Intermittent fluctuations determine the nature of chaos in turbulence

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 $\lambda \propto {\mathrm{Re}}^{\alpha }$ 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 $\lambda \propto \sqrt{\mathrm{Re}}$ 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.