Statistical modeling of preferential concentration of heavy particles in turbulence

Preferential concentration in turbulent flows is a process that causes heavy particles to cluster in regions of high strain (in-between high vorticity regions), with specifics depending on their stopping time or Stokes number. This process is thought to be of importance in various problems including cloud droplet formation, aerosol transport in the atmosphere, sprays, and the formation of asteroid and comets in protoplanetary nebulae. Here, we present the statistical determination of particle multiplier distributions from large numerical simulations of particle-laden isotopic turbulence, and a cascade model for modeling turbulent concentration at scales and Reynolds numbers not accessible by numerical simulations. We find that the multiplier distributions are scale dependent at scales within a decade or so of the inertial scale, and have properties that differ from widely used "beta-function" models.