Information production in homogeneous isotropic turbulence

TL;DR

This paper investigates how the complexity of three-dimensional homogeneous isotropic turbulence, measured by Lyapunov spectra and attractor dimension, scales with Reynolds number using direct numerical simulations.

Contribution

It provides new empirical data on the Reynolds number scaling of chaos measures in turbulence, showing a larger-than-expected growth of attractor dimension.

Findings

Attractor dimension scales as Re^2.35, exceeding theoretical predictions.

Lyapunov exponents distribution is finite near zero, contrary to some models.

Reynolds number influences chaos measures in turbulence significantly.

Abstract

We study the Reynolds number scaling of the Kolmogorov-Sinai entropy and attractor dimension for three dimensional homogeneous isotropic turbulence through the use of direct numerical simulation. To do so, we obtain Lyapunov spectra for a range of different Reynolds numbers by following the divergence of a large number of orthogonal fluid trajectories. We find that the attractor dimension grows with the Reynolds number as Re$^{2.35}$ with this exponent being larger than predicted by either dimensional arguments or intermittency models. The distribution of Lyapunov exponents is found to be finite around $\lambda \approx 0$ contrary to a possible divergence suggested by Ruelle. The relevance of the Kolmogorov-Sinai entropy and Lyapunov spectra in comparing complex physical systems is discussed.