  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.
