/[MITgcm]/manual/s_algorithm/text/mom_fluxform.tex
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revision 1.11 by jmc, Mon Jun 26 01:03:47 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 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 mom\_fluxform.F})  v4F} (local to {\em mom\_fluxform.F})
284  \end{minipage} }  \end{minipage} }
285    
# 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 mom\_fluxform.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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