\begin{table}%t4
%\centering
\par
\caption{The initial behaviour of the $M=5$ and $M=10$ simulations
shown in Fig.~\ref{fig:mvar_alp-1.5} can be determined from the
solution to a Riemann problem, which yields the resulting wave
velocities in the system ($v_{\rm l}$, $v_{\rm cd}$, and $v_{\rm r}$ being the
velocity into the left state, the velocity of the contact discontinuity, and
the velocity into the right state).  
The left state is defined as the CDL, while
the right state is defined as the pre-shock flow (see
Fig.~\ref{fig:isoimp}). While the values quoted are for the initial
conditions, they should be a good representation of the conditions
which exist at the exact moment that the cooling layer disappears when
$\alpha \ll \alpha_{\rm cr}$.\label{tab:riemann}}
\begin{tabular}{cccccccccc}
\hline\hline
    & \multicolumn{3}{c}{Left state} & \multicolumn{3}{c}{Right state} & \multicolumn{3}{c}{Wave velocities} \\
$M$ & $\rho$ & $p$ & $v$ & $\rho$ & $p$ & $v$ & $v_{\rm l}$ & $v_{\rm cd}$ & $v_{\rm r}$ \\
\hline  
5 & 41.67 & 1.0 & --0.024 & 1.0 & 0.024 & --1.0 & --0.243 & --0.052 & 0.295 \\
10 & 166.67 & 1.0 & --0.006 & 1.0 & 0.006 & --1.0 & --0.117 & --0.022 & 0.312 \\
\hline
\end{tabular}
\end{table}