Paths to caustic formation in turbulent aerosols

Abstract

The dynamics of small, yet heavy, identical particles in turbulence exhibits singularities, called caustics, that lead to large fluctuations in the spatial particle-number density, and in collision velocities. For large particle, inertia the fluid velocity at the particle position is essentially a white-noise signal and caustic formation is analogous to Kramers escape. Here we show that caustic formation at small particle inertia is different. Caustics tend to form in the vicinity of particle trajectories that experience a specific history of fluid-velocity gradients, characterised by low vorticity and a violent strain exceeding a large threshold. We develop a theory that explains our findings in terms of an optimal path to caustic formation that is approached in the small inertia limit.

arXiv comment6 pages, 3 figures, supplementary material

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Cited by in corpus (8)

• Statistical models for the dynamics of heavy particles in turbulence
• Caustics in turbulent aerosols form along the Vieillefosse line at weak particle inertia
• Quantitative prediction of sling events in turbulence at high Reynolds numbers
• Rate of formation of caustics in heavy particles advected by turbulence
• Caustic formation in a non-Gaussian model for turbulent aerosols
• Dissecting inertial clustering and sling dynamics in high-Reynolds number particle-laden turbulence
• Active Caustics
• Caustics of finitely dense inertial particles