Strong field, scale separated, ultra low viscosity dynamos

TL;DR

This paper presents advanced numerical simulations of Earth's dynamo with ultra-low viscosity, revealing scale separation and force balances that resemble Earth's magnetic field generation, emphasizing the importance of magnetic forces and Ohmic dissipation.

Contribution

It introduces self-consistent spherical shell models with ultra-low viscosities, demonstrating significant scale separation and magnetostrophic balance similar to Earth's core dynamics.

Findings

Magnetic and velocity fields exhibit different dominant scales.

Viscous forces are negligible compared to Lorentz forces outside boundary layers.

Ohmic dissipation in the model aligns with Earth's estimated 10 TW.

Abstract

The mechanism by which the Earth's magnetic field is generated is thought to be thermal convection in the metallic liquid iron core. Computational considerations previously restricted most numerical simulations to a regime where the diffusivities of momentum and electric current are roughly equal, leading to similar spectra for both velocities and magnetic fields. Here we present results of a suite of self-consistent spherical shell computations with ultra-low viscosities. The most Earth-like of our models (S4) has a twenty-fold difference in the aforementioned diffusivities, leading to significant scale separation between magnetic and velocity fields, the latter being dominated by small scales. This has repercussions for the leading force balance, which can be magnetostrophic at large scales (with a major role played by the Lorentz force) whereas small scales require a different balance. This is the so-called strong field limit. Outside boundary layers, viscous forces have a magnitude which is about one thousandth of the Lorentz force. In this dynamo dissipation is almost exclusively Ohmic, as in the Earth, with convection inside the so-called tangent cylinder playing a crucial role. Our most extreme dynamo has significantly more magnetic energy than kinetic energy (as in the Earth). Our model suggests Ohmic dissipation in the Earth's core is as high as 10TW.