Universality of oscillatory instabilities in fluid mechanical systems

TL;DR

This paper demonstrates that the complex Ginzburg-Landau equation with global coupling can universally describe the transition to oscillatory instability in various turbulent fluid systems, revealing a common route mediated by global coupling.

Contribution

It introduces a unified theoretical framework using GCGLE to explain the universal oscillatory instability behavior observed across different turbulent fluid systems.

Findings

Universal scaling behavior identified via Hurst exponent and spectral measures.

GCGLE captures the transition from defect to phase turbulence.

Global coupling mediates the route to oscillatory instability.

Abstract

Oscillatory instability (OI) emerges amidst turbulent states in experiments in various turbulent fluid and thermo-fluid systems such as aero-acoustic, thermoacoustic and aeroelastic systems. For the time series of the relevant dynamic variable at the onset of the OI, universal scaling behavior have been discovered in experiments via the Hurst exponent and certain spectral measures. By means of a center manifold reduction, the spatiotemporal dynamics of these real systems can be mapped to a complex Ginzburg-Landau equation with a linear global coupling (GCGLE). In this work, we show that the GCGLE is able to capture the universal behavior of the route to OI, elucidating it as a transition from defect to phase turbulence mediated by the global coupling.