/[MITgcm]/MITgcm/pkg/mom_vecinv/mom_vecinv.F
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revision 1.37 by jmc, Sat Apr 30 20:26:21 2005 UTC revision 1.54 by jmc, Wed Oct 12 01:52:09 2005 UTC
# Line 5  C $Name$ Line 5  C $Name$
5    
6        SUBROUTINE MOM_VECINV(        SUBROUTINE MOM_VECINV(
7       I        bi,bj,iMin,iMax,jMin,jMax,k,kUp,kDown,       I        bi,bj,iMin,iMax,jMin,jMax,k,kUp,kDown,
8       I        dPhiHydX,dPhiHydY,KappaRU,KappaRV,       I        KappaRU, KappaRV,
9       U        fVerU, fVerV,       U        fVerU, fVerV,
10       O        guDiss, gvDiss,       O        guDiss, gvDiss,
11       I        myTime, myIter, myThid)       I        myTime, myIter, myThid)
# Line 42  C     == Global variables == Line 42  C     == Global variables ==
42  C     == Routine arguments ==  C     == Routine arguments ==
43  C     fVerU  :: Flux of momentum in the vertical direction, out of the upper  C     fVerU  :: Flux of momentum in the vertical direction, out of the upper
44  C     fVerV  :: face of a cell K ( flux into the cell above ).  C     fVerV  :: face of a cell K ( flux into the cell above ).
 C     dPhiHydX,Y :: Gradient (X & Y dir.) of Hydrostatic Potential  
45  C     guDiss :: dissipation tendency (all explicit terms), u component  C     guDiss :: dissipation tendency (all explicit terms), u component
46  C     gvDiss :: dissipation tendency (all explicit terms), v component  C     gvDiss :: dissipation tendency (all explicit terms), v component
47  C     bi, bj, iMin, iMax, jMin, jMax - Range of points for which calculation  C     bi, bj, iMin, iMax, jMin, jMax - Range of points for which calculation
48  C                                      results will be set.  C                                      results will be set.
49  C     kUp, kDown                     - Index for upper and lower layers.  C     kUp, kDown                     - Index for upper and lower layers.
50  C     myThid - Instance number for this innvocation of CALC_MOM_RHS  C     myThid :: my Thread Id number
       _RL dPhiHydX(1-Olx:sNx+Olx,1-Oly:sNy+Oly)  
       _RL dPhiHydY(1-Olx:sNx+Olx,1-Oly:sNy+Oly)  
51        _RL KappaRU(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)        _RL KappaRU(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
52        _RL KappaRV(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)        _RL KappaRV(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
53        _RL fVerU(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2)        _RL fVerU(1-OLx:sNx+OLx,1-OLy:sNy+OLy,2)
# Line 66  C     myThid - Instance number for this Line 63  C     myThid - Instance number for this
63  #ifdef ALLOW_MOM_VECINV  #ifdef ALLOW_MOM_VECINV
64    
65  C     == Functions ==  C     == Functions ==
66        LOGICAL  DIFF_BASE_MULTIPLE        LOGICAL  DIFFERENT_MULTIPLE
67        EXTERNAL DIFF_BASE_MULTIPLE        EXTERNAL DIFFERENT_MULTIPLE
68    
69  C     == Local variables ==  C     == Local variables ==
70        _RL      vF (1-OLx:sNx+OLx,1-OLy:sNy+OLy)        _RL      vF (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
71        _RL      vrF (1-OLx:sNx+OLx,1-OLy:sNy+OLy)        _RL      vrF(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
72        _RL      uCf (1-OLx:sNx+OLx,1-OLy:sNy+OLy)        _RL      uCf(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
73        _RL      vCf (1-OLx:sNx+OLx,1-OLy:sNy+OLy)        _RL      vCf(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
74  c     _RL      mT (1-OLx:sNx+OLx,1-OLy:sNy+OLy)  c     _RL      mT (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
75        _RL del2u(1-OLx:sNx+OLx,1-OLy:sNy+OLy)        _RS hFacZ   (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
76        _RL del2v(1-OLx:sNx+OLx,1-OLy:sNy+OLy)        _RS r_hFacZ (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
77        _RL tension(1-OLx:sNx+OLx,1-OLy:sNy+OLy)        _RL uFld    (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
78        _RL strain(1-OLx:sNx+OLx,1-OLy:sNy+OLy)        _RL vFld    (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
79        _RS hFacZ(1-OLx:sNx+OLx,1-OLy:sNy+OLy)        _RL del2u   (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
80        _RS r_hFacZ(1-OLx:sNx+OLx,1-OLy:sNy+OLy)        _RL del2v   (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
81        _RL uFld(1-OLx:sNx+OLx,1-OLy:sNy+OLy)        _RL dStar   (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
82        _RL vFld(1-OLx:sNx+OLx,1-OLy:sNy+OLy)        _RL zStar   (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
83        _RL dStar(1-OLx:sNx+OLx,1-OLy:sNy+OLy)        _RL tension (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
84        _RL zStar(1-OLx:sNx+OLx,1-OLy:sNy+OLy)        _RL strain  (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
85  C     I,J,K - Loop counters        _RL KE      (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
86          _RL omega3  (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
87          _RL vort3   (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
88          _RL hDiv    (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
89          _RL viscAh_Z(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
90          _RL viscAh_D(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
91          _RL viscA4_Z(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
92          _RL viscA4_D(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
93    C     i,j,k  :: Loop counters
94        INTEGER i,j,k        INTEGER i,j,k
95  C     xxxFac - On-off tracer parameters used for switching terms off.  C     xxxFac - On-off tracer parameters used for switching terms off.
