Long term time dependent frequency analysis of chaotic waves in the weakly magnetized spherical Couette system

TL;DR

This paper investigates the long-term behavior of chaotic flows in a magnetized spherical Couette system using advanced frequency analysis, revealing the robustness of certain flow frequencies and the effectiveness of Laskar's algorithm in classifying chaos.

Contribution

It demonstrates that Laskar's frequency algorithm accurately detects strange attractors and classifies chaotic flows in high-dimensional systems, improving understanding of magnetic field effects.

Findings

Main flow frequency is robust and close to unstable rotating wave frequency.

Volume-averaged properties' frequency varies significantly with magnetic forcing.

Laskar's algorithm effectively identifies strange attractors in complex flows.

Abstract

The long therm behavior of chaotic flows is investigated by means of time dependent frequency analysis. The system under test consists of an electrically conducting fluid, confined between two differentially rotating spheres. The spherical setup is exposed to an axial magnetic field. The classical Fourier Transform method provides a first estimation of the time dependence of the frequencies associated to the flow, as well as its volume-averaged properties. It is however unable to detect strange attractors close to regular solutions in the Feigenbaum as well as Newhouse-Ruelle-Takens bifurcation scenarios. It is shown that Laskar's frequency algorithm is sufficiently accurate to identify these strange attractors and thus is an efficient tool for classification of chaotic flows in high dimensional dynamical systems. Our analysis of several chaotic solutions, obtained at different magnetic field strengths, reveals a strong robustness of the main frequency of the flow. This frequency is associated to an azimuthal drift and it is very close to the frequency of the underlying unstable rotating wave. In contrast, the main frequency of volume-averaged properties can vary almost one order of magnitude as the magnetic forcing is decreased. We conclude that, at the moderate differential rotation considered, unstable rotating waves provide a good description of the variation of the main time scale of any flow with respective variations in the magnetic field.