Stability investigation of Hartmann flow with the convective approximation

I. Yu. Kalashnikov

National Research Nuclear University MEPhI, department 32, Schmidt Institute of Physics of the Earth, RAS, Moscow, Russia

Abstract
This research is focused on linear analysis of a plane-parallel flow stability in a transverse magnetic field (Hartmann flow) within a convective approximation. We derive and solve equations describing the perturbation growth. Perturbation modes and their non-excitation conditions have been determined. An equation for the instability increment has been derived and it is shown that the equation has an unstable root. Additionally, we show that the resulting instabilities qualitatively agree with the experimental data. Figs 3, Refs 5.