Distribution of relative velocities in turbulent aerosols

Abstract

We compute the distribution of relative velocities for a one-dimensional model of heavy particles suspended in a turbulent flow, quantifying the caustic contribution to the moments of relative velocities. The same principles determine the corresponding caustic contribution in $d$ spatial dimensions. The distribution of relative velocities Δv at small separations R acquires the universal form ρ(Δv,R) ~ R^{d-1}|Δv|^{D_2-2d} for large (but not too large) values of |Δv|. Here D_2 is the phase-space correlation dimension. Our conclusions are in excellent agreement with numerical simulations of particles suspended in a randomly mixing flow in two dimensions, and in quantitative agreement with published data on direct numerical simulations of particles in turbulent flows.

Revised version, as published. 4 pages, 2 figures