Period doubling route to chaos in Taylor-Green dynamo

TL;DR

This paper investigates the transition to chaos in a Taylor-Green dynamo system, revealing a period-doubling route to chaos through spectral simulations and identifying complex magnetic field behaviors.

Contribution

It demonstrates the existence of a period-doubling route to chaos in Taylor-Green dynamo simulations, highlighting multiple attractors and complex dynamo states.

Findings

Dynamo transition occurs via supercritical pitchfork bifurcation.

Multiple attractors exist for different initial conditions.

A period-doubling route to chaos is observed.

Abstract

We perform spectral simulations of dynamo for magnetic Prandtl number of one with Taylor-Green forcing. We observe dynamo transition through a supercritical pitchfork bifurcation. Beyond the transition, the numerical simulations reveal complex dynamo states with windows of constant, periodic, quasiperiodic, and chaotic magnetic field configurations. For some forcing amplitudes, multiple attractors were obtained for different initial conditions. We show that one of the chaotic windows follows the period-doubling route to chaos.