Effects of horizontal magnetic fields on turbulent Rayleigh–Bénard convection in a cuboid vessel with aspect ratio Γ = 5

Abstract

Direct numerical simulations have been conducted to investigate turbulent Rayleigh– Bénard convection (RBC) of liquid metal in a cuboid vessel with aspect ratio $\varGamma =5$ under an imposed horizontal magnetic field. Flows with Prandtl number $Pr=0.033$ , Rayleigh numbers ranging up to $Ra\leq 10^{7}$ , and Chandrasekhar numbers up to $Q\leq 9 \times 10^6$ are considered. For weak magnetic fields, our findings reveal that a previously undiscovered decreasing region precedes the enhancement of heat transfer and kinetic energy. For moderate magnetic fields, we have reproduced the reversals of the large-scale flow, which are considered a reorganization process of the roll-like structures that were reported experimentally by Yanagisawa et al. (Phys. Rev. E, vol. 83, 2011, 036307). Nevertheless, the proposed approach of skewed-varicose instability has been substantiated as insufficient to elucidate fundamentally the phenomenon of flow reversal, an occurrence bearing a striking resemblance to the large-scale intermittency observed in magnetic channel flows. As we increase the magnetic field strength further, we observe that the energy dissipation of the system comes primarily from the viscous dissipation within the boundary layer. Consequently, the dependence of Reynolds number $Re$ on $Q$ approaches a scaling as $Re\,Pr/Ra^{2/3} \sim Q^{-1/3}$ . At the same time, we find the law for the cutoff frequency that separates large quasi-two-dimensional scales from small three-dimensional ones in RBC flow, which scales with the interaction parameter as ${\sim }N^{1/3}$ .