--- manual/s_algorithm/text/tracer.tex 2001/10/25 18:36:53 1.8 +++ manual/s_algorithm/text/tracer.tex 2001/11/13 18:15:26 1.10 @@ -1,4 +1,4 @@ -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_algorithm/text/tracer.tex,v 1.8 2001/10/25 18:36:53 cnh Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_algorithm/text/tracer.tex,v 1.10 2001/11/13 18:15:26 adcroft Exp $ % $Name: $ \section{Tracer equations} @@ -43,7 +43,7 @@ everywhere else. This term is therefore referred to as the surface correction term. Global conservation is not possible using the flux-form (as here) and a linearized free-surface -(\cite{Griffies00,Campin02}). +(\cite{griffies:00,campin:02}). The continuity equation can be recovered by setting $G_{diff}=G_{forc}=0$ and $\tau=1$. @@ -200,7 +200,7 @@ For non-divergent flow, this discretization can be shown to conserve the tracer both locally and globally and to globally conserve tracer -variance, $\tau^2$. The proof is given in \cite{Adcroft95,Adcroft97}. +variance, $\tau^2$. The proof is given in \cite{adcroft:95,adcroft:97}. \fbox{ \begin{minipage}{4.75in} {\em S/R GAD\_C2\_ADV\_X} ({\em gad\_c2\_adv\_x.F}) @@ -675,7 +675,7 @@ phenomenon. Finally, the bottom left and right panels use the same advection -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 Courant number this appears to not matter but for moderate Courant number severe distortion of the feature is apparent. Moreover, the stability of the multi-dimensional scheme is determined by the maximum @@ -704,6 +704,6 @@ non-linear schemes have the most stability (up to Courant number 1). \item If you need to know how much diffusion/dissipation has occurred you will have a lot of trouble figuring it out with a non-linear method. -\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 strongest argument for using a positive scheme. \end{itemize}