Diffusion of heavy particles in a turbulent flow

Abstract

Simple expressions are derived for the far-field eddy diffusivity and particle velocity statistics of a cloud of heavy particles in isotropic turbulence, in terms of statistics of the fluid flow. The analysis leads to the following outcomes: (1) Using a linearised solution of the equation of motion for a heavy particle in a fluid and a kinematic analysis of dispersion, the particle diffusivity K P is expressed in terms of the time scale Tp of the fluid (not particle) velocity along the particle path. This yields the simple result K P /K F = T P /T F , where K F is the diffusivity and T F the Lagrangian time scale for passive fluid elements. (2) The time scale Tp is evaluated in terms of the particle-fluid relative speed V R , using two alternative hypotheses (elliptic and triangular) about the mixed space-time velocity covariance function in isotropic turbulence. Under both hypotheses, Tp depends explicitly on the mean of V R (the drift velocity) and implicitly on the variance of V R . (3) The theory is compared with two sets of observations, providing reasonable overall agreement and experimental support for the elliptic hypothesis. (4) The theory and observations together provide an estimate for the ratio of the fluid Lagrangian time scale to the Eulerian turbulent time scale.