Magnetohydrodynamic discontinuities in space plasmas: Interrelation between stability and structure

It is believed that shock waves and other discontinuous flows form the basis of a wide range of phenomena in space medium. We review the results concerning the particular property of MHD discontinuities, the interrelation between their stability and structure. Such an interrelation is associated primarily with the requirement of their evolutionarity. For a non-evolutionary discontinuity the amplitudes of reflected and refracted waves caused by a small amplitude incident wave are not determined unambiguously from the conservation laws at the discontinuity surface. Since the problem of the further time evolution of the initial small perturbation does not have a unique solution, such a discontinuity cannot exist in a real medium as a single steady-state configuration. Therefore it is unstable with respect to a disintegration into several discontinuities or to a transition to some more general unsteady flow. This is confirmed by the fact that, in the studied cases, the non-evolutionary shock transitions can, while the evolutionary ones cannot, be represented as a set of several discontinuities and waves of rarefaction. One more fundamental property of the non-evolutionary shocks that argues for their non-existence is that they do not have a unique structure for all values of the dissipative transport coefficients. At the same time, the possibility of their existence cannot be excluded when the shock has a unique structure or when the disintegration is forbidden for some reasons. Besides the non-evolutionarity, which is a direct reason for a disintegration, there is an indirect one. It can be shown that the hydrodynamic shocks without magnetic field that are corrugationally unstable also allow the shock transitions through more than one discontinuity. This suggests that the shocks unstable in the ordinary sense, for which the small perturbation grows with time, do not exist at all, but they disintegrate into stable ones. However, the physical mechanism that distinguishes between these two scenarios remains unclear. The interrelation between the stability and structure of MHD discontinuities thus governs their nonlinear evolution. This fact is essential when describing shock waves and other discontinuous flows in the space medium.