The instability of a layer of fluid heated below and subject to the simultaneous action of a magnetic field and rotation

Abstract

This paper is devoted to an examination of the stability of a horizontal layer of fluid heated below, subject to an effective gravity g acting (approximately) in the direction of the vertical, a magnetic field H and the Coriolis acceleration resulting from a rotation Ω. When g, H and Ω are parallel, the critical Rayleigh number (R_c) at which convection sets in depends on H and Ω through the non-dimensional parameters Q = μ²H²d²σ/ρ ν and T = 4Ω²d⁴/ν² where μ, σ and ν are the coefficients of magnetic permeability, electrical conductivity and kinematic viscosity, respectively, and d is the depth of the layer considered. In the case when the liquid is confined between two free boundaries the dependence of R_c on Q and T is explicitly established. The results reveal some very unexpected features and illustrate the complex behaviour of a fluid under the simultaneous action of a magnetic field and rotation.