Axial dipolar dynamo action in the Taylor-Green vortex

TL;DR

This paper numerically investigates how the Taylor-Green vortex can generate magnetic fields through dynamo action, highlighting the influence of boundary conditions, symmetries, and velocity fluctuations on the dynamo threshold and magnetic field geometry.

Contribution

It demonstrates that axial dipolar dynamos can be modeled using symmetry-preserving boundary conditions and provides a simple model for the magnetic Prandtl number dependence of the dynamo transition.

Findings

Periodic boundary conditions can mimic realistic boundaries.

An axial dipolar dynamo similar to experiments is achievable.

A model explains the Prandtl number effect on dynamo transition.

Abstract

We present a numerical study of the magnetic field generated by the Taylor-Green vortex. We show that periodic boundary conditions can be used to mimic realistic boundary conditions by prescribing the symmetries of the velocity and magnetic fields. This gives insight in some problems of central interest for dynamos: the possible effect of velocity fluctuations on the dynamo threshold, the role of boundary conditions on the threshold and on the geometry of the magnetic field generated by dynamo action. In particular, we show that an axial dipolar dynamo similar to the one observed in a recent experiment can be obtained with an appropriate choice of the symmetries of the magnetic field. The nonlinear saturation is studied and a simple model explaining the magnetic Prandtl number dependence of the super/sub critical nature of the dynamo transition is given.