# Dynamo saturation down to vanishing viscosity: strong-field and inertial scaling regimes

## TL;DR

This paper provides analytical models of fluid dynamos that saturate through Coriolis and inertial effects, revealing different scaling regimes and bifurcation types depending on rotation and flow conditions, applicable down to very low viscosity.

## Contribution

It introduces analytical examples of dynamo saturation mechanisms that operate across various viscosity regimes and elucidates the conditions leading to different scaling laws and bifurcation behaviors.

## Key findings

- Magnetic energy scales with rotation rate, independent of viscosity in strong-field regimes.
- Dynamo bifurcation can be supercritical or subcritical based on flow orientation.
- Saturated magnetic energy follows specific scaling laws depending on bifurcation type.

## Abstract

We present analytical examples of fluid dynamos that saturate through the action of the Coriolis and inertial terms of the Navier-Stokes equation. The flow is driven by a body force and is subject to global rotation and uniform sweeping velocity. The model can be studied down to arbitrarily low viscosity and naturally leads to the strong-field scaling regime for the magnetic energy produced above threshold: the magnetic energy is proportional to the global rotation rate and independent of the viscosity. Depending on the relative orientations of global rotation and large-scale sweeping, the dynamo bifurcation is either supercritical or subcritical. In the supercritical case, the magnetic energy follows the scaling-law for supercritical strong-field dynamos predicted on dimensional grounds by Petrelis & Fauve (2001). In the subcritical case, the system jumps to a finite-amplitude dynamo branch. The magnetic energy obeys a magneto-geostrophic scaling-law (Roberts & Soward 1972), with a turbulent Elsasser number of the order of unity, where the magnetic diffusivity of the standard Elsasser number appears to be replaced by an eddy diffusivity. In the absence of global rotation, the dynamo bifurcation is subcritical and the saturated magnetic energy obeys the equipartition scaling regime. We consider both the vicinity of the dynamo threshold and the limit of large distance from threshold to put these various scaling behaviors on firm analytical ground.