Chaotic properties of a turbulent isotropic fluid

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.