Clustering of randomly advected low-inertia particles: a solvable model.

Measurements and simulations indicate that the particle-pair radial distribution function in isotropic turbulence is a power law in a range of length scales below the Kolmogorov scale for Stokes number St<<1. In this range, the exponent is proportional to St1St2 for unlike particles (1 and 2) in a bidispersion, hence St2 for a monodispersion. Here, this result is derived from a model of particle response to random advection. The analysis generalizes a geometrical interpretation of clustering to polydispersions and suggests an economical Monte Carlo simulation method.