# Systematic parameter study of dynamo bifurcations in geodynamo simulations

## TL;DR

This paper explores the complex bifurcation behavior of geodynamo simulations, revealing bistability, hysteresis, and the influence of initial conditions on magnetic field topology, with implications for understanding planetary magnetic reversals.

## Contribution

It demonstrates the existence of bistability and hysteresis in dynamo bifurcations, highlighting the role of initial magnetic fields and flow regimes in geodynamo models.

## Key findings

- Bistability and hysteresis depend on initial magnetic field strength.
- Different flow regimes influence magnetic field topology.
- Lorentz forces significantly impact flow and heat transfer at high Rayleigh numbers.

## Abstract

We investigate the nature of the dynamo bifurcation in a configuration applicable to the Earth's liquid outer core. Numerical studies on the stability domain of dipolar magnetic fields found a dichotomy between non-reversing dipole-dominated dynamos and the reversing non-dipole-dominated multipolar solutions. We show that, by considering weak initial fields, the above transition disappears and is replaced by a region of bistability. Such a result was also observed in models with free-slip boundaries in which the geostrophic zonal flow can develop and participate to the dynamo mechanism for non-dipolar fields. We show that a similar process develops in no-slip models when viscous effects are reduced sufficiently. The following three regimes are distinguished: (i) Close to the onset of convection ($Ra_c$) with only the most critical convective mode (wave number) being present, dynamos set in supercritically and are dipole-dominated. (ii) in the range $3<Ra/Ra_c<Ra_c$, the bifurcations are subcritical and only dipole-dominated dynamos exist. (iii) $(Ra/Ra_c>10)$, the relative importance of zonal flows increases with $Ra$ in non-magnetic models. The field topology depends on the magnitude of the initial magnetic field. The dipolar branch has a subcritical behavior whereas the multipolar branch has a supercritical behavior. By approaching more realistic parameters, the extension of this bistable regime increases. A hysteretic behavior questions the common interpretation for geomagnetic reversals. Far above the dynamo threshold (by increasing the magnetic Prandtl number), Lorentz forces contribute to the first order force balance, as predicted for planetary dynamos. When $Ra$ is sufficiently high, dipolar fields affect significantly the flow speed, the flow structure and heat transfer which is reduced by the Lorentz force regardless of the field strength.