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Updated: Jun 14, 2026

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
Published on: February 22, 2018
Clustering criterion for inertial particles in two-dimensional time-periodic and three-dimensional steady flows
Themistoklis Sapsis1, George Haller
1Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Abstract:
We derive an analytic condition that predicts the exact location of inertial particle clustering in three-dimensional steady or two-dimensional time-periodic flows. The particles turn out to cluster on attracting inertial Lagrangian coherent structures that are smooth deformations of invariant tori. We illustrate our results on three-dimensional steady flows, including the Hill's spherical vortex and the Arnold-Beltrami-Childress flow, as well as on a two-dimensional time and space periodic flow that models a meandering jet in a channel.
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