Instability of the free-convection type in magnetohydrodynamics

Abstract

The processes occurring in an electroconductive fluid in a magnetic field and subjected to an electric current flowing through it are discussed. In a fluid whose electrical conductivity rises with temperature, a phenomenon similar to free convection occurs when the entropy drops along the direction of the force j × B. The joint action of this phenomenon and the overheating instability which also stems from the temperature dependence of the electrical conductivity and the effect of electromagnetic braking is considered. In this case, the criterion of stability is obtained. Instability in the form of free convection also appears due to a Hall current jH flowing along the electrodes of a magnetohydrodynamic channel when a high temperature gradient occurs along the direction of the force jH × B. The instability arises near the cathode and the appearance of one is determined by the value of a dimensionless parameter identical to the Rayleigh number Ra = (dlnσ/dT) g̃l4 ‖∇T‖ /νχ where g̃ = jH B/ρ plays the role of the gravitational acceleration and dlnσ/dT plays the role of the expansion coefficient.