The compressible plane current-vortex sheet

Abstract

The plane current-vortex sheet is a magnetohydrodynamic configuration in which a vortex sheet lies at the location of an electric current sheet. Most previous research on this structure has focused on the incompressible situation. In this paper some effects of compressibility on the linear stability properties of the plane current-vortex sheet are examined. The relevant compressible equations are derived and then solved by a new magnetohydrodynamic extension of the SPEctral Compressible Linear Stability (SPECLS) algorithm, a Chebyshev collocation code. Of particular interest is an investigation of how the properties of the low sonic Mach number (M) analogs of previously investigated incompressible unstable modes vary as M is increased to supersonic values. It is found that, in general, the growth rates of these modes decrease as M increases. However, new unstable modes are found to appear at high M. These new modes, which have a finite phase velocity, are also found to be weakly evanescent and oscillatory in the cross-stream direction. Further data is presented on the influence of the streamwise and spanwise wave numbers, and also the Alfvén number. The morphology of the perturbations is also discussed, with an emphasis on the temperature and mass density structure. A short discussion is also given of the effect of spatial variation of the zeroth-order temperature and mass density fields, a situation that would arise when magnetofluids with different thermodynamic properties are brought into contact with each other.