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heimbach |
1.4.6.2 |
C $Header: /u/gcmpack/MITgcm/pkg/mom_fluxform/mom_fluxform.F,v 1.12 2003/04/17 13:44:10 jmc Exp $ |
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adcroft |
1.2 |
C $Name: $ |
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adcroft |
1.1 |
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adcroft |
1.3 |
CBOI |
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C !TITLE: pkg/mom\_advdiff |
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C !AUTHORS: adcroft@mit.edu |
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adcroft |
1.4 |
C !INTRODUCTION: Flux-form Momentum Equations Package |
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adcroft |
1.3 |
C |
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C Package "mom\_fluxform" provides methods for calculating explicit terms |
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C in the momentum equation cast in flux-form: |
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C \begin{eqnarray*} |
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C G^u & = & -\frac{1}{\rho} \partial_x \phi_h |
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C -\nabla \cdot {\bf v} u |
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C -fv |
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C +\frac{1}{\rho} \nabla \cdot {\bf \tau}^x |
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C + \mbox{metrics} |
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C \\ |
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C G^v & = & -\frac{1}{\rho} \partial_y \phi_h |
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C -\nabla \cdot {\bf v} v |
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C +fu |
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C +\frac{1}{\rho} \nabla \cdot {\bf \tau}^y |
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C + \mbox{metrics} |
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C \end{eqnarray*} |
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C where ${\bf v}=(u,v,w)$ and $\tau$, the stress tensor, includes surface |
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C stresses as well as internal viscous stresses. |
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CEOI |
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adcroft |
1.1 |
#include "CPP_OPTIONS.h" |
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adcroft |
1.3 |
CBOP |
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C !ROUTINE: MOM_FLUXFORM |
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C !INTERFACE: ========================================================== |
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adcroft |
1.1 |
SUBROUTINE MOM_FLUXFORM( |
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I bi,bj,iMin,iMax,jMin,jMax,k,kUp,kDown, |
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heimbach |
1.4.6.1 |
I dPhihydX,dPhiHydY,KappaRU,KappaRV, |
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adcroft |
1.1 |
U fVerU, fVerV, |
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heimbach |
1.4.6.1 |
I myTime,myIter,myThid) |
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adcroft |
1.3 |
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C !DESCRIPTION: |
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C Calculates all the horizontal accelerations except for the implicit surface |
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C pressure gradient and implciit vertical viscosity. |
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adcroft |
1.1 |
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adcroft |
1.3 |
C !USES: =============================================================== |
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adcroft |
1.1 |
C == Global variables == |
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adcroft |
1.3 |
IMPLICIT NONE |
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adcroft |
1.1 |
#include "SIZE.h" |
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#include "DYNVARS.h" |
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#include "FFIELDS.h" |
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#include "EEPARAMS.h" |
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#include "PARAMS.h" |
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#include "GRID.h" |
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#include "SURFACE.h" |
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adcroft |
1.3 |
C !INPUT PARAMETERS: =================================================== |
