Large-Scale Magnetic-Field Generation by Randomly Forced Shearing Waves

TL;DR

This paper develops a rigorous theoretical model for large-scale magnetic field generation by random shearing motions in conducting fluids, providing analytical insights into a recently observed dynamo effect in sheared turbulence.

Contribution

It offers the first analytical proof of the shear dynamo effect in a low Rm, weak shear regime, connecting numerical observations with a minimal theoretical framework.

Findings

Analytical derivation of scaling laws for growth rate and wavenumber of the dynamo

Confirmation that shear dynamo is a generic feature of sheared MHD turbulence

Establishment of a minimal model for understanding shear-induced magnetic field amplification

Abstract

A rigorous theory for the generation of a large-scale magnetic field by random non-helically forced motions of a conducting fluid combined with a linear shear is presented in the analytically tractable limit of low Rm and weak shear. The dynamo is kinematic and due to fluctuations in the net (volume-averaged) electromotive force. This is a minimal proof-of-concept quasilinear calculation aiming to put the shear dynamo, a new effect recently found in numerical experiments, on a firm theoretical footing. Numerically observed scalings of the wavenumber and growth rate of the fastest growing mode, previously not understood, are derived analytically. The simplicity of the model suggests that shear dynamo action may be a generic property of sheared magnetohydrodynamic turbulence.