A minimal phase-coupling model for intermittency in turbulent systems

TL;DR

This paper introduces a minimal phase-coupling model to understand intermittency in turbulence, linking phase synchronization and non-Gaussian statistics through dynamical systems theory and simulations.

Contribution

It identifies spectral power-law steepness as a key control parameter for phase coupling and intermittency, providing a dynamical systems perspective on turbulence.

Findings

Intermediate spectral slopes lead to strongest non-Gaussianity.

Phase synchronization correlates with a lower-dimensional attractor.

Model captures turbulence intermittency phenomena.

Abstract

Turbulent systems exhibit a remarkable multi-scale complexity, in which spatial structures induce scale-dependent statistics with strong departures from Gaussianity. In Fourier space, this is reflected by pronounced phase synchronization. A quantitative relation between real-space structure, statistics, and phase synchronization is currently missing. Here, we address this problem in the framework of a minimal phase-coupling model, which enables a detailed investigation by means of dynamical systems theory and multi-scale high-resolution simulations. We identify the spectral power-law steepness, which controls the phase coupling, as the control parameter for tuning the non-Gaussian properties of the system. Whereas both very steep and very shallow spectra exhibit close-to-Gaussian statistics, the strongest departures are observed for intermediate slopes comparable to the ones in hydrodynamic and Burgers turbulence. We show that the non-Gaussian regime of the model coincides with a collapse of the dynamical system to a lower-dimensional attractor and the emergence of phase synchronization, thereby establishing a dynamical-systems perspective on turbulent intermittency.