Role of uniform horizontal magnetic field on convective flow

Abstract

The effect of uniform magnetic field applied along a fixed horizontal direction in Rayleigh-B\'enard convection in low-Prandtl-number fluids has been studied using a low dimensional model. The model shows the onset of convection (primary instability) in the form of two dimensional stationary rolls in the absence of magnetic field, when the Rayleigh number $R$ is raised above a critical value $R_c$. The flow becomes three dimensional at slightly higher values of Rayleigh number via wavy instability. These wavy rolls become chaotic for slightly higher values of $R$ in low-Prandtl-number ($P_r$) fluids. A uniform magnetic field along horizontal plane strongly affects all kinds of convective flows observed at higher values of $R$ in its absence. As the magnetic field is raised above certain value, it orients the convective rolls in its own direction. Although the horizontal magnetic field does not change the threshold for the primary instability, it affects the threshold for secondary (wavy) instability. It inhibits the onset of wavy instability. The critical Rayleigh number $R_o (Q,P_r)$ at the onset of wavy instability, which depends on Chandrasekhar's number $Q$ and $P_r$, increases monotonically with $Q$ for a fixed value of $P_r$. The dimensionless number $R_o (Q, P_r)/(R_c Q P_r)$ scales with $Q$ as $Q^{-1}$. A stronger magnetic field suppresses chaos and makes the flow two dimensional with roll pattern aligned along its direction.