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C bi,bj :: tile indices |
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C iMin,iMax,jMin,jMAx :: loop ranges |
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C k :: vertical level |
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C kUp :: =1 or 2 for consecutive k |
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C kDown :: =2 or 1 for consecutive k |
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heimbach |
1.4.6.1 |
C dPhiHydX,Y :: Gradient (X & Y dir.) of Hydrostatic Potential |
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adcroft |
1.3 |
C KappaRU :: vertical viscosity |
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C KappaRV :: vertical viscosity |
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C fVerU :: vertical flux of U, 2 1/2 dim for pipe-lining |
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C fVerV :: vertical flux of V, 2 1/2 dim for pipe-lining |
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heimbach |
1.4.6.1 |
C myTime :: current time |
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adcroft |
1.3 |
C myIter :: current time-step number |
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C myThid :: thread number |
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INTEGER bi,bj,iMin,iMax,jMin,jMax |
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INTEGER k,kUp,kDown |
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heimbach |
1.4.6.1 |
_RL dPhiHydX(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL dPhiHydY(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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adcroft |
1.1 |
_RL KappaRU(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL KappaRV(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr) |
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_RL fVerU(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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_RL fVerV(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2) |
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heimbach |
1.4.6.1 |
_RL myTime |
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adcroft |
1.2 |
INTEGER myIter |
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adcroft |
1.1 |
INTEGER myThid |
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adcroft |
1.3 |
C !OUTPUT PARAMETERS: ================================================== |
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C None - updates gU() and gV() in common blocks |
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C !LOCAL VARIABLES: ==================================================== |
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C i,j :: loop indices |
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C aF :: advective flux |
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C vF :: viscous flux |
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C v4F :: bi-harmonic viscous flux |
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C vrF :: vertical viscous flux |
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C cF :: Coriolis acceleration |
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C mT :: Metric terms |
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C pF :: Pressure gradient |
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C fZon :: zonal fluxes |
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C fMer :: meridional fluxes |
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INTEGER i,j |
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_RL aF(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL vF(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL v4F(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL vrF(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL cF(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL mT(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL pF(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL fZon(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL fMer(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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adcroft |
1.1 |
C wMaskOverride - Land sea flag override for top layer. |
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C afFacMom - Tracer parameters for turning terms |
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C vfFacMom on and off. |
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C pfFacMom afFacMom - Advective terms |
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C cfFacMom vfFacMom - Eddy viscosity terms |
