Low-Prandtl-number B\'enard-Marangoni convection in a vertical magnetic field

TL;DR

This study investigates how a magnetic field influences surface-tension-driven Bénard convection in liquid metals, revealing flow pattern changes and transitions from stationary to time-dependent convection through numerical simulations.

Contribution

It provides a detailed numerical analysis of magnetic effects on Bénard-Marangoni convection at low Prandtl numbers, including flow state comparisons and pattern transitions.

Findings

Magnetic fields alter flow structures and suppress certain convection patterns.

Transition from stationary to time-dependent convection occurs at zero Prandtl number.

Flow states show qualitative differences from non-magnetic cases.

Abstract

The effect of a homogeneous magnetic field on surface-tension-driven B\'{e}nard convection is studied by means of direct numerical simulations. The flow is computed in a rectangular domain with periodic horizontal boundary conditions and the free-slip condition on the bottom wall using a pseudospectral Fourier-Chebyshev discretization. Deformations of the free surface are neglected. Two- and three-dimensional flows are computed for either vanishing or small Prandtl number, which are typical of liquid metals. The main focus of the paper is on a qualitative comparison of the flow states with the non-magnetic case, and on the effects associated with the possible near-cancellation of the nonlinear and pressure terms in the momentum equations for two-dimensional rolls. In the three-dimensional case, the transition from a stationary hexagonal pattern at the onset of convection to three-dimensional time-dependent convection is explored by a series of simulations at zero Prandtl number.