A map for heavy inertial particles in fluid flows

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.

arXiv comment10 pages, 5 figures

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