A model for Rayleigh-Bénard magnetoconvection

Abstract

A model for three-dimensional Rayleigh-Bénard convection in low-Prandtl-number fluids near onset with rigid horizontal boundaries in the presence of a uniform vertical magnetic field is constructed and analyzed in detail. The kinetic energy K, the convective entropy Φ and the convective heat flux (Nu − 1) show scaling behaviour with ε = r − 1 near onset of convection, where r is the reduced Rayleigh number. The model is also used to investigate various magneto-convective structures close to the onset. Straight rolls, which appear at the primary instability, become unstable with increase in r and bifurcate to three-dimensional structures. The straight rolls become periodically varying wavy rolls or quasiperiodically varying structures in time with increase in r depending on the values of Prandtl number Pr. They become irregular in time, with increase in r. These standing wave solutions bifurcate first to periodic and then to quasiperiodic traveling wave solutions, as r is raised further. The variations of the critical Rayleigh number R a _os and the frequency ω _os at the onset of the secondary instability with Pr are also studied for different values of Chandrasekhar’s number Q.