Direct numerical simulations of optimal thermal convection in rotating plane layer dynamos

TL;DR

This study uses direct numerical simulations to explore how magnetic fields influence heat transfer in rotating convection, revealing an optimal thermal forcing that maximizes heat transfer and highlighting the role of Lorentz forces in boundary layers.

Contribution

It demonstrates the existence of an optimal thermal forcing for maximum heat transfer in rotating dynamos and uncovers the role of boundary layer Lorentz forces in turbulence enhancement.

Findings

Maximum heat transfer occurs at a specific Rayleigh number.

Lorentz force increases in the thermal boundary layer due to magnetic field stretching.

Magnetic fields mitigate turbulence suppression by the Coriolis force.

Abstract

The heat transfer behavior of convection-driven dynamos in a rotating plane layer between two parallel plates, heated from below and cooled from the top, is investigated. At a fixed rotation rate (Ekman Number, $E=10^{-6}$) and fluid properties (thermal and magnetic Prandtl numbers, $Pr=Pr_m=1$), both dynamo convection (DC) and non-magnetic rotating convection (RC) simulations are performed to demarcate the effect of magnetic field on heat transport at different thermal forcings (Rayleigh Number, $Ra=3.83\times10^{9}-3.83\times10^{10}$). In this range, our turbulence resolving simulations demonstrate the existence of an optimum thermal forcing, at which heat transfer between the plates in DC exhibits maximum enhancement, as compared to the heat transport in the RC simulations. Unlike any global force balance reported in the literature, the present simulations reveal an increase in the Lorentz force in the \textit{thermal boundary layer}, due to stretching of magnetic field line by the vortices near the walls with no-slip boundary condition. This increase in Lorentz force mitigates turbulence suppression owing to the Coriolis force, resulting in enhanced turbulence and heat transfer