Investigation of the dispersion of heavy-particle pairs and Richardson’s law using kinematic simulation

Abstract

In this paper we investigate the dispersion of heavy-particle pairs (particles with inertia in a gravity field). We vary the particles' inertia when there is no gravity, and the particles' drift at constant inertia. We use kinematic simulation (KS) for which large values of the Reynolds number can be achieved. We investigate the pair diffusivity to discuss Richardson's law, and the locality-in-scale hypothesis that underlies that law, for different particle drifts and Stokes numbers. The effect of inertia and gravity on Richardson's law and the autocorrelation in time of the pair's separation are studied for an inertial scale ratio of 1000 and different initial separations delta0 . We extend results from F. Nicolleau and J. C. Vassilicos, Phys. Rev. Lett. 90, 024503 (2003) to three-dimensional (3D) KS and the diffusivity-based analysis of F. Nicolleau and G. Yu, Phys. Fluids 16, 2309 (2004) to particles with inertia and gravity. We find that inertia impedes the locality-in-scale hypothesis whereas gravity improves it. However, the overall effect of gravity and inertia is to decrease the pair's diffusivity in the inertial range.