Inertial-particle dynamics in turbulent flows: caustics, concentration fluctuations and random uncorrelated motion

We have performed numerical simulations of inertial particles in random model flows in the white-noise limit (at zero Kubo number, Ku = 0) and at finite Kubo numbers. Our results for the moments of relative inertial-particle velocities are in good agreement with recent theoretical results (Gustavsson and Mehlig 2011a) based on the formation of phase-space singularities in the inertial-particle dynamics (caustics). We discuss the relation between three recent approaches describing the dynamics and spatial distribution of inertial particles suspended in turbulent flows: caustic formation, real-space singularities of the deformation tensor and random uncorrelated motion. We discuss how the phase-and real-space singularities are related. Their formation is well understood in terms of a local theory. We summarise the implications for random uncorrelated motion.