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 spatial dimensions. The distribution of relative velocities \Delta v at small separations R acquires the universal form \rho(\Delta v,R) ~ 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.
Keywords
Cite
@article{arxiv.1012.1789,
title = {Distribution of relative velocities in turbulent aerosols},
author = {K. Gustavsson and B. Mehlig},
journal= {arXiv preprint arXiv:1012.1789},
year = {2012}
}
Comments
Revised version, as published. 4 pages, 2 figures