/[MITgcm]/manual/s_algorithm/text/tracer.tex
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revision 1.8 by cnh, Thu Oct 25 18:36:53 2001 UTC revision 1.10 by adcroft, Tue Nov 13 18:15:26 2001 UTC
# Line 43  only affects the surface layer since the Line 43  only affects the surface layer since the
43  everywhere else. This term is therefore referred to as the surface  everywhere else. This term is therefore referred to as the surface
44  correction term. Global conservation is not possible using the  correction term. Global conservation is not possible using the
45  flux-form (as here) and a linearized free-surface  flux-form (as here) and a linearized free-surface
46  (\cite{Griffies00,Campin02}).  (\cite{griffies:00,campin:02}).
47    
48  The continuity equation can be recovered by setting  The continuity equation can be recovered by setting
49  $G_{diff}=G_{forc}=0$ and $\tau=1$.  $G_{diff}=G_{forc}=0$ and $\tau=1$.
# Line 200  W & = & {\cal A}_c w Line 200  W & = & {\cal A}_c w
200    
201  For non-divergent flow, this discretization can be shown to conserve  For non-divergent flow, this discretization can be shown to conserve
202  the tracer both locally and globally and to globally conserve tracer  the tracer both locally and globally and to globally conserve tracer
203  variance, $\tau^2$. The proof is given in \cite{Adcroft95,Adcroft97}.  variance, $\tau^2$. The proof is given in \cite{adcroft:95,adcroft:97}.
204    
205  \fbox{ \begin{minipage}{4.75in}  \fbox{ \begin{minipage}{4.75in}
206  {\em S/R GAD\_C2\_ADV\_X} ({\em gad\_c2\_adv\_x.F})  {\em S/R GAD\_C2\_ADV\_X} ({\em gad\_c2\_adv\_x.F})
# Line 675  Figs.~\ref{fig:advect-1d-lo} and \ref{fi Line 675  Figs.~\ref{fig:advect-1d-lo} and \ref{fi
675  phenomenon.  phenomenon.
676    
677  Finally, the bottom left and right panels use the same advection  Finally, the bottom left and right panels use the same advection
678  scheme but the right does not use the mutli-dimensional method. At low  scheme but the right does not use the multi-dimensional method. At low
679  Courant number this appears to not matter but for moderate Courant  Courant number this appears to not matter but for moderate Courant
680  number severe distortion of the feature is apparent. Moreover, the  number severe distortion of the feature is apparent. Moreover, the
681  stability of the multi-dimensional scheme is determined by the maximum  stability of the multi-dimensional scheme is determined by the maximum
# Line 704  flux limited scheme is almost essential. Line 704  flux limited scheme is almost essential.
704  non-linear schemes have the most stability (up to Courant number 1).  non-linear schemes have the most stability (up to Courant number 1).
705  \item If you need to know how much diffusion/dissipation has occurred you  \item If you need to know how much diffusion/dissipation has occurred you
706  will have a lot of trouble figuring it out with a non-linear method.  will have a lot of trouble figuring it out with a non-linear method.
707  \item The presence of false extrema is unphysical and this alone is the  \item The presence of false extrema is non-physical and this alone is the
708  strongest argument for using a positive scheme.  strongest argument for using a positive scheme.
709  \end{itemize}  \end{itemize}
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