Nonlinear Dynamo

TL;DR

This paper develops a nonlinear multiscale theory explaining how large-scale magnetic and velocity structures form in stratified conductive media with small-scale oscillations, highlighting the stabilization of linear instability.

Contribution

It introduces a new nonlinear system of equations describing large-scale structure formation in stratified media with small-scale oscillations, extending previous linear instability analyses.

Findings

Large-scale magnetic structures can stabilize linear instabilities.

The theory applies to low Reynolds number regimes.

Stationary large-scale structures emerge from nonlinear interactions.

Abstract

In this manuscript using the asymptotic method of multiscale nonlinear theory we construct a nonlinear theory of the appearance of large-scale structures in the stratified conductive medium with the presence of small-scale oscillations of the velocity field and magnetic fields. These small-scale stationary oscillations are maintained by small external sources at low Reynolds numbers. We obtain a nonlinear system of equations describing the evolution of large-scale structures of the velocity field and magnetic fields. The linear stage of evolution leads to the known instability. In this article we consider the stationary large-scale structures of a magnetic field arising at stabilization of linear instability.