96        _RL  ArDudrFac        _RL  ArDudrFac
       _RL  phxFac  
97  c     _RL  mtFacU  c     _RL  mtFacU
98        _RL  ArDvdrFac        _RL  ArDvdrFac
       _RL  phyFac  
99  c     _RL  mtFacV  c     _RL  mtFacV
100          _RL  sideMaskFac
101        LOGICAL bottomDragTerms        LOGICAL bottomDragTerms
102        LOGICAL writeDiag        LOGICAL writeDiag
103        _RL KE(1-OLx:sNx+OLx,1-OLy:sNy+OLy)        LOGICAL harmonic,biharmonic,useVariableViscosity
       _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)  
104    
105  #ifdef ALLOW_MNC  #ifdef ALLOW_MNC
106        INTEGER offsets(9)        INTEGER offsets(9)
107          CHARACTER*(1) pf
108  #endif  #endif
109    
110  #ifdef ALLOW_AUTODIFF_TAMC  #ifdef ALLOW_AUTODIFF_TAMC
# Line 114  C--   (at least in part) Line 116  C--   (at least in part)
116        fVerV(1,1,kUp) = fVerV(1,1,kUp)        fVerV(1,1,kUp) = fVerV(1,1,kUp)
117  #endif  #endif
118    
119        writeDiag = DIFF_BASE_MULTIPLE(baseTime, diagFreq,        writeDiag = DIFFERENT_MULTIPLE(diagFreq, myTime, deltaTClock)
      &                               myTime, deltaTClock)  
120    
121  #ifdef ALLOW_MNC  #ifdef ALLOW_MNC
122        IF (useMNC .AND. snapshot_mnc .AND. writeDiag) THEN        IF (useMNC .AND. snapshot_mnc .AND. writeDiag) THEN
123            IF ( writeBinaryPrec .EQ. precFloat64 ) THEN
124              pf(1:1) = 'D'
125            ELSE
126              pf(1:1) = 'R'
127            ENDIF
128          IF ((bi .EQ. 1).AND.(bj .EQ. 1).AND.(k .EQ. 1)) THEN          IF ((bi .EQ. 1).AND.(bj .EQ. 1).AND.(k .EQ. 1)) THEN
129            CALL MNC_CW_SET_UDIM('mom_vi', -1, myThid)            CALL MNC_CW_SET_UDIM('mom_vi', -1, myThid)
130            CALL MNC_CW_I_W_S('I','mom_vi',0,0,'T',myIter,myThid)            CALL MNC_CW_RL_W_S('D','mom_vi',0,0,'T',myTime,myThid)
131            CALL MNC_CW_SET_UDIM('mom_vi', 0, myThid)            CALL MNC_CW_SET_UDIM('mom_vi', 0, myThid)
132              CALL MNC_CW_I_W_S('I','mom_vi',0,0,'iter',myIter,myThid)
133          ENDIF          ENDIF
134          DO i = 1,9          DO i = 1,9
135            offsets(i) = 0            offsets(i) = 0
# Line 148  c       mT(i,j)    = 0. Line 155  c       mT(i,j)    = 0.
155          gvDiss(i,j)= 0.          gvDiss(i,j)= 0.
156          vort3(i,j) = 0.          vort3(i,j) = 0.
157          omega3(i,j)= 0.          omega3(i,j)= 0.
158          ke(i,j)    = 0.          KE(i,j)    = 0.
159            viscAh_Z(i,j) = 0.
160            viscAh_D(i,j) = 0.
161            viscA4_Z(i,j) = 0.
162            viscA4_D(i,j) = 0.
163    
164  #ifdef ALLOW_AUTODIFF_TAMC  #ifdef ALLOW_AUTODIFF_TAMC
165          strain(i,j)  = 0. _d 0          strain(i,j)  = 0. _d 0
166          tension(i,j) = 0. _d 0          tension(i,j) = 0. _d 0
# Line 160  C--   Term by term tracer parmeters Line 172  C--   Term by term tracer parmeters
172  C     o U momentum equation  C     o U momentum equation
173        ArDudrFac    = vfFacMom*1.        ArDudrFac    = vfFacMom*1.
174  c     mTFacU       = mtFacMom*1.  c     mTFacU       = mtFacMom*1.
       phxFac       = pfFacMom*1.  
175  C     o V momentum equation  C     o V momentum equation
176        ArDvdrFac    = vfFacMom*1.        ArDvdrFac    = vfFacMom*1.
177  c     mTFacV       = mtFacMom*1.  c     mTFacV       = mtFacMom*1.
178        phyFac       = pfFacMom*1.  
179    C note: using standard stencil (no mask) results in under-estimating
180    C       vorticity at a no-slip boundary by a factor of 2 = sideDragFactor
181          IF ( no_slip_sides ) THEN
182            sideMaskFac = sideDragFactor
183          ELSE
184            sideMaskFac = 0. _d 0
185          ENDIF
186    
187        IF (     no_slip_bottom        IF (     no_slip_bottom
188       &    .OR. bottomDragQuadratic.NE.0.       &    .OR. bottomDragQuadratic.NE.0.
# Line 174  c     mTFacV       = mtFacMom*1. Line 192  c     mTFacV       = mtFacMom*1.
192         bottomDragTerms=.FALSE.         bottomDragTerms=.FALSE.
193        ENDIF        ENDIF
194    
 C-- with stagger time stepping, grad Phi_Hyp is directly incoporated in TIMESTEP  
       IF (staggerTimeStep) THEN  
         phxFac = 0.  
         phyFac = 0.  
