Table 4: The initial behaviour of the M=5 and M=10 simulations shown in Fig. 9 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. 3). 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 $\alpha \ll \alpha _{\rm cr}$ .
Left state Right state Wave velocities

M $\rho$ p v $\rho$ p v $v_{\rm l}$ $v_{\rm cd}$ $v_{\rm r}$

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

**Table 4:** The initial behaviour of the M=5 and M=10 simulations shown in Fig. 9 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. 3). 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 $\alpha \ll \alpha _{\rm cr}$ .
	Left state	Right state	Wave velocities
M	$\rho$	p	v	$\rho$	p	v	$v_{\rm l}$	$v_{\rm cd}$	$v_{\rm r}$
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

Source LaTeX | All tables | In the text

	1 Introduction
	2 Properties of low Mach number shocks
	3 Hydrodynamical simulations
	4 Discussion
	5 Summary
	References