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C mTFacMom pfFacMom - Pressure terms |
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C cfFacMom - Coriolis terms |
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C foFacMom - Forcing |
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C mTFacMom - Metric term |
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C uDudxFac, AhDudxFac, etc ... individual term tracer parameters |
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_RS hFacZ(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RS r_hFacZ(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RS xA(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RS yA(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL uTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL vTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL uFld(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL vFld(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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heimbach |
1.4.6.1 |
_RL rTransU(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL rTransV(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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adcroft |
1.1 |
C I,J,K - Loop counters |
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C rVelMaskOverride - Factor for imposing special surface boundary conditions |
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C ( set according to free-surface condition ). |
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C hFacROpen - Lopped cell factos used tohold fraction of open |
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C hFacRClosed and closed cell wall. |
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_RL rVelMaskOverride |
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C xxxFac - On-off tracer parameters used for switching terms off. |
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_RL uDudxFac |
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_RL AhDudxFac |
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_RL A4DuxxdxFac |
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_RL vDudyFac |
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_RL AhDudyFac |
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_RL A4DuyydyFac |
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_RL rVelDudrFac |
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_RL ArDudrFac |
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_RL fuFac |
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_RL phxFac |
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_RL mtFacU |
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_RL uDvdxFac |
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_RL AhDvdxFac |
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_RL A4DvxxdxFac |
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_RL vDvdyFac |
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_RL AhDvdyFac |
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_RL A4DvyydyFac |
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_RL rVelDvdrFac |
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_RL ArDvdrFac |
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_RL fvFac |
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_RL phyFac |
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_RL vForcFac |
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_RL mtFacV |
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INTEGER km1,kp1 |
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_RL wVelBottomOverride |
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LOGICAL bottomDragTerms |
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_RL KE(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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adcroft |
1.3 |
CEOP |
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adcroft |
1.1 |
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km1=MAX(1,k-1) |
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kp1=MIN(Nr,k+1) |
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rVelMaskOverride=1. |
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IF ( k .EQ. 1 ) rVelMaskOverride=freeSurfFac |
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wVelBottomOverride=1. |
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IF (k.EQ.Nr) wVelBottomOverride=0. |
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C Initialise intermediate terms |
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DO J=1-OLy,sNy+OLy |
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DO I=1-OLx,sNx+OLx |