       ENDIF  
   
195  C--   Calculate open water fraction at vorticity points  C--   Calculate open water fraction at vorticity points
196        CALL MOM_CALC_HFACZ(bi,bj,k,hFacZ,r_hFacZ,myThid)        CALL MOM_CALC_HFACZ(bi,bj,k,hFacZ,r_hFacZ,myThid)
197    
# Line 195  C note (jmc) : Dissipation and Vort3 adv Line 207  C note (jmc) : Dissipation and Vort3 adv
207  C              use the same maskZ (and hFacZ)  => needs 2 call(s)  C              use the same maskZ (and hFacZ)  => needs 2 call(s)
208  c     CALL MOM_VI_HFACZ_DISS(bi,bj,k,hFacZ,r_hFacZ,myThid)  c     CALL MOM_VI_HFACZ_DISS(bi,bj,k,hFacZ,r_hFacZ,myThid)
209    
210        CALL MOM_CALC_KE(bi,bj,k,2,uFld,vFld,KE,myThid)        CALL MOM_CALC_KE(bi,bj,k,selectKEscheme,uFld,vFld,KE,myThid)
   
       CALL MOM_CALC_HDIV(bi,bj,k,2,uFld,vFld,hDiv,myThid)  
211    
212        CALL MOM_CALC_RELVORT3(bi,bj,k,uFld,vFld,hFacZ,vort3,myThid)        CALL MOM_CALC_RELVORT3(bi,bj,k,uFld,vFld,hFacZ,vort3,myThid)
213    
       IF (useAbsVorticity)  
      & CALL MOM_CALC_ABSVORT3(bi,bj,k,vort3,omega3,myThid)  
   
214        IF (momViscosity) THEN        IF (momViscosity) THEN
215    C--    For viscous term, compute horizontal divergence, tension & strain
216    C      and mask relative vorticity (free-slip case):
217    
218           CALL MOM_CALC_HDIV(bi,bj,k,2,uFld,vFld,hDiv,myThid)
219    
220           CALL MOM_CALC_TENSION(bi,bj,k,uFld,vFld,tension,myThid)
221    
222           CALL MOM_CALC_STRAIN(bi,bj,k,uFld,vFld,hFacZ,strain,myThid)
223    
224    C-     account for no-slip / free-slip BC:
225           DO j=1-Oly,sNy+Oly
226            DO i=1-Olx,sNx+Olx
227              IF ( hFacZ(i,j).EQ.0. ) THEN
228                vort3(i,j)  = sideMaskFac*vort3(i,j)
229                strain(i,j) = sideMaskFac*strain(i,j)
230              ENDIF
231            ENDDO
232           ENDDO
233    
234    C--    Calculate Viscosities
235           CALL MOM_CALC_VISC(
236         I        bi,bj,k,
237         O        viscAh_Z,viscAh_D,viscA4_Z,viscA4_D,
238         O        harmonic,biharmonic,useVariableViscosity,
239         I        hDiv,vort3,tension,strain,KE,hfacZ,
240         I        myThid)
241    
242  C      Calculate del^2 u and del^2 v for bi-harmonic term  C      Calculate del^2 u and del^2 v for bi-harmonic term
243         IF ( (viscA4.NE.0. .AND. no_slip_sides)         IF (biharmonic) THEN
      &     .OR. viscA4D.NE.0. .OR. viscA4Z.NE.0.  
      &     .OR. viscA4Grid.NE.0.  
      &     .OR. viscC4leith.NE.0.  
      &     .OR. viscC4leithD.NE.0.  
      &    ) THEN  
244           CALL MOM_VI_DEL2UV(bi,bj,k,hDiv,vort3,hFacZ,           CALL MOM_VI_DEL2UV(bi,bj,k,hDiv,vort3,hFacZ,
245       O                      del2u,del2v,       O                      del2u,del2v,
246       &                      myThid)       &                      myThid)
247           CALL MOM_CALC_HDIV(bi,bj,k,2,del2u,del2v,dStar,myThid)           CALL MOM_CALC_HDIV(bi,bj,k,2,del2u,del2v,dStar,myThid)
248           CALL MOM_CALC_RELVORT3(           CALL MOM_CALC_RELVORT3(bi,bj,k,
249       &                         bi,bj,k,del2u,del2v,hFacZ,zStar,myThid)       &                          del2u,del2v,hFacZ,zStar,myThid)
250         ENDIF         ENDIF
251  C      Calculate dissipation terms for U and V equations  
252  C      in terms of vorticity and divergence  C-    Strain diagnostics:
253         IF (    viscAhD.NE.0. .OR. viscAhZ.NE.0.         IF ( writeDiag ) THEN
254       &    .OR. viscA4D.NE.0. .OR. viscA4Z.NE.0.          IF (snapshot_mdsio) THEN
255       &    .OR. viscAhGrid.NE.0. .OR. viscA4Grid.NE.0.            CALL WRITE_LOCAL_RL('Ds','I10',1,strain,bi,bj,k,myIter,myThid)
256       &    .OR. viscC2leith.NE.0. .OR. viscC4leith.NE.0.          ENDIF
257       &    .OR. viscC2leithD.NE.0. .OR. viscC4leithD.NE.0.  #ifdef ALLOW_MNC
258       &    ) THEN          IF (useMNC .AND. snapshot_mnc) THEN
259           CALL MOM_VI_HDISSIP(bi,bj,k,hDiv,vort3,hFacZ,dStar,zStar,            CALL MNC_CW_RL_W_OFFSET(pf,'mom_vi',bi,bj,'Ds',strain,
260       O                       guDiss,gvDiss,       &          offsets, myThid)
261       &                       myThid)          ENDIF
262    #endif /*  ALLOW_MNC  */
263         ENDIF         ENDIF
264  C      or in terms of tension and strain  #ifdef ALLOW_DIAGNOSTICS
265         IF (viscAstrain.NE.0. .OR. viscAtension.NE.0.         IF ( useDiagnostics ) THEN
266       O      .OR. viscC2smag.ne.0) THEN          CALL DIAGNOSTICS_FILL(strain, 'Strain  ',k,1,2,bi,bj,myThid)
267           CALL MOM_CALC_TENSION(bi,bj,k,uFld,vFld,         ENDIF
268       O                         tension,  #endif /* ALLOW_DIAGNOSTICS */
269       I                         myThid)  
270           CALL MOM_CALC_STRAIN(bi,bj,k,uFld,vFld,hFacZ,  C---   Calculate dissipation terms for U and V equations
271       O                        strain,  
272       I                        myThid)  C      in terms of tension and strain
273           CALL MOM_HDISSIP(bi,bj,k,         IF (useStrainTensionVisc) THEN
274       I                    tension,strain,hFacZ,viscAtension,viscAstrain,  C        mask strain as if free-slip since side-drag is computed separately
275             DO j=1-Oly,sNy+Oly
276              DO i=1-Olx,sNx+Olx
277                IF ( hFacZ(i,j).EQ.0. ) strain(i,j) = 0. _d 0
278              ENDDO
279             ENDDO
280             CALL MOM_HDISSIP(bi,bj,k,hDiv,vort3,tension,strain,KE,
281         I                    hFacZ,
282         I                    viscAh_Z,viscAh_D,viscA4_Z,viscA4_D,
283         I                    harmonic,biharmonic,useVariableViscosity,
284       O                    guDiss,gvDiss,       O                    guDiss,gvDiss,
285       I                    myThid)       I                    myThid)
286           ELSE
287    C      in terms of vorticity and divergence
288             CALL MOM_VI_HDISSIP(bi,bj,k,hDiv,vort3,tension,strain,KE,
289         I                       hFacZ,dStar,zStar,
290         I                       viscAh_Z,viscAh_D,viscA4_Z,viscA4_D,
291         I                       harmonic,biharmonic,useVariableViscosity,
292         O                       guDiss,gvDiss,
293         &                       myThid)        
