The stability of nonisothermal plasma flow in a flat MHD channel

Abstract

Papers [1, 2] were devoted to questions of the stability of the laminar flow of a conducting fluid in a transverse magnetic field with Hartmann flow. It was assumed in these papers, however, that the transport coefficients are quantities independent of the flow characteristics; in particular, the temperature and the effect of energy dissipation were not taken into account. When these factors are allowed for it turns out that even for relatively small subsonic velocities, when the medium may be regarded as incompressible, the temperature distribution exerts a considerable influence on the dynamic flow characteristics. Papers [3,4] deal with this type of flow in an MHD channel which will be called nonisothermal in what follows. It has been shown that under specific conditions the velocity profiles are grossly deformed, and non-monotonic profiles with inflection points may even appear.

However, the influence of nonisothermal flow on stability is not confined to an alteration of the stability criteria as a result of the change in the velocity profile. When energy dissipation and the fact that the transport coefficients are not constant are taken into account new “dissipative” instability branches appear, as, for example, the overheat instability [5, 8], This article considers the problem of the hydrodynamic stability of a nonisothermal plasma flow in constant crossed electric and magnetic fields in a flat channel with dielectric walls. The system of equations derived in this paper for the perturbations does, of course, take into account all the instability mechanisms mentioned above, but is difficult to solve. The general system of equations may be investigated in two limiting cases corresponding to the overheat and hydrodynamic instabilities.