Inertial-particle dynamics in turbulent flows: caustics, concentration fluctuations, and random uncorrelated motion

TL;DR

This paper explores the complex behavior of inertial particles in turbulent flows, linking phase-space singularities, real-space deformations, and uncorrelated motion, supported by numerical simulations.

Contribution

It provides a unified understanding of different approaches to inertial particle dynamics and their interrelations in turbulent flows.

Findings

Phase- and real-space singularities are interconnected.

Formation of singularities is explained by a local theory.

Numerical simulations support the theoretical insights.

Abstract

We discuss the relation between three recent approaches of describing the dynamics and the spatial distribution of particles suspended in turbulent flows: phase-space singularities in the inertial particle dynamics (caustics), real-space singularities of the deformation tensor, and random uncorrelated motion. We discuss how the phase- and real-space singularities are related. Their formation is well understood in terms of a local theory. We discuss implications for random uncorrelated motion. Our results are supported by results of direct numerical simulations of inertial particles in model flows.