Transition to chaos and modal structure of magnetized Taylor-Couette flow

TL;DR

This paper investigates the transition to chaos in magnetized Taylor-Couette flow, revealing complex flow structures and modulating frequencies using a data-driven approach, and constructs a reduced nonlinear model of the transition.

Contribution

It introduces a data-driven analysis of the transition to chaos in magnetized Taylor-Couette flow using Dynamic Mode Decomposition, moving beyond traditional Floquet analysis.

Findings

Identification of flow structures related to modulating frequencies

Development of a nonlinear reduced model for the transition to chaos

Demonstration of complex coexistence of chaos and quasi-periodic behavior

Abstract

Taylor-Couette flow is often used as a simplified model for complex rotating flows in the interior of stars and accretion disks. The flow dynamics in these objects is influenced by magnetic fields. For example, quasi-Keplerian flows in Taylor-Couette geometry become unstable to a travelling or standing wave in an external magnetic field if the fluid is conducting; there is an instability even when the flow is hydrodynamically stable. This magnetorotational instability leads to the development of chaotic states and, eventually, turbulence, when the cylinder rotation is sufficiently fast. The transition to turbulence in this flow can be complex, with the coexistence of parameter regions with spatio-temporal chaos and regions with quasi-periodic behaviour, involving one or two additional modulating frequencies. Although the unstable modes of a periodic flow can be identified with Floquet analysis, here we adopt a more flexible equation-free data-driven approach. We analyse the data from the transition to chaos in the magnetized Taylor-Couette flow and identify the flow structures related to the modulating frequencies with Dynamic Mode Decomposition; this method is based on approximating nonlinear dynamics with a linear infinite-dimensional Koopman operator. With the use of these structures, one can construct a nonlinear reduced model for the transition.