Transition to turbulent dynamo saturation

TL;DR

This study investigates how magnetic energy saturation in dynamo processes transitions from viscosity-dependent to viscosity-independent regimes at very low magnetic Prandtl numbers using reduced models, revealing a turbulent scaling regime.

Contribution

It introduces a reduced model to explore dynamo saturation at extremely low magnetic Prandtl numbers, surpassing the limitations of full 3D simulations.

Findings

Magnetic energy transitions to a viscosity-independent turbulent regime at low Pm.

The transition occurs around Pm ≈ 10^{-3}.

Reduced models can access parameter regimes unreachable by full DNS.

Abstract

While the saturated magnetic energy is independent of viscosity in dynamo experiments, it remains viscosity-dependent in state-of-the-art 3D direct numerical simulations (DNS). Extrapolating such viscous scaling-laws to realistic parameter values leads to an underestimation of the magnetic energy by several orders of magnitude. The origin of this discrepancy is that fully 3D DNS cannot reach low enough values of the magnetic Prandtl number $Pm$. To bypass this limitation and investigate dynamo saturation at very low $Pm$, we focus on the vicinity of the dynamo threshold in a rapidly rotating flow: the velocity field then depends on two spatial coordinates only, while the magnetic field consists of a single Fourier mode in the third direction. We perform numerical simulations of the resulting set of reduced equations for $Pm$ down to $2\cdot 10^{-5}$. This parameter regime is currently out of reach to fully 3D DNS. We show that the magnetic energy transitions from a high-$Pm$ viscous scaling regime to a low-$Pm$ turbulent scaling regime, the latter being independent of viscosity. The transition to the turbulent saturation regime occurs at a low value of the magnetic Prandtl number, $Pm \simeq 10^{-3}$, which explains why it has been overlooked by numerical studies so far.