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arXiv · 1212.1844

Synchronization of Chaos in Fully-Developed Turbulence

Cristian C Lalescu·Charles Meneveau·Gregory L Eyink
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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.

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Cristian C Lalescu, Charles Meneveau, Gregory L Eyink. 2012-12-09. Synchronization of Chaos in Fully-Developed Turbulence. https://doi.org/10.1103/physrevlett.110.084102

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