Eur. Phys. J. Special Topics 226, 2079-2088 (2017)
https://doi.org/10.1140/epjst/e2017-70035-3

Regular Article

A map for heavy inertial particles in fluid flows

¹ CMCC, Universidade Federal do ABC, Santo André, SP, Brazil
² Instituto de Física, Universidade de São Paulo, São Paulo, SP, Brazil

^a e-mail: rafael.vilela@ufabc.edu.br

Received: 31 January 2017
Revised: 18 March 2017
Published online: 21 June 2017

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.