# Approaching Earth's core conditions in high-resolution geodynamo simulations

## TL;DR

This study uses high-resolution simulations to explore Earth's core conditions, revealing how scale separation influences magnetic and flow structures, and improving the alignment with theoretical models of the geodynamo.

## Contribution

It advances geodynamo modeling by increasing resolution and relaxing hyperdiffusive approximations, approaching more realistic Earth's core conditions and validating quasi-geostrophic and MAC force balances.

## Key findings

- Kinetic energy spectra broaden with increased resolution.
- Large-scale magnetic structures remain stable after upsizing.
- Simulations align better with QG-MAC theory, with some residual deviations.

## Abstract

The geodynamo features a broad separation between the large scale at which Earth's magnetic field is sustained against ohmic dissipation and the small scales of the turbulent and electrically conducting underlying fluid flow in the outer core. Here, the properties of this scale separation are analysed using high-resolution numerical simulations that approach closer to Earth's core conditions than earlier models. The new simulations are obtained by increasing the resolution and gradually relaxing the hyperdiffusive approximation of previously published low-resolution cases. This upsizing process does not perturb the previously obtained large-scale, leading-order quasi-geostrophic (QG), and first-order magneto-Archimedes-Coriolis (MAC) force balances. As Earth's core conditions are approached in the upsized simulations, kinetic energy spectra feature a gradually broadening self-similar, power-law spectral range extending over more than a decade in length scale. In this range, the spectral energy density profile of vorticity is shown to be approximately flat between the large scale at which the magnetic field draws its energy from convection through the QG-MAC force balance and the small scale at which this energy is dissipated. The resulting velocity and density anomaly planforms in the physical space consist in large-scale columnar sheets and plumes, respectively co-existing with small-scale vorticity filaments and density anomaly ramifications. In contrast, magnetic field planforms keep their large-scale structure after upsizing. The diagnostic outputs of the upsized simulations are more consistent with the asymptotic QG-MAC theory than those of the low-resolution cases that they originate from, but still feature small residual deviations that may call for further theoretical refinements to account for the structuring constraints of the magnetic field on the flow.