/[MITgcm]/manual/s_algorithm/text/mom_fluxform.tex
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revision 1.10 by molod, Thu Apr 6 00:38:17 2006 UTC revision 1.14 by jmc, Mon Aug 30 23:09:18 2010 UTC
# Line 2  Line 2 
2  % $Name$  % $Name$
3    
4  \section{Flux-form momentum equations}  \section{Flux-form momentum equations}
5  \label{sect:flux-form_momentum_equations}  \label{sec:flux-form_momentum_equations}
6  \begin{rawhtml}  \begin{rawhtml}
7  <!-- CMIREDIR:flux-form_momentum_eqautions: -->  <!-- CMIREDIR:flux-form_momentum_equations: -->
8  \end{rawhtml}  \end{rawhtml}
9    
10  The original finite volume model was based on the Eulerian flux form  The original finite volume model was based on the Eulerian flux form
# Line 29  In the hydrostatic limit, $G_w=0$ and $\ Line 29  In the hydrostatic limit, $G_w=0$ and $\
29  vertical momentum to hydrostatic balance.  vertical momentum to hydrostatic balance.
30    
31  These terms are calculated in routines called from subroutine {\em  These terms are calculated in routines called from subroutine {\em
32  CALC\_MOM\_RHS} a collected into the global arrays {\bf Gu}, {\bf Gv},  MOM\_FLUXFORM} a collected into the global arrays {\bf Gu}, {\bf Gv},
33  and {\bf Gw}.  and {\bf Gw}.
34    
35  \fbox{ \begin{minipage}{4.75in}  \fbox{ \begin{minipage}{4.75in}
36  {\em S/R CALC\_MOM\_RHS} ({\em pkg/mom\_fluxform/calc\_mom\_rhs.F})  {\em S/R MOM\_FLUXFORM} ({\em pkg/mom\_fluxform/mom\_fluxform.F})
37    
38  $G_u$: {\bf Gu} ({\em DYNVARS.h})  $G_u$: {\bf Gu} ({\em DYNVARS.h})
39    
# Line 90  conserves kinetic energy. Line 90  conserves kinetic energy.
90    
91  {\em S/R MOM\_U\_ADV\_WV} ({\em mom\_u\_adv\_wv.F})  {\em S/R MOM\_U\_ADV\_WV} ({\em mom\_u\_adv\_wv.F})
92    
93  $uu$, $uv$, $vu$, $vv$: {\bf aF} (local to {\em calc\_mom\_rhs.F})  $uu$, $uv$, $vu$, $vv$: {\bf aF} (local to {\em mom\_fluxform.F})
94  \end{minipage} }  \end{minipage} }
95    
96    
# Line 149  useEnergyConservingCoriolis} to {\em tru Line 149  useEnergyConservingCoriolis} to {\em tru
149    
150  {\em S/R MOM\_V\_CORIOLIS} ({\em mom\_v\_coriolis.F})  {\em S/R MOM\_V\_CORIOLIS} ({\em mom\_v\_coriolis.F})
151    
152  $G_u^{Cor}$, $G_v^{Cor}$: {\bf cF} (local to {\em calc\_mom\_rhs.F})  $G_u^{Cor}$, $G_v^{Cor}$: {\bf cF} (local to {\em mom\_fluxform.F})
153  \end{minipage} }  \end{minipage} }
154    
155    
# Line 188  respectively. Line 188  respectively.
188    
189  {\em S/R MOM\_V\_METRIC\_SPHERE} ({\em mom\_v\_metric\_sphere.F})  {\em S/R MOM\_V\_METRIC\_SPHERE} ({\em mom\_v\_metric\_sphere.F})
190    
191  $G_u^{metric}$, $G_v^{metric}$: {\bf mT} (local to {\em calc\_mom\_rhs.F})  $G_u^{metric}$, $G_v^{metric}$: {\bf mT} (local to {\em mom\_fluxform.F})
192  \end{minipage} }  \end{minipage} }
193    
194    
# Line 223  G_w^{metric} & = & Line 223  G_w^{metric} & = &
223    
224  {\em S/R MOM\_V\_METRIC\_NH} ({\em mom\_v\_metric\_nh.F})  {\em S/R MOM\_V\_METRIC\_NH} ({\em mom\_v\_metric\_nh.F})
225    
226  $G_u^{metric}$, $G_v^{metric}$: {\bf mT} (local to {\em calc\_mom\_rhs.F})  $G_u^{metric}$, $G_v^{metric}$: {\bf mT} (local to {\em mom\_fluxform.F})
227  \end{minipage} }  \end{minipage} }
228    
229    
# Line 256  The lateral viscous stresses are discret Line 256  The lateral viscous stresses are discret
256  where the non-dimensional factors $c_{lm\Delta^n}(\varphi), \{l,m,n\} \in  where the non-dimensional factors $c_{lm\Delta^n}(\varphi), \{l,m,n\} \in
257  \{1,2\}$ define the ``cosine'' scaling with latitude which can be  \{1,2\}$ define the ``cosine'' scaling with latitude which can be
258  applied in various ad-hoc ways. For instance, $c_{11\Delta} =  applied in various ad-hoc ways. For instance, $c_{11\Delta} =
259  c_{21\Delta} = (\cos{\varphi})^{3/2}$, $c_{12\Delta}=c_{22\Delta}=0$ would  c_{21\Delta} = (\cos{\varphi})^{3/2}$, $c_{12\Delta}=c_{22\Delta}=1$ would
260  represent the an-isotropic cosine scaling typically used on the  represent the an-isotropic cosine scaling typically used on the
261  ``lat-lon'' grid for Laplacian viscosity.  ``lat-lon'' grid for Laplacian viscosity.
