Stochastic suspensions of heavy particles

TL;DR

This paper reviews recent advances in understanding the relative motion of inertial heavy particles in turbulent flows, introducing a time-dependent Stokes number and confirming predictions through simulations.

Contribution

It introduces a time-dependent Stokes number and uses perturbation methods to analyze inertial particle dispersion, providing new insights into their dynamics in simplified flow models.

Findings

Inertial particle dispersion asymptotically follows Richardson's diffusion.

Correlation dimension deficit varies linearly with Stokes number.

Numerical simulations confirm theoretical predictions.

Abstract

Turbulent suspensions of heavy particles in incompressible flows have gained much attention in recent years. A large amount of work focused on the impact that the inertia and the dissipative dynamics of the particles have on their dynamical and statistical properties. Substantial progress followed from the study of suspensions in model flows which, although much simpler, reproduce most of the important mechanisms observed in real turbulence. This paper presents recent developments made on the relative motion of a pair of particles suspended in time-uncorrelated and spatially self-similar Gaussian flows. This review is complemented by new results. By introducing a time-dependent Stokes number, it is demonstrated that inertial particle relative dispersion recovers asymptotically Richardson's diffusion associated to simple tracers. A perturbative (homogeneization) technique is used in the small-Stokes-number asymptotics and leads to interpreting first-order corrections to tracer dynamics in terms of an effective drift. This expansion implies that the correlation dimension deficit behaves linearly as a function of the Stokes number. The validity and the accuracy of this prediction is confirmed by numerical simulations.