Universality in the emergence of oscillatory instabilities in turbulent flows

TL;DR

This paper reveals a universal scaling law governing the emergence of oscillatory instabilities in turbulent flows, showing a consistent inverse power law relation across diverse systems.

Contribution

It uncovers a universal power law scaling behavior in turbulent flows leading to oscillatory instabilities, linking spectral amplitude and Hurst exponent.

Findings

Spectral amplitude scales inversely with Hurst exponent.

The power law exponent is approximately -2 across systems.

Universal behavior observed in aeroacoustic, thermoacoustic, and aeroelastic flows.

Abstract

Spontaneous emergence of periodic oscillations due to self-organization is ubiquitous in turbulent flows. The emergence of such oscillatory instabilities in turbulent fluid mechanical systems is often studied in different system-specific frameworks. We uncover the existence of a universal scaling behaviour during self-organization in turbulent flows leading to oscillatory instability. Our experiments show that the spectral amplitude of the dominant mode of oscillations scales inversely with the Hurst exponent of a fluctuating state variable following an inverse power law relation. Interestingly, we observe the same power law behaviour with a constant exponent near -2 across various turbulent systems such as aeroacoustic, thermoacoustic and aeroelastic systems.