Distribution of relative velocities in turbulent aerosols

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 Delta v at small separations R acquires the universal form rho(Delta v, R) similar to R-d (1)|Delta v|(D)(2) (2d) for large (but not too large) values of |Delta v|. 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.