The Instability of a Layer of Fluid Heated below and Subject to the Simultaneous Action of a Magnetic Field and Rotation

Physics

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Scientific paper

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 (Rc) at which convection sets in depends on H and Ω through the non-dimensional parameters Q = μ 2H2d2σ /ρ ν and T = 4Ω 2d4/ν 2 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 Rc 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.

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