Lyapunov exponents of inertial particles in isotropic turbulence

The Lyapunov exponents of inertial particles in isotropic turbulence are calculated using direct numerical simulation (DNS), filtered DNS and large-eddy simulation (LES). Here, filter operators are taken as Eulerian space filter and Lagrangian time filter. The Lyapunov exponents obtained are qualitatively consistent but their magnitudes are different: the Lyapunov exponents from DNS are largest and the ones from LES are smallest while the ones from filter DNS are in between. The comparisons imply that the filters could reduce both stretching and compression in turbulent flows. Furthermore, the Lagrangian time filter allows the filtered trajectories to share the similar statistics of true particle trajectories in turbulent flows.