Boundary layers in quasi-static magnetoconvection with a vertical field and their implications for heat transport

TL;DR

This paper investigates heat transport in quasi-static magnetoconvection with a vertical magnetic field, revealing persistent boundary layers and their impact on heat transfer scaling at high Chandrasekhar numbers.

Contribution

It combines direct numerical simulations and asymptotic theory to analyze boundary layer behavior and heat transport scaling in magnetoconvection at large Chandrasekhar numbers.

Findings

Thermal and magnetic boundary layers scale as Q^{-1/6}.

Nusselt number depends on Q, no asymptotic heat transport state independent of Q.

Boundary layer behavior is consistent across different boundary conditions.

Abstract

Heat transport in quasi-static magnetoconvection with a vertical magnetic field in a plane layer geometry is investigated with direct numerical simulations and asymptotic theory in the limit of large Chandrasekhar number ($Q$). It is shown that thermal and magnetic boundary layers with thickness $O(Q^{-1/6})$, of the same order as the horizontal scale of the convection, are persistent over the range of investigated parameters. Thermal boundary layer control of the heat transport indicates that the Nusselt number depends on $Q$, suggesting that no asymptotic state of heat transport independent of $Q$ occurs in this system. The magnetic boundary layers necessitate leading order modifications to the dominant vertical force balance as well as the amplitude of the horizontal induced magnetic field near the boundaries. The scaling behavior of the thermal boundary layer and resulting heat transport is found to be independent of the choice of mechanical and electromagnetic boundary conditions.