Caustic formation in a non-Gaussian model for turbulent aerosols

Abstract

Caustics in the dynamics of heavy particles in turbulence accelerate particle collisions. The rate $\mathcal{J}$ at which these singularities form depends sensitively on the Stokes number St, the non-dimensional inertia parameter. Exact results for this sensitive dependence have been obtained using Gaussian statistical models for turbulent aerosols. However, direct numerical simulations of heavy particles in turbulence yield much larger caustic-formation rates than predicted by the Gaussian theory. In order to understand possible mechanisms explaining this difference, we analyse a non-Gaussian statistical model for caustic formation in the limit of small St. We show that at small St, $\mathcal{J}$ depends sensitively on the tails of the distribution of Lagrangian fluid-velocity gradients. This explains why different authors obtained different St-dependencies of $\mathcal{J}$ in numerical-simulation studies. The most-likely gradient fluctuation that induces caustics at small St, by contrast, is the same in the non-Gaussian and Gaussian models. Direct-numerical simulation results for particles in turbulence show that the optimal fluctuation is similar, but not identical, to that obtained by the model calculations.

12 pages, 3 figures, 1 table

References in corpus (8)

• The large deviation approach to statistical mechanics
• Sling effect in collisions of water droplets in turbulent clouds
• Lyapunov exponents of heavy particles in turbulence
• Statistical models for the dynamics of heavy particles in turbulence
• Distribution of velocity gradients and rate of caustic formation in turbulent aerosols at finite Kubo numbers
• Quantitative prediction of sling events in turbulence at high Reynolds numbers
• Caustics in turbulent aerosols form along the Vieillefosse line at weak particle inertia
• Rate of formation of caustics in heavy particles advected by turbulence

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