Multi-scale geometrical Lagrangian statistics: Extensions and applications to particle-laden turbulent flows

We present multi-scale statistics of particle trajectories in isotropic turbulence and compare the behavior of fluid and inertial particles. The directional change of inertial particles is quantified by considering the curvature angle for different time increments. Distinct scaling behaviors of the mean angle are observed for short, intermediate and long time lags. We also introduce the scale-dependent torsion angle, which quantifies the directional change of particles moving out of a reference plane. The influence of the Stokes number on the mean angles and on the probability distributions are analyzed. Finally, we assess the impact of LES and particle SGS modeling on these statistics