Rayleigh-Bénard convection with uniform vertical magnetic field

Abstract

We present the results of direct numerical simulations of Rayleigh-Bénard convection in the presence of a uniform vertical magnetic field near instability onset. We have done simulations in boxes with square as well as rectangular cross-sections in the horizontal plane. We have considered horizontal aspect ratio $\eta =L_y/L_x=1$ and $2$. The onset of the primary and secondary instabilities are strongly suppressed in the presence of the vertical magnetic field for $\eta =1$. The Nusselt number $\mathrm{Nu}$ scales with Rayleigh number $\mathrm{Ra}$ close to the primary instability as $[\{\mathrm{Ra}-\mathrm{R}{\mathrm{a}}_{\mathrm{c}}(\mathrm{Q})\}/R{\mathrm{a}}_{\mathrm{c}}(\mathrm{Q}){]}^{0.91}$, where $\mathrm{R}{\mathrm{a}}_{\mathrm{c}}(\mathrm{Q})$ is the threshold for onset of stationary convection at a given value of the Chandrasekhar number $\mathrm{Q}$. $\mathrm{Nu}$ also scales with $Ra/Q$ as $(Ra/Q{)}^{\mu }$. The exponent $\mu$ varies in the range $0.39\le \mu \le 0.57$ for $Ra/Q\ge 25$. The primary instability is stationary as predicted by Chandrasekhar. The secondary instability is temporally periodic for $\mathrm{Pr}=0.1$ but quasiperiodic for $\mathrm{Pr}=0.025$ for moderate values of $\mathrm{Q}$. Convective patterns for higher values of $\mathrm{Ra}$ consist of periodic, quasiperiodic and chaotic wavy rolls above onset of the secondary instability for $\eta =1$. In addition, stationary as well as time dependent cross-rolls are observed, as $\mathrm{Ra}$ is further raised. The ratio $r_{\circ }/\mathrm{Pr}$ is independent of $\mathrm{Q}$ for smaller values of $\mathrm{Q}$. The delay in onset of the oscillatory instability is significantly reduced in a simulation box with $\eta =2$. We also observe inclined stationary rolls for smaller values of $\mathrm{Q}$ for $\eta =2$.

9 pages, 11 figures (A slightly modified version is published in Physical Review E)

Cited by in corpus (3)

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