Magnetic field correlations in a random flow with strong steady shear

TL;DR

This paper investigates how magnetic fields grow and behave in a conducting fluid with a steady shear flow combined with weak random fluctuations, analyzing different regimes and correlation functions.

Contribution

It provides a detailed analysis of magnetic dynamo behavior in shear flows with weak randomness, including explicit solutions for short-correlated velocity fields.

Findings

Growth rates of magnetic field moments are linked to flow statistics.

Magnetic field correlation functions exhibit specific growth and scaling behaviors.

Explicit solutions demonstrate the model's dynamics in short-correlated velocity fields.

Abstract

We analyze magnetic kinematic dynamo in a conducting fluid where the stationary shear flow is accompanied by relatively weak random velocity fluctuations. The diffusionless and diffusion regimes are described. The growth rates of the magnetic field moments are related to the statistical characteristics of the flow describing divergence of the Lagrangian trajectories. The magnetic field correlation functions are examined, we establish their growth rates and scaling behavior. General assertions are illustrated by explicit solution of the model where the velocity field is short-correlated in time.