294         ENDIF         ENDIF
295    C--   if (momViscosity) end of block.
296        ENDIF        ENDIF
297    
298  C-    Return to standard hfacZ (min-4) and mask vort3 accordingly:  C-    Return to standard hfacZ (min-4) and mask vort3 accordingly:
299  c     CALL MOM_VI_MASK_VORT3(bi,bj,k,hFacZ,r_hFacZ,vort3,myThid)  c     CALL MOM_VI_MASK_VORT3(bi,bj,k,hFacZ,r_hFacZ,vort3,myThid)
300    
301  C---- Zonal momentum equation starts here  C---  Other dissipation terms in Zonal momentum equation
302    
303  C--   Vertical flux (fVer is at upper face of "u" cell)  C--   Vertical flux (fVer is at upper face of "u" cell)
304    
305  C     Eddy component of vertical flux (interior component only) -> vrF  C     Eddy component of vertical flux (interior component only) -> vrF
306        IF (momViscosity.AND..NOT.implicitViscosity) THEN        IF (momViscosity.AND..NOT.implicitViscosity) THEN
307         CALL MOM_U_RVISCFLUX(bi,bj,k,uVel,KappaRU,vrF,myThid)         CALL MOM_U_RVISCFLUX(bi,bj,k+1,uVel,KappaRU,vrF,myThid)
308    
309  C     Combine fluxes  C     Combine fluxes
310         DO j=jMin,jMax         DO j=jMin,jMax
# Line 272  C--   Tendency is minus divergence of th Line 320  C--   Tendency is minus divergence of th
320       &   -_recip_hFacW(i,j,k,bi,bj)*recip_drF(k)       &   -_recip_hFacW(i,j,k,bi,bj)*recip_drF(k)
321       &   *recip_rAw(i,j,bi,bj)       &   *recip_rAw(i,j,bi,bj)
322       &  *(       &  *(
323       &   +fVerU(i,j,kUp)*rkFac - fVerU(i,j,kDown)*rkFac       &    fVerU(i,j,kDown) - fVerU(i,j,kUp)
324       &   )       &   )*rkSign
325          ENDDO          ENDDO
326         ENDDO         ENDDO
327        ENDIF        ENDIF
# Line 281  C--   Tendency is minus divergence of th Line 329  C--   Tendency is minus divergence of th
329  C-- No-slip and drag BCs appear as body forces in cell abutting topography  C-- No-slip and drag BCs appear as body forces in cell abutting topography
330        IF (momViscosity.AND.no_slip_sides) THEN        IF (momViscosity.AND.no_slip_sides) THEN
331  C-     No-slip BCs impose a drag at walls...  C-     No-slip BCs impose a drag at walls...
332         CALL MOM_U_SIDEDRAG(bi,bj,k,uFld,del2u,hFacZ,vF,myThid)         CALL MOM_U_SIDEDRAG(
333         I        bi,bj,k,
334         I        uFld, del2u, hFacZ,
335         I        viscAh_Z,viscA4_Z,
336         I        harmonic,biharmonic,useVariableViscosity,
337         O        vF,
338         I        myThid)
339         DO j=jMin,jMax         DO j=jMin,jMax
340          DO i=iMin,iMax          DO i=iMin,iMax
341           guDiss(i,j) = guDiss(i,j)+vF(i,j)           guDiss(i,j) = guDiss(i,j)+vF(i,j)
342          ENDDO          ENDDO
343         ENDDO         ENDDO
344        ENDIF        ENDIF
   
345  C-    No-slip BCs impose a drag at bottom  C-    No-slip BCs impose a drag at bottom
346        IF (momViscosity.AND.bottomDragTerms) THEN        IF (momViscosity.AND.bottomDragTerms) THEN
347         CALL MOM_U_BOTTOMDRAG(bi,bj,k,uFld,KE,KappaRU,vF,myThid)         CALL MOM_U_BOTTOMDRAG(bi,bj,k,uFld,KE,KappaRU,vF,myThid)
# Line 299  C-    No-slip BCs impose a drag at botto Line 352  C-    No-slip BCs impose a drag at botto
352         ENDDO         ENDDO
353        ENDIF        ENDIF
354    
355  C--   Metric terms for curvilinear grid systems  C---  Other dissipation terms in Meridional momentum equation
 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  
356    
357  C--   Vertical flux (fVer is at upper face of "v" cell)  C--   Vertical flux (fVer is at upper face of "v" cell)
358    
359  C     Eddy component of vertical flux (interior component only) -> vrF  C     Eddy component of vertical flux (interior component only) -> vrF
360        IF (momViscosity.AND..NOT.implicitViscosity) THEN        IF (momViscosity.AND..NOT.implicitViscosity) THEN
361         CALL MOM_V_RVISCFLUX(bi,bj,k,vVel,KappaRV,vrf,myThid)         CALL MOM_V_RVISCFLUX(bi,bj,k+1,vVel,KappaRV,vrF,myThid)
362    
363  C     Combine fluxes -> fVerV  C     Combine fluxes -> fVerV
364         DO j=jMin,jMax         DO j=jMin,jMax
# Line 332  C--   Tendency is minus divergence of th Line 374  C--   Tendency is minus divergence of th
374       &   -_recip_hFacS(i,j,k,bi,bj)*recip_drF(k)       &   -_recip_hFacS(i,j,k,bi,bj)*recip_drF(k)
375       &    *recip_rAs(i,j,bi,bj)       &    *recip_rAs(i,j,bi,bj)
376       &  *(       &  *(
377       &   +fVerV(i,j,kUp)*rkFac - fVerV(i,j,kDown)*rkFac       &    fVerV(i,j,kDown) - fVerV(i,j,kUp)
378       &   )       &   )*rkSign
379          ENDDO          ENDDO
380         ENDDO         ENDDO
381        ENDIF        ENDIF
# Line 341  C--   Tendency is minus divergence of th Line 383  C--   Tendency is minus divergence of th
383  C-- No-slip and drag BCs appear as body forces in cell abutting topography  C-- No-slip and drag BCs appear as body forces in cell abutting topography
