Inertial-particle dynamics in turbulent flows: caustics, concentration   fluctuations, and random uncorrelated motion
  We discuss the relation between three recent approaches of describing the dynamics and the spatial distribution of particles suspended in turbulent flows: phase-space singularities in the inertial particle dynamics (caustics), 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 discuss implications for random uncorrelated motion. Our results are supported by results of direct numerical simulations of inertial particles in model flows. 
K. Gustavsson, E. Meneguz, M. Reeks, and B. Mehlig
physics.flu-dyn