Autooscillating MHD flow in a channel with a longitudinal magnetic field

O. A. Likhachev - V. N. Shtern

Abstract
We investigate the stability of a parallel flow between two planes in a constant external magnetic field directed along the flow velocity. The nonlinear equations for the perturbations are analyzed assuming that the magnetic Reynolds number is small. For Reynolds numbers that are critical with respect to linear stability theory, an autooscillating solution branches out from the fundamental flow. If the Hartmann number is greater than 15.5, then autooscillations branch out for Reynolds numbers greater than critical, and they are stable. This allows us, in principle, to observe them experimentally. We calculate the energy of the autooscillations assuming them to be sinusoidal with respect to homogeneous coordinates.