384        IF (momViscosity.AND.no_slip_sides) THEN        IF (momViscosity.AND.no_slip_sides) THEN
385  C-     No-slip BCs impose a drag at walls...  C-     No-slip BCs impose a drag at walls...
386         CALL MOM_V_SIDEDRAG(bi,bj,k,vFld,del2v,hFacZ,vF,myThid)         CALL MOM_V_SIDEDRAG(
387         I        bi,bj,k,
388         I        vFld, del2v, hFacZ,
389         I        viscAh_Z,viscA4_Z,
390         I        harmonic,biharmonic,useVariableViscosity,
391         O        vF,
392         I        myThid)
393         DO j=jMin,jMax         DO j=jMin,jMax
394          DO i=iMin,iMax          DO i=iMin,iMax
395           gvDiss(i,j) = gvDiss(i,j)+vF(i,j)           gvDiss(i,j) = gvDiss(i,j)+vF(i,j)
# Line 358  C-    No-slip BCs impose a drag at botto Line 406  C-    No-slip BCs impose a drag at botto
406         ENDDO         ENDDO
407        ENDIF        ENDIF
408    
409  C--   Metric terms for curvilinear grid systems  C-    Vorticity diagnostics:
410  c     IF (usingSphericalPolarMTerms) THEN        IF ( writeDiag ) THEN
411  C      o Spherical polar grid metric terms          IF (snapshot_mdsio) THEN
412  c      CALL MOM_V_METRIC_NH(bi,bj,k,vFld,wVel,mT,myThid)            CALL WRITE_LOCAL_RL('Z3','I10',1,vort3, bi,bj,k,myIter,myThid)
413  c      DO j=jMin,jMax          ENDIF
414  c       DO i=iMin,iMax  #ifdef ALLOW_MNC
415  c        gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+mTFacV*mT(i,j)          IF (useMNC .AND. snapshot_mnc) THEN
416  c       ENDDO            CALL MNC_CW_RL_W_OFFSET(pf,'mom_vi',bi,bj,'Z3',vort3,
417  c      ENDDO       &          offsets, myThid)
418  c     ENDIF          ENDIF
419    #endif /*  ALLOW_MNC  */
420          ENDIF
421    #ifdef ALLOW_DIAGNOSTICS
422          IF ( useDiagnostics ) THEN
423            CALL DIAGNOSTICS_FILL(vort3,  'momVort3',k,1,2,bi,bj,myThid)
424          ENDIF
425    #endif /* ALLOW_DIAGNOSTICS */
426    
427    C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|
428    
429    C---  Prepare for Advection & Coriolis terms:
430    C-    Mask relative vorticity and calculate absolute vorticity
431          DO j=1-Oly,sNy+Oly
432           DO i=1-Olx,sNx+Olx
433             IF ( hFacZ(i,j).EQ.0. ) vort3(i,j) = 0.
434           ENDDO
435          ENDDO
436          IF (useAbsVorticity)
437         &  CALL MOM_CALC_ABSVORT3(bi,bj,k,vort3,omega3,myThid)
438    
439  C--   Horizontal Coriolis terms  C--   Horizontal Coriolis terms
440  c     IF (useCoriolis .AND. .NOT.useCDscheme  c     IF (useCoriolis .AND. .NOT.useCDscheme
441  c    &    .AND. .NOT. useAbsVorticity) THEN  c    &    .AND. .NOT. useAbsVorticity) THEN
442  C- jmc: change it to keep the Coriolis terms when useAbsVorticity=T & momAdvection=F  C- jmc: change it to keep the Coriolis terms when useAbsVorticity=T & momAdvection=F
