The effect of an external magnetic field on oscillatory instability of convective flows in a rectangular cavity

Abstract

The present study is devoted to the problem of onset of oscillatory instability in convective flow of an electrically conducting fluid under an externally imposed time-independent uniform magnetic field. Convection of a low-Prandtl-number fluid in a laterally heated two-dimensional horizontal cavity is considered. Fixed values of the aspect ratio (length/height=4) and Prandtl number (Pr=0.015), which are associated with the horizontal Bridgman crystal growth process and are commonly used for benchmarking purposes, are considered. The effect of a uniform magnetic field with different magnitudes and orientations on the stability of the two distinct branches (with a single-cell or a two-cell pattern) of the steady state flows is investigated. Stability diagrams showing the dependence of the critical Grashof number on the Hartmann number are presented. It is shown that a vertical magnetic field provides the strongest stabilization effect, and also that multiplicity of steady states is suppressed by the electromagnetic effect, so that at a certain field level only the single-cell flows remain stable. An analysis of the most dangerous flow perturbations shows that starting with a certain value of the Hartmann number, single-cell flows are destabilized inside thin Hartmann boundary layers. This can lead to destabilization of the flow with an increase of the field magnitude, as is seen from the stability diagrams obtained. Contrary to the expected monotonicity of the stabilization process with an increase of the field strength, the marginal stability curves show nonmonotonic behavior and may contain hysteresis loops.