Scaling of strong-field spherical dynamos

TL;DR

This paper investigates the scaling laws and force balances of strong-field spherical dynamos, providing insights into Earth's magnetic field generation and introducing a new parameter to identify strong-field regimes.

Contribution

It demonstrates the persistence of the strong-field dynamo branch and introduces a new output parameter to better identify and analyze strong magnetic field solutions.

Findings

Strong-field solutions maintain Earth's core force balance.

Scaling laws for the onset of strong-field dynamos are established.

A new parameter effectively captures strong-field regimes across parameter space.

Abstract

Numerical experiments of dynamo action designed to understand the generation of Earth's magnetic field produce different regime branches identified within bifurcation diagrams. Notable are distinct branches where the resultant magnetic field is either weak or strong. Weak-field solutions are identified by the prominent role of viscosity (and/or inertia) on the motion, whereas the magnetic field has a leading-order effect on the flow in strong-field solutions. We demonstrate the persistence of the strong-field branch, preserving the expected force balance of Earth's core, and provide scaling laws governing its onset as parameters move toward values appropriate for the Geodynamo. We introduce a new output parameter, based on dynamically important parts of rotational and magnetic forces, that captures expected $O(1)$ values of strong-field solutions throughout input parameter space. This new measure of the field strength and our bounds on scaling laws can guide future studies in locating strong-field dynamos in parameter space.