443        IF ( useCoriolis .AND.        IF ( useCoriolis .AND.
444       &     .NOT.( useCDscheme .OR. useAbsVorticity.AND.momAdvection )       &     .NOT.( useCDscheme .OR. useAbsVorticity.AND.momAdvection )
445       &   ) THEN       &   ) THEN
446         IF (useAbsVorticity) THEN         IF (useAbsVorticity) THEN
# Line 387  C- jmc: change it to keep the Coriolis t Line 454  C- jmc: change it to keep the Coriolis t
454         ENDIF         ENDIF
455         DO j=jMin,jMax         DO j=jMin,jMax
456          DO i=iMin,iMax          DO i=iMin,iMax
457           gU(i,j,k,bi,bj) = uCf(i,j) - phxFac*dPhiHydX(i,j)           gU(i,j,k,bi,bj) = uCf(i,j)
458           gV(i,j,k,bi,bj) = vCf(i,j) - phyFac*dPhiHydY(i,j)           gV(i,j,k,bi,bj) = vCf(i,j)
459          ENDDO          ENDDO
460         ENDDO         ENDDO
461    
462         IF ( writeDiag ) THEN         IF ( writeDiag ) THEN
463           IF (snapshot_mdsio) THEN           IF (snapshot_mdsio) THEN
464             CALL WRITE_LOCAL_RL('fV','I10',1,uCf,bi,bj,k,myIter,myThid)             CALL WRITE_LOCAL_RL('fV','I10',1,uCf,bi,bj,k,myIter,myThid)
# Line 398  C- jmc: change it to keep the Coriolis t Line 466  C- jmc: change it to keep the Coriolis t
466           ENDIF           ENDIF
467  #ifdef ALLOW_MNC  #ifdef ALLOW_MNC
468           IF (useMNC .AND. snapshot_mnc) THEN           IF (useMNC .AND. snapshot_mnc) THEN
469             CALL MNC_CW_RL_W_OFFSET('D','mom_vi',bi,bj, 'fV', uCf,             CALL MNC_CW_RL_W_OFFSET(pf,'mom_vi',bi,bj, 'fV', uCf,
470       &          offsets, myThid)       &          offsets, myThid)
471             CALL MNC_CW_RL_W_OFFSET('D','mom_vi',bi,bj, 'fU', vCf,             CALL MNC_CW_RL_W_OFFSET(pf,'mom_vi',bi,bj, 'fU', vCf,
472       &          offsets, myThid)       &          offsets, myThid)
473           ENDIF           ENDIF
474  #endif /*  ALLOW_MNC  */  #endif /*  ALLOW_MNC  */
475         ENDIF         ENDIF
476    #ifdef ALLOW_DIAGNOSTICS
477           IF ( useDiagnostics ) THEN
478             CALL DIAGNOSTICS_FILL(uCf,'Um_Cori ',k,1,2,bi,bj,myThid)
479             CALL DIAGNOSTICS_FILL(vCf,'Vm_Cori ',k,1,2,bi,bj,myThid)
480           ENDIF
481    #endif /* ALLOW_DIAGNOSTICS */
482    
483        ELSE        ELSE
484         DO j=jMin,jMax         DO j=jMin,jMax
485          DO i=iMin,iMax          DO i=iMin,iMax
486           gU(i,j,k,bi,bj) = -phxFac*dPhiHydX(i,j)           gU(i,j,k,bi,bj) = 0. _d 0
487           gV(i,j,k,bi,bj) = -phyFac*dPhiHydY(i,j)           gV(i,j,k,bi,bj) = 0. _d 0
488          ENDDO          ENDDO
489         ENDDO         ENDDO
490        ENDIF        ENDIF
491    
492        IF (momAdvection) THEN        IF (momAdvection) THEN
493  C--   Horizontal advection of relative vorticity  C--   Horizontal advection of relative (or absolute) vorticity
494         IF (useAbsVorticity) THEN         IF (highOrderVorticity.AND.useAbsVorticity) THEN
495            CALL MOM_VI_U_CORIOLIS_C4(bi,bj,k,vFld,omega3,r_hFacZ,
496         &                         uCf,myThid)
497           ELSEIF (highOrderVorticity) THEN
498            CALL MOM_VI_U_CORIOLIS_C4(bi,bj,k,vFld,vort3, r_hFacZ,
499         &                         uCf,myThid)
500           ELSEIF (useAbsVorticity) THEN
501          CALL MOM_VI_U_CORIOLIS(bi,bj,K,vFld,omega3,hFacZ,r_hFacZ,          CALL MOM_VI_U_CORIOLIS(bi,bj,K,vFld,omega3,hFacZ,r_hFacZ,
502       &                         uCf,myThid)       &                         uCf,myThid)
503         ELSE         ELSE
504          CALL MOM_VI_U_CORIOLIS(bi,bj,k,vFld,vort3,hFacZ,r_hFacZ,          CALL MOM_VI_U_CORIOLIS(bi,bj,k,vFld,vort3, hFacZ,r_hFacZ,
505       &                         uCf,myThid)       &                         uCf,myThid)
506         ENDIF         ENDIF
 c      CALL MOM_VI_U_CORIOLIS_C4(bi,bj,K,vFld,vort3,r_hFacZ,uCf,myThid)  
507         DO j=jMin,jMax         DO j=jMin,jMax
508          DO i=iMin,iMax          DO i=iMin,iMax
509           gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+uCf(i,j)           gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+uCf(i,j)
510          ENDDO          ENDDO
511         ENDDO         ENDDO
512         IF (useAbsVorticity) THEN         IF (highOrderVorticity.AND.useAbsVorticity) THEN
513            CALL MOM_VI_V_CORIOLIS_C4(bi,bj,K,uFld,omega3,r_hFacZ,
514         &                         vCf,myThid)
515           ELSEIF (highOrderVorticity) THEN
516            CALL MOM_VI_V_CORIOLIS_C4(bi,bj,K,uFld,vort3, r_hFacZ,
517         &                         vCf,myThid)
518           ELSEIF (useAbsVorticity) THEN