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aF(i,j) = 0. |
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vF(i,j) = 0. |
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v4F(i,j) = 0. |
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vrF(i,j) = 0. |
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cF(i,j) = 0. |
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mT(i,j) = 0. |
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pF(i,j) = 0. |
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fZon(i,j) = 0. |
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fMer(i,j) = 0. |
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heimbach |
1.4.6.1 |
rTransU(i,j) = 0. |
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rTransV(i,j) = 0. |
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adcroft |
1.1 |
ENDDO |
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ENDDO |
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C-- Term by term tracer parmeters |
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C o U momentum equation |
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uDudxFac = afFacMom*1. |
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AhDudxFac = vfFacMom*1. |
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A4DuxxdxFac = vfFacMom*1. |
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vDudyFac = afFacMom*1. |
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AhDudyFac = vfFacMom*1. |
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A4DuyydyFac = vfFacMom*1. |
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rVelDudrFac = afFacMom*1. |
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ArDudrFac = vfFacMom*1. |
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mTFacU = mtFacMom*1. |
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fuFac = cfFacMom*1. |
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phxFac = pfFacMom*1. |
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C o V momentum equation |
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uDvdxFac = afFacMom*1. |
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AhDvdxFac = vfFacMom*1. |
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A4DvxxdxFac = vfFacMom*1. |
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vDvdyFac = afFacMom*1. |
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AhDvdyFac = vfFacMom*1. |
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A4DvyydyFac = vfFacMom*1. |
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rVelDvdrFac = afFacMom*1. |
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ArDvdrFac = vfFacMom*1. |
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mTFacV = mtFacMom*1. |
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fvFac = cfFacMom*1. |
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phyFac = pfFacMom*1. |
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vForcFac = foFacMom*1. |
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IF ( no_slip_bottom |
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& .OR. bottomDragQuadratic.NE.0. |
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& .OR. bottomDragLinear.NE.0.) THEN |
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bottomDragTerms=.TRUE. |
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ELSE |
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bottomDragTerms=.FALSE. |
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ENDIF |
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| 220 |
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C-- with stagger time stepping, grad Phi_Hyp is directly incoporated in TIMESTEP |
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IF (staggerTimeStep) THEN |
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phxFac = 0. |
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phyFac = 0. |
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ENDIF |
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C-- Calculate open water fraction at vorticity points |
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CALL MOM_CALC_HFACZ(bi,bj,k,hFacZ,r_hFacZ,myThid) |
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C---- Calculate common quantities used in both U and V equations |
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C Calculate tracer cell face open areas |
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DO j=1-OLy,sNy+OLy |
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DO i=1-OLx,sNx+OLx |
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xA(i,j) = _dyG(i,j,bi,bj) |
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& *drF(k)*_hFacW(i,j,k,bi,bj) |
