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\title{Hot disk issues}
\date{\today,~ $ $Revision: 1.3 $ $}
\begin{document}
\maketitle

\section{Convection develops}

Convection does develop after all; see \Fig{pruymz10_Strat_H5.0e-05_z35d}.
This can be seen nicely in $\overline{\rho u_y}$.
However, the timestep became very short and the velocity is still
increasing; see \Fig{ptstep_Strat_H5.0e-05_z35d}.
Toward the end, however, the timestep becomes somewhat longer again.

\begin{figure}[h!]\begin{center}
\includegraphics[width=\columnwidth]{pruymz10_Strat_H5.0e-05_z35d.ps}
\end{center}\caption[]{
Contours of $\overline{\rho u_y}$.
Convection starts first in the lower disk half.
}\label{pruymz10_Strat_H5.0e-05_z35d}\end{figure}

\begin{figure}[h!]\begin{center}
\includegraphics[width=\columnwidth]{ptstep_Strat_H5.0e-05_z35d.ps}
\end{center}\caption[]{
Evolution of timestep and rms velocity.
}\label{ptstep_Strat_H5.0e-05_z35d}\end{figure}

\section{Early energy fluxes}

At these early time, the convective flux, i.e., the sum
of enthalpy and kinetic flux, goes still inward, i.e., it
does not contribute to outward energy transport;
see \Fig{pTTlast_Strat_H5.0e-05_z35d}.
We have to wait longer (but it is expensive).
The temperature profile looks normal;
see \Fig{pTTlast_Strat_H5.0e-05_z35d}.

\begin{figure}[h!]\begin{center}
\includegraphics[width=\columnwidth]{pflux_last_Strat_H5.0e-05_z35d.ps}
\end{center}\caption[]{
Profiles if total flux (black), radiative flux (red),
convective [=kinetic+enthalpy] flux (green),
and just kinetic flux (blue) at the last time.
}\label{pTTlast_Strat_H5.0e-05_z35d}\end{figure}

\begin{figure}[h!]\begin{center}
\includegraphics[width=\columnwidth]{pTTlast_Strat_H5.0e-05_z35d.ps}
\end{center}\caption[]{
Temperature profile at the last time.
The positions where the optical depth is unity
are marked as red dots.
}\label{pTTlast_Strat_H5.0e-05_z35d}\end{figure}

$$
\nabla-\nabla_{\rm ad}\equiv{\dd s/\cp\over\dd\ln P}
$$

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