519          CALL MOM_VI_V_CORIOLIS(bi,bj,K,uFld,omega3,hFacZ,r_hFacZ,          CALL MOM_VI_V_CORIOLIS(bi,bj,K,uFld,omega3,hFacZ,r_hFacZ,
520       &                         vCf,myThid)       &                         vCf,myThid)
521         ELSE         ELSE
522          CALL MOM_VI_V_CORIOLIS(bi,bj,k,uFld,vort3,hFacZ,r_hFacZ,          CALL MOM_VI_V_CORIOLIS(bi,bj,k,uFld,vort3, hFacZ,r_hFacZ,
523       &                         vCf,myThid)       &                         vCf,myThid)
524         ENDIF         ENDIF
 c      CALL MOM_VI_V_CORIOLIS_C4(bi,bj,K,uFld,vort3,r_hFacZ,vCf,myThid)  
525         DO j=jMin,jMax         DO j=jMin,jMax
526          DO i=iMin,iMax          DO i=iMin,iMax
527           gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+vCf(i,j)           gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+vCf(i,j)
# Line 450  c      CALL MOM_VI_V_CORIOLIS_C4(bi,bj,K Line 535  c      CALL MOM_VI_V_CORIOLIS_C4(bi,bj,K
535           ENDIF           ENDIF
536  #ifdef ALLOW_MNC  #ifdef ALLOW_MNC
537           IF (useMNC .AND. snapshot_mnc) THEN           IF (useMNC .AND. snapshot_mnc) THEN
538             CALL MNC_CW_RL_W_OFFSET('D','mom_vi',bi,bj, 'zV', uCf,             CALL MNC_CW_RL_W_OFFSET(pf,'mom_vi',bi,bj, 'zV', uCf,
539       &          offsets, myThid)       &          offsets, myThid)
540             CALL MNC_CW_RL_W_OFFSET('D','mom_vi',bi,bj, 'zU', vCf,             CALL MNC_CW_RL_W_OFFSET(pf,'mom_vi',bi,bj, 'zU', vCf,
541       &          offsets, myThid)       &          offsets, myThid)
542           ENDIF           ENDIF
543  #endif /*  ALLOW_MNC  */  #endif /*  ALLOW_MNC  */
544         ENDIF         ENDIF
545    
546  #ifdef ALLOW_TIMEAVE  #ifdef ALLOW_TIMEAVE
 #ifndef MINIMAL_TAVE_OUTPUT  
547         IF (taveFreq.GT.0.) THEN         IF (taveFreq.GT.0.) THEN
548           CALL TIMEAVE_CUMUL_1K1T(uZetatave,vCf,deltaTClock,           CALL TIMEAVE_CUMUL_1K1T(uZetatave,vCf,deltaTClock,
549       &                           Nr, k, bi, bj, myThid)       &                           Nr, k, bi, bj, myThid)
550           CALL TIMEAVE_CUMUL_1K1T(vZetatave,uCf,deltaTClock,           CALL TIMEAVE_CUMUL_1K1T(vZetatave,uCf,deltaTClock,
551       &                           Nr, k, bi, bj, myThid)       &                           Nr, k, bi, bj, myThid)
552         ENDIF         ENDIF
 #endif /* ndef MINIMAL_TAVE_OUTPUT */  
553  #endif /* ALLOW_TIMEAVE */  #endif /* ALLOW_TIMEAVE */
554    #ifdef ALLOW_DIAGNOSTICS
555           IF ( useDiagnostics ) THEN
556             CALL DIAGNOSTICS_FILL(uCf,'Um_AdvZ3',k,1,2,bi,bj,myThid)
557             CALL DIAGNOSTICS_FILL(vCf,'Vm_AdvZ3',k,1,2,bi,bj,myThid)
558           ENDIF
559    #endif /* ALLOW_DIAGNOSTICS */
560    
561  C--   Vertical shear terms (-w*du/dr & -w*dv/dr)  C--   Vertical shear terms (-w*du/dr & -w*dv/dr)
562         IF ( .NOT. momImplVertAdv ) THEN         IF ( .NOT. momImplVertAdv ) THEN
# Line 483  C--   Vertical shear terms (-w*du/dr & - Line 572  C--   Vertical shear terms (-w*du/dr & -
572            gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+vCf(i,j)            gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+vCf(i,j)
573           ENDDO           ENDDO
574          ENDDO          ENDDO
575    #ifdef ALLOW_DIAGNOSTICS
576            IF ( useDiagnostics ) THEN
577             CALL DIAGNOSTICS_FILL(uCf,'Um_AdvRe',k,1,2,bi,bj,myThid)
578             CALL DIAGNOSTICS_FILL(vCf,'Vm_AdvRe',k,1,2,bi,bj,myThid)
579            ENDIF
580    #endif /* ALLOW_DIAGNOSTICS */
581         ENDIF         ENDIF
582    
583  C--   Bernoulli term  C--   Bernoulli term
# Line 505  C--   Bernoulli term Line 600  C--   Bernoulli term
600           ENDIF           ENDIF
601  #ifdef ALLOW_MNC  #ifdef ALLOW_MNC
602           IF (useMNC .AND. snapshot_mnc) THEN           IF (useMNC .AND. snapshot_mnc) THEN
603             CALL MNC_CW_RL_W_OFFSET('D','mom_vi',bi,bj, 'KEx', uCf,             CALL MNC_CW_RL_W_OFFSET(pf,'mom_vi',bi,bj, 'KEx', uCf,
604       &          offsets, myThid)       &          offsets, myThid)
605             CALL MNC_CW_RL_W_OFFSET('D','mom_vi',bi,bj, 'KEy', vCf,             CALL MNC_CW_RL_W_OFFSET(pf,'mom_vi',bi,bj, 'KEy', vCf,
606       &          offsets, myThid)       &          offsets, myThid)
607          ENDIF           ENDIF
608  #endif /*  ALLOW_MNC  */  #endif /*  ALLOW_MNC  */
609         ENDIF         ENDIF
610    
611  C--   end if momAdvection  C--   end if momAdvection
612        ENDIF        ENDIF
613    
614    C--   Metric terms for curvilinear grid systems
615    c     IF (usingSphericalPolarMTerms) THEN
616    C      o Spherical polar grid metric terms
