Coherent structures and the saturation of a nonlinear dynamo

TL;DR

This paper uses Eulerian and Lagrangian tools to analyze coherent structures in a nonlinear dynamo, revealing detailed flow features and chaotic magnetic field transport during different dynamo stages.

Contribution

It compares traditional finite-time Lyapunov exponent methods with a new function M approach for detecting Lagrangian coherent structures in dynamo simulations.

Findings

Lagrangian analysis reveals more detailed structures.

Function M provides clearer identification of hyperbolic regions.

Chaotic transport of magnetic field lines is enhanced in hyperbolic regions.

Abstract

Eulerian and Lagrangian tools are used to detect coherent structures in the velocity and magnetic fields of a mean--field dynamo, produced by direct numerical simulations of the three--dimensional compressible magnetohydrodynamic equations with an isotropic helical forcing and moderate Reynolds number. Two distinct stages of the dynamo are studied, the kinematic stage, where a seed magnetic field undergoes exponential growth, and the saturated regime. It is shown that the Lagrangian analysis detects structures with greater detail, besides providing information on the chaotic mixing properties of the flow and the magnetic fields. The traditional way of detecting Lagrangian coherent structures using finite--time Lyapunov exponents is compared with a recently developed method called function M. The latter is shown to produce clearer pictures which readily permit the identification of hyperbolic regions in the magnetic field, where chaotic transport/dispersion of magnetic field lines is highly enhanced.