt','I10',1,tension,bi,bj,k,myIter,myThid)
470	adcroft	1.2	CALL WRITE_LOCAL_RL('fV','I10',1,uCf,bi,bj,k,myIter,myThid)
471			CALL WRITE_LOCAL_RL('fU','I10',1,vCf,bi,bj,k,myIter,myThid)
472			CALL WRITE_LOCAL_RL('Du','I10',1,uDiss,bi,bj,k,myIter,myThid)
473			CALL WRITE_LOCAL_RL('Dv','I10',1,vDiss,bi,bj,k,myIter,myThid)
474	adcroft	1.3	CALL WRITE_LOCAL_RL('Z3','I10',1,vort3,bi,bj,k,myIter,myThid)
475	jmc	1.5	c CALL WRITE_LOCAL_RL('W3','I10',1,omega3,bi,bj,k,myIter,myThid)
476	adcroft	1.3	CALL WRITE_LOCAL_RL('KE','I10',1,KE,bi,bj,k,myIter,myThid)
477			CALL WRITE_LOCAL_RL('D','I10',1,hdiv,bi,bj,k,myIter,myThid)
478	adcroft	1.1	ENDIF
479
480			RETURN
481			END