Stability of MHD shear flows: Application to space physics

Abstract

Shear slows of magnetised plasmas are routinely observed in the solar atmosphere, in planetary magnetospheres, and in interplanetary space. They are also ubiquitous elements of models of remote astrophysical objects like the interacting stellar winds in binary stellar systems. Studying stability of such flows is paramount for understanding physical processes in space. The simplest shear flow is a tangential magnetohydrodynamic (MHD) discontinuity. We start our review from considering the instability of tangential MHD discontinuity (called the Kelvin-Helmholtz (KH) instability) first in incompressible plasmas, and then taking the compressibility into account. We introduce the notion of the absolute and convective instabilities. The physical behaviour of absolutely unstable flows is qualitatively different from that of convectively unstable flows. Studying the absolute and convective instabilities is based on the analysis of asymptotic behaviour (for large time) of the solution of the initial value problem. The initial value problem for a tangential discontinuity is ill-posed: the instability increment is unbounded. This implies that the absolute and convective instabilities of tangential discontinuities cannot be studied. To obtain a well-posed problem we have either to take dissipation into account, or to consider a continuous velocity profile. In both cases we obtain a surprising result: the account of either of these two effects decreases the threshold value of the velocity jump needed for instability. This phenomenon is related to negative energy waves. We show that, in both cases, the instability is the so-called negative energy instability rather than the KH instability. Finally we consider two examples of the theory application: the heliopause stability and the stability of the Earth's magnetopause.