Strong-Field Spherical Dynamos

TL;DR

This paper introduces a third dynamo branch in numerical models of the geodynamo, characterized by a force balance between Coriolis and Lorentz forces, challenging traditional classifications and emphasizing the importance of the strong-field limit.

Contribution

It demonstrates the existence of a strong-field dynamo branch numerically, co-existing with known branches, and highlights the need for a different approach to modeling geodynamo phenomena.

Findings

Identification of a third dynamo branch with Coriolis-Lorentz force balance.

Transition observed from weak-field to strong-field dynamo regimes.

Minimizing magnetic Prandtl number is misleading for geodynamo modeling.

Abstract

Numerical models of the geodynamo are usually classified in two categories: those denominated dipolar modes, observed when the inertial term is small enough, and multipolar fluctuating dynamos, for stronger forcing. We show that a third dynamo branch corresponding to a dominant force balance between the Coriolis force and the Lorentz force can be produced numerically. This force balance is usually referred to as the strong-field limit. This solution co-exists with the often described viscous branch. Direct numerical simulations exhibit a transition from a weak-field dynamo branch, in which viscous effects set the dominant length scale, and the strong-field branch in which viscous and inertial effects are largely negligible. These results indicate that a distinguished limit needs to be sought to produce numerical models relevant to the geodynamo and that the usual approach of minimizing the magnetic Prandtl number (ratio of the fluid kinematic viscosity to its magnetic diffusivity) at a given Ekman number is misleading.