617    c      CALL MOM_U_METRIC_NH(bi,bj,k,uFld,wVel,mT,myThid)
618    c      DO j=jMin,jMax
619    c       DO i=iMin,iMax
620    c        gU(i,j,k,bi,bj) = gU(i,j,k,bi,bj)+mTFacU*mT(i,j)
621    c       ENDDO
622    c      ENDDO
623    c      CALL MOM_V_METRIC_NH(bi,bj,k,vFld,wVel,mT,myThid)
624    c      DO j=jMin,jMax
625    c       DO i=iMin,iMax
626    c        gV(i,j,k,bi,bj) = gV(i,j,k,bi,bj)+mTFacV*mT(i,j)
627    c       ENDDO
628    c      ENDDO
629    c     ENDIF
630    
631  C--   Set du/dt & dv/dt on boundaries to zero  C--   Set du/dt & dv/dt on boundaries to zero
632        DO j=jMin,jMax        DO j=jMin,jMax
633         DO i=iMin,iMax         DO i=iMin,iMax
# Line 536  C--   Set du/dt & dv/dt on boundaries to Line 648  C--   Set du/dt & dv/dt on boundaries to
648    
649        IF ( writeDiag ) THEN        IF ( writeDiag ) THEN
650          IF (snapshot_mdsio) THEN          IF (snapshot_mdsio) THEN
651            CALL WRITE_LOCAL_RL('Ds','I10',1,strain,bi,bj,k,myIter,myThid)           CALL WRITE_LOCAL_RL('W3','I10',1,omega3, bi,bj,k,myIter,myThid)
652            CALL WRITE_LOCAL_RL('Dt','I10',1,tension,bi,bj,k,myIter,           CALL WRITE_LOCAL_RL('KE','I10',1,KE,     bi,bj,k,myIter,myThid)
653       &         myThid)           CALL WRITE_LOCAL_RL('D', 'I10',1,hDiv,   bi,bj,k,myIter,myThid)
654            CALL WRITE_LOCAL_RL('Du','I10',1,guDiss,bi,bj,k,myIter,myThid)           CALL WRITE_LOCAL_RL('Dt','I10',1,tension,bi,bj,k,myIter,myThid)
655            CALL WRITE_LOCAL_RL('Dv','I10',1,gvDiss,bi,bj,k,myIter,myThid)           CALL WRITE_LOCAL_RL('Du','I10',1,guDiss, bi,bj,k,myIter,myThid)
656            CALL WRITE_LOCAL_RL('Z3','I10',1,vort3,bi,bj,k,myIter,myThid)           CALL WRITE_LOCAL_RL('Dv','I10',1,gvDiss, bi,bj,k,myIter,myThid)
           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)  
657          ENDIF          ENDIF
658  #ifdef ALLOW_MNC  #ifdef ALLOW_MNC
659          IF (useMNC .AND. snapshot_mnc) THEN          IF (useMNC .AND. snapshot_mnc) THEN
660            CALL MNC_CW_RL_W_OFFSET('D','mom_vi',bi,bj,'Ds',strain,            CALL MNC_CW_RL_W_OFFSET(pf,'mom_vi',bi,bj,'W3',omega3,
      &          offsets, myThid)  
           CALL MNC_CW_RL_W_OFFSET('D','mom_vi',bi,bj,'Dt',tension,  
      &          offsets, myThid)  
           CALL MNC_CW_RL_W_OFFSET('D','mom_vi',bi,bj,'Du',guDiss,  
661       &          offsets, myThid)       &          offsets, myThid)
662            CALL MNC_CW_RL_W_OFFSET('D','mom_vi',bi,bj,'Dv',gvDiss,            CALL MNC_CW_RL_W_OFFSET(pf,'mom_vi',bi,bj,'KE',KE,
663       &          offsets, myThid)       &          offsets, myThid)
664            CALL MNC_CW_RL_W_OFFSET('D','mom_vi',bi,bj,'Z3',vort3,            CALL MNC_CW_RL_W_OFFSET(pf,'mom_vi',bi,bj,'D', hDiv,
665       &          offsets, myThid)       &          offsets, myThid)
666            CALL MNC_CW_RL_W_OFFSET('D','mom_vi',bi,bj,'W3',omega3,            CALL MNC_CW_RL_W_OFFSET(pf,'mom_vi',bi,bj,'Dt',tension,
667       &          offsets, myThid)       &          offsets, myThid)
668            CALL MNC_CW_RL_W_OFFSET('D','mom_vi',bi,bj,'KE',KE,            CALL MNC_CW_RL_W_OFFSET(pf,'mom_vi',bi,bj,'Du',guDiss,
669       &          offsets, myThid)       &          offsets, myThid)
670            CALL MNC_CW_RL_W_OFFSET('D','mom_vi',bi,bj,'D', hdiv,            CALL MNC_CW_RL_W_OFFSET(pf,'mom_vi',bi,bj,'Dv',gvDiss,
671       &          offsets, myThid)       &          offsets, myThid)
672          ENDIF          ENDIF
673  #endif /*  ALLOW_MNC  */  #endif /*  ALLOW_MNC  */
674        ENDIF        ENDIF
675          
676    #ifdef ALLOW_DIAGNOSTICS
677          IF ( useDiagnostics ) THEN
678            CALL DIAGNOSTICS_FILL(KE,     'momKE   ',k,1,2,bi,bj,myThid)
679           IF (momViscosity) THEN
680            CALL DIAGNOSTICS_FILL(hDiv,   'momHDiv ',k,1,2,bi,bj,myThid)
681            CALL DIAGNOSTICS_FILL(tension,'Tension ',k,1,2,bi,bj,myThid)
682            CALL DIAGNOSTICS_FILL(guDiss, 'Um_Diss ',k,1,2,bi,bj,myThid)
683            CALL DIAGNOSTICS_FILL(gvDiss, 'Vm_Diss ',k,1,2,bi,bj,myThid)
684           ENDIF
685            CALL DIAGNOSTICS_FILL(gU(1-Olx,1-Oly,k,bi,bj),
686         &                                'Um_Advec',k,1,2,bi,bj,myThid)
687            CALL DIAGNOSTICS_FILL(gV(1-Olx,1-Oly,k,bi,bj),
688         &                                'Vm_Advec',k,1,2,bi,bj,myThid)
689          ENDIF
690    #endif /* ALLOW_DIAGNOSTICS */
691    
692  #endif /* ALLOW_MOM_VECINV */  #endif /* ALLOW_MOM_VECINV */
693    
694        RETURN        RETURN
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