Universality of oscillatory instabilities in fluid mechanical systems

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.