Synchronization of Chaos in Fully-Developed Turbulence
Abstract
We investigate chaos synchronization of small-scale motions in the three-dimensional turbulent energy cascade, via pseudo-spectral simulations of the incompressible Navier-Stokes equations. The modes of the turbulent velocity field below about 20 Kolmogorov dissipation lengths are found to be slaved to the chaotic dynamics of larger-scale modes. The dynamics of all dissipation-range modes can be recovered to full numerical precision by solving small-scale dynamical equations with the given large-scale solution as an input, regardless of initial condition. The synchronization rate exponent scales with the Kolmogorov dissipation time-scale, with possible weak corrections due to intermittency. Our results suggest that all sub-Kolmogorov length modes should be fully recoverable from numerical simulations with standard, Kolmogorov-length grid resolutions.
Keywords
Cite
@article{arxiv.1212.1844,
title = {Synchronization of Chaos in Fully-Developed Turbulence},
author = {Cristian C Lalescu and Charles Meneveau and Gregory L Eyink},
journal= {arXiv preprint arXiv:1212.1844},
year = {2015}
}
Comments
4 pages, two-column, 4 figures