High dimensional tori and chaotic and intermittent transients in magnetohydrodynamic Couette flows

TL;DR

This paper investigates the bifurcations to high-dimensional invariant tori and chaotic transients in magnetohydrodynamic Couette flows, revealing the role of Hopf bifurcations, resonances, and crises in complex dynamical behavior.

Contribution

It provides numerical evidence for the origin of chaotic transients and intermittent behavior from bifurcations involving high-dimensional tori in magnetohydrodynamic flows.

Findings

Existence of crisis events destroying chaotic attractors.

Chaotic transients involve unstable invariant tori.

On-off intermittent behavior observed in chaotic transients.

Abstract

The magnetised spherical Couette (MSC) problem, a three dimensional magnetohydrodynamic paradigmatic model in geo- and astrophysics, is considered to investigate bifurcations to high-dimensional invariant tori and chaotic flows in large scale dissipative dynamical systems with symmetry. The main goal of the present study is to elucidate the origin of chaotic transients and intermittent behaviour from two different sequences of Hopf bifurcations involving invariant tori with four fundamental frequencies, which may be resonant. Numerical evidence of the existence of a crisis event destroying chaotic attractors and giving rise to the chaotic transients is provided. It is also shown that unstable invariant tori take part in the time evolution of these chaotic transients. For one sequence of bifurcations, the study demonstrates that chaotic transients display on-off intermittent behaviour. A possible explanatory mechanism is discussed.