Convection-driven kinematic dynamos at low Rossby and magnetic Prandtl numbers

TL;DR

This study investigates how low Rossby number convection influences kinematic dynamo action in low magnetic Prandtl number fluids, revealing decreased efficiency with increased buoyancy forcing and weak dependence of large-scale magnetic field on flow changes.

Contribution

It introduces an asymptotic, rapidly rotating dynamo model for low magnetic Prandtl number fluids, analyzing flow regimes and magnetic field characteristics in a plane layer geometry.

Findings

Dynamo efficiency decreases with increased buoyancy forcing.

Large-scale magnetic field shows weak dependence on flow behavior.

Small-scale magnetic field varies significantly with convective flow.

Abstract

Most large-scale planetary magnetic fields are thought to be driven by low Rossby number convection of a low magnetic Prandtl number fluid. Here kinematic dynamo action is investigated with an asymptotic, rapidly rotating dynamo model for the plane layer geometry that is intrinsically low magnetic Prandtl number. The thermal Prandtl number and Rayleigh number are varied to illustrate fundamental changes in flow regime, ranging from laminar cellular convection to geostrophic turbulence in which an inverse energy cascade is present. A decrease in the efficiency of the convection to generate a dynamo, as determined by an increase in the critical magnetic Reynolds number, is observed as the buoyancy forcing is increased. This decreased efficiency may result from both the loss of correlations associated with the increasingly disordered states of flow that are generated, and boundary layer behavior that enhances magnetic diffusion locally. We find that the spatial characteristics of $\alpha$, and thus the large-scale magnetic field, is dependent only weakly on changes in flow behavior. However, our results are limited to the linear, kinematic dynamo regime, and future simulations including the Lorentz force are therefore necessary to assess the robustness of this result. In contrast to the large-scale magnetic field, the behavior of the small-scale magnetic field is directly dependent on, and therefore shows significant variations with, the small-scale convective flow field.