Turbulent clustering of initially well-mixed buoyant particles on a free-surface by Lagrangian coherent structures

Abstract

Particles that float on the surface of a 3D incompressible turbulent flow are exposed to non-divergence-free properties that result in clustering and unmixing, a reversal of how turbulence normally acts to mix and dilute scalars. Particle clustering is dominated by Lagrangian processes that depend on the time history of the flow; this suggests that Lagrangian coherent structures (LCS) might serve as templates for cluster formation. In this study, non-divergence-free clustering is examined both experimentally and numerically to elucidate the role of LCS in the formation of particle clusters and voids. Experiments are performed on the free-surface of a water-filled tank with turbulence driven by the random pulsing of centrifugal pumps on the tank bottom. Clustering is quantified by imaging fluorescent, buoyant particles that are placed in an initially random distribution on the free-surface. Within clusters, concentrations are observed to increase by an order of magnitude, with the likelihood of observing enhanced concentrations increasing by two orders of magnitude. LCS, obtained from velocity fields utilizing particle image velocimetry, are shown to act as templates for cluster formation. In addition, LCS are shown to possess a dilatation component in non-divergence-free flows that is responsible for unmixing. Numerically, a non-divergence-free chaotic model consisting of interacting Taylor vortices is utilized to investigate processes responsible for cluster formation seen in the experiments. The model results support the experimental finding that LCS act as templates for particle clusters, with scalar unmixing driven by the dilatation component.