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  • Letter
  • Open Access

Minimal phase-coupling model for intermittency in turbulent systems

José-Agustín Arguedas-Leiva1, Enda Carroll2, Luca Biferale3, Michael Wilczek1,4,*, and Miguel D. Bustamante2

  • 1Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany
  • 2School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland
  • 3Department Physics and Istituto Nazionale Fisica Nucleare (INFN), University of Rome Tor Vergata, Via Ricerca Scientifica 1, 00133 Rome, Italy
  • 4Theoretical Physics I, University of Bayreuth, Universitätsstraße 30, 95447 Bayreuth, Germany

  • *michael.wilczek@ds.mpg.de
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Phys. Rev. Research 4, L032035 – Published 29 August, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.L032035

Abstract

Turbulent systems exhibit a remarkable multiscale 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 deterministic phase-coupling model, which enables a detailed investigation by means of dynamical systems theory and multiscale 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 with 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.

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Phys. Rev. Research 4, L032035– Published 29 August, 2022
  • Received 29 July 2021
  • Accepted 12 July 2022
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

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