title: 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.
authors.affiliation: Department of Physics, Gothenburg University, S-41296 Gothenburg, Sweden.
authors.forename: K
authors.initials: K
authors.lastname: Gustavsson
authors.forename: B
authors.initials: B
authors.lastname: Mehlig