The evolution of plane current–vortex sheets

Abstract

The linear and nonlinear evolution of the plane current–vortex sheet, with a basic magnetic field given by B0(y)=tanh yêz, and a basic velocity field given by W0(y)=V tanh Ryêz, is examined. The discovery of an ideal instability in a large region of parameter space previously found to be stable is reported. In this paper numerical evidence is presented that this parameter regime is in fact highly unstable, with growth rates exceeding those of the modes existing in the region of parameter space previously found to be unstable. An examination of the perturbation energy balance indicates that enhanced energy transfer from the basic velocity field to the perturbed velocity and magnetic fields is responsible for the enhanced growth rate. This occurs due to processes absent from both the resistive and Kelvin–Helmholtz instabilities. Nonlinearly it is found that magnetic reconnection can occur on an ideal time scale in certain cases. These faster instabilities lead to a more violent cascade of excitation in the streamwise direction, as evidenced by the rapid formation of higher harmonics of the initial disturbance. A nonlinear saturation due to increased correlation of the perturbed velocity and magnetic field occurs for all cases.