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yA(i,j) = _dxG(i,j,bi,bj) |
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& *drF(k)*_hFacS(i,j,k,bi,bj) |
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ENDDO |
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ENDDO |
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| 240 |
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C Make local copies of horizontal flow field |
| 241 |
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DO j=1-OLy,sNy+OLy |
| 242 |
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DO i=1-OLx,sNx+OLx |
| 243 |
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uFld(i,j) = uVel(i,j,k,bi,bj) |
| 244 |
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vFld(i,j) = vVel(i,j,k,bi,bj) |
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ENDDO |
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ENDDO |
| 247 |
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| 248 |
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C Calculate velocity field "volume transports" through tracer cell faces. |
| 249 |
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DO j=1-OLy,sNy+OLy |
| 250 |
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DO i=1-OLx,sNx+OLx |
| 251 |
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uTrans(i,j) = uFld(i,j)*xA(i,j) |
| 252 |
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vTrans(i,j) = vFld(i,j)*yA(i,j) |
| 253 |
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ENDDO |
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ENDDO |
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| 256 |
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CALL MOM_CALC_KE(bi,bj,k,uFld,vFld,KE,myThid) |
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heimbach |
1.4.6.1 |
C--- First call (k=1): compute vertical adv. flux fVerU(kUp) & fVerV(kUp) |
| 259 |
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IF (momAdvection.AND.k.EQ.1) THEN |
| 260 |
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| 261 |
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C- Calculate vertical transports above U & V points (West & South face): |
| 262 |
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CALL MOM_CALC_RTRANS( k, bi, bj, |
| 263 |
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O rTransU, rTransV, |
| 264 |
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I myTime, myIter, myThid) |
| 265 |
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| 266 |
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C- Free surface correction term (flux at k=1) |
| 267 |
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CALL MOM_U_ADV_WU(bi,bj,k,uVel,wVel,rTransU,af,myThid) |
| 268 |
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DO j=jMin,jMax |
| 269 |
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DO i=iMin,iMax |
| 270 |
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fVerU(i,j,kUp) = af(i,j) |
| 271 |
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ENDDO |
| 272 |
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ENDDO |
| 273 |
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| 274 |
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CALL MOM_V_ADV_WV(bi,bj,k,vVel,wVel,rTransV,af,myThid) |
| 275 |
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DO j=jMin,jMax |
| 276 |
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DO i=iMin,iMax |
| 277 |
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fVerV(i,j,kUp) = af(i,j) |
| 278 |
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ENDDO |
| 279 |
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ENDDO |
| 280 |
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| 281 |
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C--- endif momAdvection & k=1 |
| 282 |
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ENDIF |
| 283 |
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| 284 |
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| 285 |
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C--- Calculate vertical transports (at k+1) below U & V points : |
| 286 |
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IF (momAdvection) THEN |
| 287 |
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CALL MOM_CALC_RTRANS( k+1, bi, bj, |
| 288 |
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O rTransU, rTransV, |
| 289 |
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I myTime, myIter, myThid) |
| 290 |
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ENDIF |
| 291 |
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| 292 |
