A minimal phase-coupling model for intermittency in turbulent systems
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.
Cite
@article{arxiv.2107.14003,
title = {A minimal phase-coupling model for intermittency in turbulent systems},
author = {José-Agustín Arguedas-Leiva and Enda Carroll and Luca Biferale and Michael Wilczek and Miguel D. Bustamante},
journal= {arXiv preprint arXiv:2107.14003},
year = {2022}
}
Comments
6 pages, 3 figures. Main changes: Improved introduction and model discussion to emphasize the deterministic system that supports a turbulent attractor. Improved figures and text to introduce a time-dependent order parameter