Wall modes in magnetoconvection at high Hartmann numbers

TL;DR

This study investigates wall modes in turbulent magnetoconvection at high Hartmann numbers, revealing their structure, extension, and boundary layer scaling in liquid gallium under strong magnetic fields.

Contribution

It provides a detailed analysis of wall modes in high Hartmann number magnetoconvection, highlighting their structure and boundary layer characteristics.

Findings

Wall modes persist beyond the critical Hartmann number, maintaining heat transfer.

Wall modes have a two-layer structure extending into the cell interior.

Boundary layer thickness scales with Shercliff layer thickness.

Abstract

Three-dimensional turbulent magnetoconvection at a Rayleigh number of $Ra=10^7$ in liquid gallium at a Prandtl number $Pr=0.025$ is studied in a closed square cell for very strong external vertical magnetic fields $B_0$ in direct numerical simulations which apply the quasistatic approximation. As $B_0$ or equivalently the Hartmann number $Ha$ are increased, the convection flow that is highly turbulent in the absence of magnetic fields crosses the Chandrasekhar linear stability limit for which thermal convection is ceased in an infinitely extended layer and which can be assigned with a critical Hartmann number $Ha_{\rm c}$. Similar to rotating Rayleigh-B\'{e}nard convection, our simulations reveal subcritical sidewall modes that maintain a small but finite convective heat transfer for $Ha>Ha_{\rm c}$. We report a detailed analysis of the complex two-layer structure of these wall modes, their extension into the cell interior and a resulting sidewall boundary layer composition that is found to scale with the Shercliff layer thickness.