Intermittent fluctuations determine the nature of chaos in turbulence

TL;DR

This paper investigates how intermittent fluctuations influence chaos in turbulence, revealing a specific Reynolds number dependence of the Lyapunov exponent that deviates from classical predictions.

Contribution

It introduces a novel approach using decorrelators to analyze the interplay of dissipation and nonlinearity in turbulence, providing a precise measurement of the Re dependence of chaos.

Findings

Lyapunov exponent scales as Re^{0.59±0.04}

Departure from classical Re^{0.5} scaling due to intermittency

Results confirmed with a local turbulence model

Abstract

We adapt recent ideas for many-body chaos in nonlinear, Hamiltonian fluids [Murugan \textit{et al.}, Phys. Rev. Lett. 127, 124501 (2021)] to revisit the question of the Reynolds number Re dependence of the Lyapunov exponent $\lambda\propto{\rm Re}^\alpha$ in fully developed turbulence. The use of such decorrelators allow us to investigate the interplay of the competing effects of viscous dissipation and nonlinearity. We obtain a precise value of $\alpha = 0.59 \pm 0.04$ and show that departure from the Kolmogorov mean field result $\lambda \propto \sqrt{{\rm Re}}$ is a consequence of the intermittent fluctuations in the velocity-gradient tensor. The robustness of our results are further confirmed in a local, dynamical systems model for turbulence.