A map for heavy inertial particles in fluid flows

TL;DR

This paper introduces a map that captures key behaviors of heavy inertial particles in fluid flows, including phase space contraction, slow-manifold dynamics, fold caustics, and attractor dimension variations, enhancing understanding of particle-fluid interactions.

Contribution

The paper presents a novel map model that qualitatively reproduces fundamental properties of heavy particle dynamics in fluid flows, providing insights into complex particle behaviors.

Findings

Reproduces volume contraction in phase space

Models fold caustics in velocity fields

Identifies a minimum in attractor dimension as a function of parameter s

Abstract

We introduce a map which reproduces qualitatively many fundamental properties of the dynamics of heavy particles in fluid flows. These include a uniform rate of decrease of volume in phase space, a slow-manifold effective dynamics when the single parameter $s$ (analogous of the Stokes number) approaches zero, the possibility of fold caustics in the "velocity field", and a minimum, as a function of $s$, of the Lyapunov (Kaplan-Yorke) dimension of the attractor where particles accumulate.