Caustics in turbulent aerosols form along the Vieillefosse line at weak particle inertia

Abstract

Caustic singularities of the spatial distribution of particles in turbulent aerosols enhance collision rates and accelerate coagulation. Here we investigate how and where caustics form at weak particle inertia, by analysing a three-dimensional Gaussian statistical model for turbulent aerosols in the persistent limit, where the flow varies slowly compared with the particle relaxation time. In this case, correlations between particle- and fluid-velocity gradients are strong, and caustics are induced by large, strain-dominated excursions of the fluid-velocity gradients. These excursions must cross a characteristic threshold in the plane spanned by the invariants $Q$ and $R$ of the fluid-velocity gradients. Our method predicts that the most likely way to reach this threshold is by a unique ``optimal fluctuation'' that propagates along the Vieillefosse line, $27R^2/4+Q^3=0$. We determine the shape of the optimal fluctuation as a function of time and show that it is dominant in numerical statistical-model simulations even for moderate particle inertia.

12 pages, 3 figures

References in corpus (7)

• The large deviation approach to statistical mechanics
• Lagrangian dynamics and statistical geometric structure of turbulence
• Sling effect in collisions of water droplets in turbulent clouds
• Stokes trapping and planet formation
• Paths to caustic formation in turbulent aerosols
• Rate of formation of caustics in heavy particles advected by turbulence
• Negative autocorrelations of disorder strongly suppress thermally activated particle motion in short-correlated quenched Gaussian disorder potentials

Cited by in corpus (6)

• Statistical models for the dynamics of heavy particles in turbulence
• Quantitative prediction of sling events in turbulence at high Reynolds numbers
• Caustic formation in a non-Gaussian model for turbulent aerosols
• Fluctuation corrections to Lifshitz tails in disordered systems
• Dissecting inertial clustering and sling dynamics in high-Reynolds number particle-laden turbulence
• Caustics of finitely dense inertial particles