To appear in The Astrophysical Journal, 449, 727, 1995.
A preprint of this paper is available in postscript form in our Preprint Library.
Radiative shocks perturbed from steady state are subject to an oscillatory overstability. We have examined the nature of this overstability in one and two dimensions using numerical hydrodynamic simulations. In our first set of simulations we modeled a 1D flow onto a solid surface (similar to the models of Imamura, Wolff, and Durisen (ApJ,1984). In the above image of gas density, the flow is entering the numerical grid from the top and impinging a solid wall on the bottom. Time is progressing to the right, so the oscillating shock front looks similar to a sin**2 function.
We find that one-dimensional simulations of a uniform flow incident upon a reflecting wall produce oscillation frequencies in agreement with those of earlier analytic (Chevalier and Imamura 1982) and numerical (Imamura, Wolff, and Durisen 1984) work. We do not, however, find any evidence for growth of the oscillation amplitude. This result is not in contradiction with previous linear analysis because the supersonic flow into a wall problem is at a saturated, nonlinear amplitude from the beginning.
In our second set of simulations, the case of 1D steady state shocks in the absence of a solid wall (ie, and interstellar shock), we find a slightly different dependence of the overstability on alpha when we assume a cooling rate proportional to T**alpha, as seen in this image. In this case oscillations in radiative shocks with alpha less than approximately 0.75 are found to saturate at a finite amplitude, i.e., the relevant critical value of alpha is at least above 0.5. As shown here, we also find high Mach-number systems to be less stable than low Mach-number systems subject to the same cooling law. Images displaying these two trends can be retrieved by clicking the icons below.
Finally, we addressed the stability of radiative shocks in 2D. In the first case we began with a planar, steady shock and perturbed it by dropping in a very small "cloud" with a slight overdensity. This was sufficient to excite oscillations in the shock front that grew to a nonlinear state but eventually decayed away. Example images and an mpeg movie of this simulation are available here.
We also examined the response of planar shocks to nonlinear perturbations. Here the shock front was perturbed by stretching it (see the mpeg clip) according to a sine function. As illustrated in these images, in all cases the discontinuity separating the cooling region from the cold gas layer was highly disrupted. Since this is the location of the recombination emission, this instability suggests that interstellar radiative shocks will not be smooth on length scales of order the local cooling length, when viewed in recombination emission.