Statistical models for spatial patterns of inertial particles in turbulence

K. Gustavsson, B. Mehlig

Published 2014-12-14Version 1

The dynamics of particles suspended in turbulent flows is of fundamental importance for a wide range of questions in astrophysics, cloud physics, oceanography, and in technology. Laboratory experiments and direct numerical simulations have demonstrated that heavy particles respond in intricate ways to turbulent fluctuations of the carrying fluid: independent particles may cluster together and form spatial patterns even though the fluid is incompressible, and the relative speeds of nearby particles may fluctuate strongly. Both phenomena depend sensitively on the parameters of the system, affect collision rates and outcomes, and thus the long-term fate of the system. This is a hard problem to describe theoretically: the turbulence determines the particle paths, but at the same time the turbulent fluctuations encountered by a particle depend sensitively upon its path through the medium. In recent years it has become clear that important aspects of the particle dynamics in turbulence can be understood in terms of statistical models. In this review we summarise how such statistical-model calculations have led to a detailed understanding of the factors that determine inertial-particle dynamics and exhibit the mechanisms at work. We concentrate on the spatial clustering of inertial particles, a surprising and important phenomenon that has been intensively investigated in the last decade.