262  \marginpar{Need to tidy up method for controlling this in code}  \marginpar{Need to tidy up method for controlling this in code}
# Line 279  viscA4}), has units of $m^4 s^{-1}$. Line 279  viscA4}), has units of $m^4 s^{-1}$.
279    
280  {\em S/R MOM\_V\_YVISCFLUX} ({\em mom\_v\_yviscflux.F})  {\em S/R MOM\_V\_YVISCFLUX} ({\em mom\_v\_yviscflux.F})
281    
282  $\tau_{11}$, $\tau_{12}$, $\tau_{22}$, $\tau_{22}$: {\bf vF}, {\bf  $\tau_{11}$, $\tau_{12}$, $\tau_{21}$, $\tau_{22}$: {\bf vF}, {\bf
283  v4F} (local to {\em calc\_mom\_rhs.F})  v4F} (local to {\em mom\_fluxform.F})
284  \end{minipage} }  \end{minipage} }
285    
286  Two types of lateral boundary condition exist for the lateral viscous  Two types of lateral boundary condition exist for the lateral viscous
# Line 318  neighboring vorticity points, e.g. $1-h_ Line 318  neighboring vorticity points, e.g. $1-h_
318    
319  {\em S/R MOM\_V\_SIDEDRAG} ({\em mom\_v\_sidedrag.F})  {\em S/R MOM\_V\_SIDEDRAG} ({\em mom\_v\_sidedrag.F})
320    
321  $G_u^{side-drag}$, $G_v^{side-drag}$: {\bf vF} (local to {\em calc\_mom\_rhs.F})  $G_u^{side-drag}$, $G_v^{side-drag}$: {\bf vF} (local to {\em mom\_fluxform.F})
322  \end{minipage} }  \end{minipage} }
323    
324    
# Line 355  is even less consistent than for the hyd Line 355  is even less consistent than for the hyd
355    
356  {\em S/R MOM\_V\_RVISCLFUX} ({\em mom\_v\_rviscflux.F})  {\em S/R MOM\_V\_RVISCLFUX} ({\em mom\_v\_rviscflux.F})
357    
358  $\tau_{13}$: {\bf urf} (local to {\em calc\_mom\_rhs.F})  $\tau_{13}$: {\bf urf} (local to {\em mom\_fluxform.F})
359    
360  $\tau_{23}$: {\bf vrf} (local to {\em calc\_mom\_rhs.F})  $\tau_{23}$: {\bf vrf} (local to {\em mom\_fluxform.F})
361  \end{minipage} }  \end{minipage} }
362    
363    
# Line 393  dimensionless with typical values in the Line 393  dimensionless with typical values in the
393    
394  {\em S/R MOM\_V\_BOTTOMDRAG} ({\em mom\_v\_bottomdrag.F})  {\em S/R MOM\_V\_BOTTOMDRAG} ({\em mom\_v\_bottomdrag.F})
395    
396  $\tau_{13}^{bottom-drag}$, $\tau_{23}^{bottom-drag}$: {\bf vf} (local to {\em calc\_mom\_rhs.F})  $\tau_{13}^{bottom-drag}/\Delta r_f$, $\tau_{23}^{bottom-drag}/\Delta r_f$:
397    {\bf vf} (local to {\em mom\_fluxform.F})
398  \end{minipage} }  \end{minipage} }
399    
400  \subsection{Derivation of discrete energy conservation}  \subsection{Derivation of discrete energy conservation}
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