# Chaotic properties of a turbulent isotropic fluid

## TL;DR

This paper investigates the chaotic behavior of turbulent isotropic fluids by measuring the Lyapunov exponent's dependence on Reynolds number through high-resolution numerical simulations, revealing scale-independent divergence growth.

## Contribution

It establishes a quantitative relationship between the Lyapunov exponent and Reynolds number in turbulent flows using direct numerical simulations.

## Key findings

- Lyapunov exponent scales as Re^{0.53}
- Trajectory divergence grows uniformly across scales after transient
- Linear divergence rate depends on energy forcing rate

## Abstract

By tracking the divergence of two initially close trajectories in phase space in an Eulerian approach to forced turbulence, the relation between the maximal Lyapunov exponent $\lambda$, and the Reynolds number $Re$ is measured using direct numerical simulations, performed on up to $2048^3$ collocation points. The Lyapunov exponent is found to solely depend on the Reynolds number with $\lambda \propto Re^{0.53}$ and that after a transient period the divergence of trajectories grows at the same rate at all scales. Finally a linear divergence is seen that is dependent on the energy forcing rate. Links are made with other chaotic systems.