Phenomenology of turbulent dynamo growth and saturation

TL;DR

This paper uses a non-local shell model to numerically study turbulent dynamo growth and saturation across different magnetic Prandtl numbers, revealing how energy transfer mechanisms influence magnetic energy evolution.

Contribution

It introduces a phenomenological framework to understand dynamo behavior in terms of local and non-local energy transfers based on Prandtl number regimes.

Findings

Magnetic energy grows at small scales during dynamo action.

Saturation occurs via an inverse cascade process.

Energy transfer nature depends on the magnetic Prandtl number.

Abstract

With a non local shell model of magnetohydrodynamic turbulence we investigate numerically the turbulent dynamo action for low and high magnetic Prandtl numbers ($Pm$). The results obtained in the kinematic regime and along the way to dynamo saturation are understood in terms of a phenomenological approach based on the local ($Pm\ll 1$) or non local ($Pm\gg 1$) nature of the energy transfers. In both cases the magnetic energy grows at small scale and saturates as an inverse `` cascade ''.