Instability of an MHD shock front in the nonlinear regime

Abstract

The stability of a shock-wave front with respect to its curvature has now been studied for approximately 20 years (see, for example, [i]). It has been found that the front of a shock wave in the so-called evolutionary propagation regime in a uniform medium is stable and regenerates its form free of distortions by random perturbations. However, in the case of propagation in a medium with decreasing density, both plane and spherical fronts are unstable. This was first shown for gasdynamic shock waves in the absence of a magnetic field [2, 3]. Qualitatively, the instability effect is associated with the fact that shock fronts are accelerated in a direction opposite to the density gradient. Therefore, for example, an element of the front which has accidentally moved ahead of the regular front is located in a region with lower density and its velocity is higher, so that its lead increases.