Evolution of localized magnetic field perturbations and the nature of turbulent dynamo

TL;DR

This paper introduces a new approach to understanding turbulent dynamo by analyzing localized magnetic field perturbations, revealing how magnetic fields grow exponentially in 3D turbulence and explaining the absence of dynamo in 2D.

Contribution

It proposes a novel method interpreting magnetic fields as superpositions of localized blobs, linking their stochastic properties to the evolution of magnetic fields in turbulent flows.

Findings

Magnetic field of a blob grows exponentially in 3D turbulence.

The approach explains the absence of dynamo in 2D flows.

Mechanism of dynamo generation in the inertial range is revealed.

Abstract

Kinematic dynamo in incompressible isotropic turbulent flows with high magnetic Prandtl number is considered. The approach interpreting an arbitrary magnetic field distribution as a superposition of localized perturbations (blobs) is proposed. We derive a relation between stochastic properties of a blob and a stochastically homogenous distribution of magnetic field advected by the same stochastic flow. This relation allows to investigate the evolution of a localized blob at late stage when its size exceeds the viscous scale. It is shown that in 3-dimansional flows, the average magnetic field of the blob increases exponentially in the inertial range of turbulence, as opposed to the late-Batchelor stage when it decreases. Our approach reveals the mechanism of dynamo generation in the inertial range both for blobs and homogenous contributions. It explains the absence of dynamo in the two-dimensional case and its efficiency in three dimensions. We propose the way to observe the mechanism in numerical simulations.