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adcroft |
1.1 |
C---- Zonal momentum equation starts here |
| 294 |
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| 295 |
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C Bi-harmonic term del^2 U -> v4F |
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heimbach |
1.4.6.1 |
IF (momViscosity .AND. viscA4.NE.0. ) |
| 297 |
adcroft |
1.1 |
& CALL MOM_U_DEL2U(bi,bj,k,uFld,hFacZ,v4f,myThid) |
| 298 |
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| 299 |
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C--- Calculate mean and eddy fluxes between cells for zonal flow. |
| 300 |
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| 301 |
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C-- Zonal flux (fZon is at east face of "u" cell) |
| 302 |
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| 303 |
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C Mean flow component of zonal flux -> aF |
| 304 |
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IF (momAdvection) |
| 305 |
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& CALL MOM_U_ADV_UU(bi,bj,k,uTrans,uFld,aF,myThid) |
| 306 |
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| 307 |
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C Laplacian and bi-harmonic terms -> vF |
| 308 |
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IF (momViscosity) |
| 309 |
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& CALL MOM_U_XVISCFLUX(bi,bj,k,uFld,v4F,vF,myThid) |
| 310 |
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| 311 |
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C Combine fluxes -> fZon |
| 312 |
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DO j=jMin,jMax |
| 313 |
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DO i=iMin,iMax |
| 314 |
|
|
fZon(i,j) = uDudxFac*aF(i,j) + AhDudxFac*vF(i,j) |
| 315 |
|
|
ENDDO |
| 316 |
|
|
ENDDO |
| 317 |
|
|
|
| 318 |
|
|
C-- Meridional flux (fMer is at south face of "u" cell) |
| 319 |
|
|
|
| 320 |
|
|
C Mean flow component of meridional flux |
| 321 |
|
|
IF (momAdvection) |
| 322 |
|
|
& CALL MOM_U_ADV_VU(bi,bj,k,vTrans,uFld,aF,myThid) |
| 323 |
|
|
|
| 324 |
|
|
C Laplacian and bi-harmonic term |
| 325 |
|
|
IF (momViscosity) |
| 326 |
|
|
& CALL MOM_U_YVISCFLUX(bi,bj,k,uFld,v4F,hFacZ,vF,myThid) |
| 327 |
|
|
|
| 328 |
|
|
C Combine fluxes -> fMer |
| 329 |
heimbach |
1.4.6.1 |
DO j=jMin,jMax+1 |
| 330 |
adcroft |
1.1 |
DO i=iMin,iMax |
| 331 |
|
|
fMer(i,j) = vDudyFac*aF(i,j) + AhDudyFac*vF(i,j) |
| 332 |
|
|
ENDDO |
| 333 |
|
|
ENDDO |
| 334 |
|
|
|
| 335 |
|
|
C-- Vertical flux (fVer is at upper face of "u" cell) |
| 336 |
|
|
|
| 337 |
|
|
C Mean flow component of vertical flux (at k+1) -> aF |
| 338 |
|
|
IF (momAdvection) |
| 339 |
heimbach |
1.4.6.1 |
& CALL MOM_U_ADV_WU(bi,bj,k+1,uVel,wVel,rTransU,af,myThid) |
| 340 |
adcroft |
1.1 |
|
| 341 |
|
|
C Eddy component of vertical flux (interior component only) -> vrF |
| 342 |
|
|
IF (momViscosity.AND..NOT.implicitViscosity) |
| 343 |
|
|
& CALL MOM_U_RVISCFLUX(bi,bj,k,uVel,KappaRU,vrF,myThid) |
| 344 |
|
|
|
| 345 |
|
|
C Combine fluxes |
| 346 |
|
|
DO j=jMin,jMax |
| 347 |
|
|
DO i=iMin,iMax |
| 348 |
|
|
fVerU(i,j,kDown) = rVelDudrFac*aF(i,j) + ArDudrFac*vrF(i,j) |
| 349 |
|
|
ENDDO |
| 350 |
|
|
ENDDO |
| 351 |
|
|
|
| 352 |
|
|
C-- Tendency is minus divergence of the fluxes + coriolis + pressure term |
| 353 |
|
|
DO j=jMin,jMax |
| 354 |
|
|
DO i=iMin,iMax |
| 355 |
|
|
gU(i,j,k,bi,bj) = |
| 356 |
|
|
#ifdef OLD_UV_GEOM |
| 357 |
|
|
& -_recip_hFacW(i,j,k,bi,bj)*recip_drF(k)/ |
| 358 |
|
|
& ( 0.5 _d 0*(rA(i,j,bi,bj)+rA(i-1,j,bi,bj)) ) |
| 359 |
|
|
#else |
| 360 |
|
|
& -_recip_hFacW(i,j,k,bi,bj)*recip_drF(k) |
| 361 |
|
|
& *recip_rAw(i,j,bi,bj) |
| 362 |
|
|
#endif |
| 363 |
|
|
& *(fZon(i,j ) - fZon(i-1,j) |
| 364 |
|
|
& +fMer(i,j+1) - fMer(i ,j) |
| 365 |
|
|
& +fVerU(i,j,kUp)*rkFac - fVerU(i,j,kDown)*rkFac |
| 366 |
|
|
& ) |
| 367 |
heimbach |
1.4.6.1 |
& - phxFac*dPhiHydX(i,j) |
| 368 |
adcroft |
1.1 |
ENDDO |
| 369 |
|
|
ENDDO |
| 370 |
|
|
|
| 371 |
heimbach |
1.4.6.1 |
#ifdef NONLIN_FRSURF |
| 372 |
|
|
C-- account for 3.D divergence of the flow in rStar coordinate: |
| 373 |
|
|
IF ( momAdvection .AND. select_rStar.GT.0 ) THEN |
| 374 |
|
|
DO j=jMin,jMax |
| 375 |
|
|
DO i=iMin,iMax |
| 376 |
|
|
gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj) |
| 377 |
|
|
& - (rStarExpW(i,j,bi,bj) - 1. _d 0)/deltaTfreesurf |
| 378 |
|
|
& *uVel(i,j,k,bi,bj) |
| 379 |
|
|
ENDDO |
| 380 |
|
|
ENDDO |
| 381 |
|
|
ENDIF |
| 382 |
|
|
IF ( momAdvection .AND. select_rStar.LT.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 |
