# [cig-commits] r1339 - trunk/aspect/doc/manual

bangerth at dealii.org bangerth at dealii.org
Fri Oct 26 06:34:21 PDT 2012

Author: bangerth
Date: 2012-10-26 07:34:20 -0600 (Fri, 26 Oct 2012)
New Revision: 1339

Modified:
trunk/aspect/doc/manual/manual.tex
Log:

Modified: trunk/aspect/doc/manual/manual.tex
===================================================================
--- trunk/aspect/doc/manual/manual.tex	2012-10-26 11:56:31 UTC (rev 1338)
+++ trunk/aspect/doc/manual/manual.tex	2012-10-26 13:34:20 UTC (rev 1339)
@@ -3082,12 +3082,12 @@
\begin{figure}
\centering
\includegraphics[width=0.4\textwidth]{cookbooks/composition-passive/mass-composition-1.png}
-  \caption{Passive compositional fields: Minimum and maximum of the first compositional variable
+  \caption{Passive compositional fields: Minimum and maximum of the first compositional variable
over time, as well as the mass $m_1(t)=\int_\Omega c_1(\mathbf x,t)$ stored in this variable.}
\label{fig:compositional-passive-mass}
\end{figure}

-A different way of looking at the quality of compositional fields as opposed to
+A different way of looking at the quality of compositional fields as opposed to
tracers is to ask whether they conserve mass. In the current context, the
mass contained in the $i$th compositional field is $m_i(t)=\int_\Omega c_i(\mathbf x,t)$.
This can easily be achieve in the following way, by adding the \texttt{composition statistics}
@@ -3151,7 +3151,7 @@

This setup of the problem can be described using an input file that is almost
completely unchanged from the passive case. The only difference is the use of
-the following section (the complete input file can be found in
+the following section (the complete input file can be found in
\url{cookbooks/compositional-active.prm}:

\begin{lstlisting}[frame=single,language=prmfile,escapechar=\%]
@@ -3184,7 +3184,18 @@
end
\end{lstlisting}

-Results of this model are visualized in Fig.~\ref{\ldots}. It is easy, using the
+Results of this model are visualized in Fig.~\ref{\ldots}. What is visible is
+that over the course of the simulation, the material that starts at the bottom
+of the domain remains there. This can only happen if the circulation is
+decoupled between the bottom materail and the rest of the domain and this is
+indeed visible in the velocity vectors. As a second consequence, if the
+material at the bottom does not move away, then there needs to be a different
+way for the heat provided at the bottom to get through the bottom layer:
+either there must be a secondary convection system in the bottom layer, or
+simply through heat conduction. The pictures in the figure seem to suggest
+that the latter is the case.
+
+It is easy, using the
outline above, to play with the various factors that drive this system, namely:
\begin{itemize}
\item The magnitude of the velocity prescribed at the top.
@@ -3194,7 +3205,12 @@
described by the coefficient $\gamma$ and the magnitude of gravity.
\end{itemize}
Using the coefficients involved in these considerations, it is trivially
-possible to map out parameter space to find which of these effects is dominant.
+possible to map out the parameter space to find which of these effects is
+dominant. As mentioned in discussing the values in the input file, what is
+important is the \textit{relative} size of these parameters, not the fact
+that currently the density in the material at the bottom is 100 times larger
+than in the rest of the domain, an effect that from a physical perspective
+clearly makes no sense at all.