Convection-driven kinematic dynamos at low Rossby and magnetic Prandtl numbers: single mode solutions

TL;DR

This paper develops a low Rossby, low magnetic Prandtl number convection-driven dynamo model using single mode solutions, revealing how helicity profiles influence dynamo efficiency and oscillation frequency, with implications for planetary dynamos.

Contribution

It introduces a multiscale, asymptotically exact model of convection-driven dynamos at low Rossby and magnetic Prandtl numbers using explicit single mode solutions.

Findings

Dynamo action increases with Rayleigh number and decreases magnetic Prandtl number.

Oscillatory dynamos are more easily excited than steady ones at low magnetic Prandtl numbers.

Helicity boundary layer behavior reduces dynamo efficiency.

Abstract

The onset of dynamo action is investigated within the context of a newly developed low Rossby, low magnetic Prandtl number, convection-driven dynamo model. This multiscale model represents an asymptotically exact form of an $\alpha^2$ mean field dynamo model in which the small-scale convection is represented explicitly by finite amplitude, single mode solutions. Both steady and oscillatory convection are considered for a variety of horizontal planforms. The kinetic helicity is observed to be a monotonically increasing function of the Rayleigh number. As a result, very small magnetic Prandtl number dynamos can be found for sufficiently large Rayleigh numbers. All dynamos are found to be oscillatory with an oscillation frequency that increases as the strength of the convection is increased and the magnetic Prandtl number is reduced. Kinematic dynamo action is strongly controlled by the profile of the helicity; single mode solutions which exhibit boundary layer behavior in the helicity show a decrease in the efficiency of dynamo action due to the enhancement of magnetic diffusion in the boundary layer regions. For a given value of the Rayleigh number, lower magnetic Prandtl number dynamos are excited for the case of oscillatory convection in comparison to steady convection. With regards to planetary dynamos, these results suggest that the low magnetic Prandtl number dynamos typical of liquid metals are more easily driven by thermal convection than by compositional convection.