|
|
& - rStarDhWDt(i,j,bi,bj)*uVel(i,j,k,bi,bj) |
| 387 |
|
|
ENDDO |
| 388 |
|
|
ENDDO |
| 389 |
|
|
ENDIF |
| 390 |
|
|
#endif /* NONLIN_FRSURF */ |
| 391 |
|
|
|
| 392 |
adcroft |
1.1 |
C-- No-slip and drag BCs appear as body forces in cell abutting topography |
| 393 |
|
|
IF (momViscosity.AND.no_slip_sides) THEN |
| 394 |
|
|
C- No-slip BCs impose a drag at walls... |
| 395 |
|
|
CALL MOM_U_SIDEDRAG(bi,bj,k,uFld,v4F,hFacZ,vF,myThid) |
| 396 |
|
|
DO j=jMin,jMax |
| 397 |
|
|
DO i=iMin,iMax |
| 398 |
|
|
gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+vF(i,j) |
| 399 |
|
|
ENDDO |
| 400 |
|
|
ENDDO |
| 401 |
|
|
ENDIF |
| 402 |
|
|
C- No-slip BCs impose a drag at bottom |
| 403 |
|
|
IF (momViscosity.AND.bottomDragTerms) THEN |
| 404 |
|
|
CALL MOM_U_BOTTOMDRAG(bi,bj,k,uFld,KE,KappaRU,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 |
|
|
|
| 412 |
heimbach |
1.4.6.2 |
C-- Forcing term (moved to timestep.F) |
| 413 |
|
|
c IF (momForcing) |
| 414 |
|
|
c & CALL EXTERNAL_FORCING_U( |
| 415 |
|
|
c I iMin,iMax,jMin,jMax,bi,bj,k, |
| 416 |
|
|
c I myTime,myThid) |
| 417 |
adcroft |
1.1 |
|
| 418 |
|
|
C-- Metric terms for curvilinear grid systems |
| 419 |
heimbach |
1.4.6.1 |
IF (useNHMTerms) THEN |
| 420 |
|
|
C o Non-hydrosatic metric terms |
| 421 |
adcroft |
1.1 |
CALL MOM_U_METRIC_NH(bi,bj,k,uFld,wVel,mT,myThid) |
| 422 |
|
|
DO j=jMin,jMax |
| 423 |
|
|
DO i=iMin,iMax |
| 424 |
|
|
gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+mTFacU*mT(i,j) |
| 425 |
|
|
ENDDO |
| 426 |
|
|
ENDDO |
| 427 |
heimbach |
1.4.6.1 |
ENDIF |
| 428 |
|
|
IF (usingSphericalPolarMTerms) THEN |
| 429 |
adcroft |
1.1 |
CALL MOM_U_METRIC_SPHERE(bi,bj,k,uFld,vFld,mT,myThid) |
| 430 |
|
|
DO j=jMin,jMax |
| 431 |
|
|
DO i=iMin,iMax |
| 432 |
|
|
gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+mTFacU*mT(i,j) |
| 433 |
|
|
ENDDO |
| 434 |
|
|
ENDDO |
| 435 |
|
|
ENDIF |
| 436 |
|
|
|
| 437 |
|
|
C-- Set du/dt on boundaries to zero |
| 438 |
|
|
DO j=jMin,jMax |
| 439 |
|
|
DO i=iMin,iMax |
| 440 |
|
|
gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)*_maskW(i,j,k,bi,bj) |
| 441 |
|
|
ENDDO |
| 442 |
|
|
ENDDO |
| 443 |
|
|
|
| 444 |
|
|
|
| 445 |
|
|
C---- Meridional momentum equation starts here |
| 446 |
|
|
|
| 447 |
|
|
C Bi-harmonic term del^2 V -> v4F |
| 448 |
heimbach |
1.4.6.1 |
IF (momViscosity .AND. viscA4.NE.0. ) |
| 449 |
adcroft |
1.1 |
& CALL MOM_V_DEL2V(bi,bj,k,vFld,hFacZ,v4f,myThid) |
| 450 |
|
|
|
| 451 |
|
|
C--- Calculate mean and eddy fluxes between cells for meridional flow. |
| 452 |
|
|
|
| 453 |
|
|
C-- Zonal flux (fZon is at west face of "v" cell) |
| 454 |
|
|
|
| 455 |
|
|
C Mean flow component of zonal flux -> aF |
| 456 |
|
|
IF (momAdvection) |
| 457 |
|
|
& CALL MOM_V_ADV_UV(bi,bj,k,uTrans,vFld,af,myThid) |
| 458 |
|
|
|
| 459 |
|
|
C Laplacian and bi-harmonic terms -> vF |
| 460 |
|
|
IF (momViscosity) |
| 461 |
|
|
& CALL MOM_V_XVISCFLUX(bi,bj,k,vFld,v4f,hFacZ,vf,myThid) |
| 462 |
|
|
|
| 463 |
|
|
C Combine fluxes -> fZon |
| 464 |
|
|
DO j=jMin,jMax |
| 465 |
heimbach |
1.4.6.1 |
DO i=iMin,iMax+1 |
| 466 |
adcroft |
1.1 |
fZon(i,j) = uDvdxFac*aF(i,j) + AhDvdxFac*vF(i,j) |
| 467 |
|
|
ENDDO |
| 468 |
|
|
ENDDO |
| 469 |
|
|
|
| 470 |
|
|
C-- Meridional flux (fMer is at north face of "v" cell) |
| 471 |
|
|
|
| 472 |
|
|
C Mean flow component of meridional flux |
| 473 |
|
|
IF (momAdvection) |
| 474 |
|
|
& CALL MOM_V_ADV_VV(bi,bj,k,vTrans,vFld,af,myThid) |
| 475 |
|
|
|
| 476 |
|
|
C Laplacian and bi-harmonic term |
| 477 |
|
|
IF (momViscosity) |
| 478 |
|
|
& CALL MOM_V_YVISCFLUX(bi,bj,k,vFld,v4f,vf,myThid) |
| 479 |
|
|
|
| 480 |
|
|
C Combine fluxes -> fMer |
| 481 |
|
|
DO j=jMin,jMax |
| 482 |
|
|
DO i=iMin,iMax |
| 483 |
|
|
fMer(i,j) = vDvdyFac*aF(i,j) + AhDvdyFac*vF(i,j) |
| 484 |
|
|
ENDDO |
| 485 |
|
|
ENDDO |
| 486 |
|
|
|
| 487 |
|
|
C-- Vertical flux (fVer is at upper face of "v" cell) |
| 488 |
|
|
|
| 489 |
|
|
C o Mean flow component of vertical flux |
| 490 |
|
|
IF (momAdvection) |
| 491 |
heimbach |
1.4.6.1 |
& CALL MOM_V_ADV_WV(bi,bj,k+1,vVel,wVel,rTransV,af,myThid) |
| 492 |
adcroft |
1.1 |
|
| 493 |
|
|
C Eddy component of vertical flux (interior component only) -> vrF |
| 494 |
|
|
IF (momViscosity.AND..NOT.implicitViscosity) |
| 495 |
|
|
& CALL MOM_V_RVISCFLUX(bi,bj,k,vVel,KappaRV,vrf,myThid) |
| 496 |
|
|
|
| 497 |
|
|
C Combine fluxes -> fVerV |
| 498 |
|
|
DO j=jMin,jMax |
| 499 |
|
|
DO i=iMin,iMax |
| 500 |
|
|
fVerV(i,j,kDown) = rVelDvdrFac*aF(i,j) + ArDvdrFac*vrF(i,j) |
| 501 |
|
|
ENDDO |
| 502 |
|
|
ENDDO |
| 503 |
|
|
|
| 504 |
|
|
C-- Tendency is minus divergence of the fluxes + coriolis + pressure term |
