Universality of oscillatory instabilities in fluid mechanical systems

Oscillatory instability (OI) arises out of turbulent states in various fluid mechanical 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 behaviors have been experimentally uncovered 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 letter, we show that the GCGLE is able to capture the universal behavior of the OI, elucidating it as a transition between defect to phase turbulence mediated by the global coupling