Chaos and predictability of homogeneous-isotropic turbulence

TL;DR

This paper investigates the chaotic behavior and predictability of homogeneous-isotropic turbulence using high-resolution simulations, revealing how Lyapunov exponents scale with Reynolds number and linking chaos to turbulence predictability.

Contribution

It provides new insights into the scaling of Lyapunov exponents with Reynolds number and connects turbulence chaos with predictability through a finite-size Lyapunov exponent.

Findings

Lyapunov exponent grows with Reynolds number with an anomalous scaling

Error transfer to larger scales creates an inverse cascade in perturbations

Classical turbulence closure models are confirmed in the inertial range

Abstract

We study the chaoticity and the predictability of a turbulent flow on the basis of high-resolution direct numerical simulations at different Reynolds numbers. We find that the Lyapunov exponent of turbulence, which measures the exponential separation of two initially close solution of the Navier-Stokes equations, grows with the Reynolds number of the flow, with an anomalous scaling exponent, larger than the one obtained on dimensional grounds. For large perturbations, the error is transferred to larger, slower scales where it grows algebraically generating an "inverse cascade" of perturbations in the inertial range. In this regime our simulations confirm the classical predictions based on closure models of turbulence. We show how to link chaoticity and predictability of a turbulent flow in terms of a finite size extension of the Lyapunov exponent.