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 v at small separations R acquires the universal form ( v,R) ~ Rd-1| v|D2-2d for large (but not too large) values of | v|. Here D2 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.