| 505 |
|
|
DO j=jMin,jMax |
| 506 |
|
|
DO i=iMin,iMax |
| 507 |
|
|
gV(i,j,k,bi,bj) = |
| 508 |
|
|
#ifdef OLD_UV_GEOM |
| 509 |
|
|
& -_recip_hFacS(i,j,k,bi,bj)*recip_drF(k)/ |
| 510 |
|
|
& ( 0.5 _d 0*(_rA(i,j,bi,bj)+_rA(i,j-1,bi,bj)) ) |
| 511 |
|
|
#else |
| 512 |
|
|
& -_recip_hFacS(i,j,k,bi,bj)*recip_drF(k) |
| 513 |
|
|
& *recip_rAs(i,j,bi,bj) |
| 514 |
|
|
#endif |
| 515 |
|
|
& *(fZon(i+1,j) - fZon(i,j ) |
| 516 |
|
|
& +fMer(i,j ) - fMer(i,j-1) |
| 517 |
|
|
& +fVerV(i,j,kUp)*rkFac - fVerV(i,j,kDown)*rkFac |
| 518 |
|
|
& ) |
| 519 |
heimbach |
1.4.6.1 |
& - phyFac*dPhiHydY(i,j) |
| 520 |
adcroft |
1.1 |
ENDDO |
| 521 |
|
|
ENDDO |
| 522 |
|
|
|
| 523 |
heimbach |
1.4.6.1 |
#ifdef NONLIN_FRSURF |
| 524 |
|
|
C-- account for 3.D divergence of the flow in rStar coordinate: |
| 525 |
|
|
IF ( momAdvection .AND. select_rStar.GT.0 ) THEN |
| 526 |
|
|
DO j=jMin,jMax |
| 527 |
|
|
DO i=iMin,iMax |
| 528 |
|
|
gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj) |
| 529 |
|
|
& - (rStarExpS(i,j,bi,bj) - 1. _d 0)/deltaTfreesurf |
| 530 |
|
|
& *vVel(i,j,k,bi,bj) |
| 531 |
|
|
ENDDO |
| 532 |
|
|
ENDDO |
| 533 |
|
|
ENDIF |
| 534 |
|
|
IF ( momAdvection .AND. select_rStar.LT.0 ) THEN |
| 535 |
|
|
DO j=jMin,jMax |
| 536 |
|
|
DO i=iMin,iMax |
| 537 |
|
|
gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj) |
| 538 |
|
|
& - rStarDhSDt(i,j,bi,bj)*vVel(i,j,k,bi,bj) |
| 539 |
|
|
ENDDO |
| 540 |
|
|
ENDDO |
| 541 |
|
|
ENDIF |
| 542 |
|
|
#endif /* NONLIN_FRSURF */ |
| 543 |
|
|
|
| 544 |
adcroft |
1.1 |
C-- No-slip and drag BCs appear as body forces in cell abutting topography |
| 545 |
|
|
IF (momViscosity.AND.no_slip_sides) THEN |
| 546 |
|
|
C- No-slip BCs impose a drag at walls... |
| 547 |
|
|
CALL MOM_V_SIDEDRAG(bi,bj,k,vFld,v4F,hFacZ,vF,myThid) |
| 548 |
|
|
DO j=jMin,jMax |
| 549 |
|
|
DO i=iMin,iMax |
| 550 |
|
|
gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+vF(i,j) |
| 551 |
|
|
ENDDO |
| 552 |
|
|
ENDDO |
| 553 |
|
|
ENDIF |
| 554 |
|
|
C- No-slip BCs impose a drag at bottom |
| 555 |
|
|
IF (momViscosity.AND.bottomDragTerms) THEN |
| 556 |
|
|
CALL MOM_V_BOTTOMDRAG(bi,bj,k,vFld,KE,KappaRV,vF,myThid) |
| 557 |
|
|
DO j=jMin,jMax |
| 558 |
|
|
DO i=iMin,iMax |
| 559 |
|
|
gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+vF(i,j) |
| 560 |
|
|
ENDDO |
| 561 |
|
|
ENDDO |
| 562 |
|
|
ENDIF |
| 563 |
|
|
|
| 564 |
heimbach |
1.4.6.2 |
C-- Forcing term (moved to timestep.F) |
| 565 |
|
|
c IF (momForcing) |
| 566 |
|
|
c & CALL EXTERNAL_FORCING_V( |
| 567 |
|
|
c I iMin,iMax,jMin,jMax,bi,bj,k, |
| 568 |
|
|
c I myTime,myThid) |
| 569 |
adcroft |
1.1 |
|
| 570 |
|
|
C-- Metric terms for curvilinear grid systems |
| 571 |
heimbach |
1.4.6.1 |
IF (useNHMTerms) THEN |
| 572 |
adcroft |
1.1 |
C o Spherical polar grid metric terms |
| 573 |
|
|
CALL MOM_V_METRIC_NH(bi,bj,k,vFld,wVel,mT,myThid) |
| 574 |
|
|
DO j=jMin,jMax |
| 575 |
|
|
DO i=iMin,iMax |
| 576 |
|
|
gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+mTFacV*mT(i,j) |
| 577 |
|
|
ENDDO |
| 578 |
|
|
ENDDO |
| 579 |
heimbach |
1.4.6.1 |
ENDIF |
| 580 |
|
|
IF (usingSphericalPolarMTerms) THEN |
| 581 |
adcroft |
1.1 |
CALL MOM_V_METRIC_SPHERE(bi,bj,k,uFld,mT,myThid) |
| 582 |
|
|
DO j=jMin,jMax |
| 583 |
|
|
DO i=iMin,iMax |
| 584 |
|
|
gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+mTFacV*mT(i,j) |
| 585 |
|
|
ENDDO |
| 586 |
|
|
ENDDO |
| 587 |
|
|
ENDIF |
| 588 |
|
|
|
| 589 |
|
|
C-- Set dv/dt on boundaries to zero |
| 590 |
|
|
DO j=jMin,jMax |
| 591 |
|
|
DO i=iMin,iMax |
| 592 |
|
|
gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)*_maskS(i,j,k,bi,bj) |
| 593 |
|
|
ENDDO |
| 594 |
|
|
ENDDO |
| 595 |
|
|
|
| 596 |
|
|
C-- Coriolis term |
| 597 |
|
|
C Note. As coded here, coriolis will not work with "thin walls" |
| 598 |
heimbach |
1.4.6.2 |
c IF (useCDscheme) THEN |
| 599 |
|
|
c CALL MOM_CDSCHEME(bi,bj,k,dPhiHydX,dPhiHydY,myThid) |
| 600 |
|
|
c ELSE |
| 601 |
|
|
IF (.NOT.useCDscheme) THEN |
| 602 |
|
|
CALL MOM_U_CORIOLIS(bi,bj,k,vFld,cf,myThid) |
| 603 |
|
|
DO j=jMin,jMax |
| 604 |
|
|
DO i=iMin,iMax |
| 605 |
|
|
gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+fuFac*cf(i,j) |
| 606 |
|
|
ENDDO |
| 607 |
|
|
ENDDO |
| 608 |
|
|
CALL MOM_V_CORIOLIS(bi,bj,k,uFld,cf,myThid) |
| 609 |
|
|
DO j=jMin,jMax |
| 610 |
|
|
DO i=iMin,iMax |
| 611 |
|
|
gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+fvFac*cf(i,j) |
| 612 |
|
|
ENDDO |
| 613 |
|
|
ENDDO |
| 614 |
|
|
ENDIF |
| 615 |
|
|
|
| 616 |
heimbach |
1.4.6.1 |
IF (nonHydrostatic.OR.quasiHydrostatic) THEN |
| 617 |
|
|
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 |
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