Chaotic properties of a turbulent isotropic fluid

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 λ and the Reynolds number Re is measured using direct numerical simulations, performed on up to 20483 collocation points. The Lyapunov exponent is found to solely depend on the Reynolds number with λ∝Re0.53 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.