Paths to caustic formation in turbulent aerosols

TL;DR

This paper investigates the formation of caustics in turbulent aerosols, revealing that at small particle inertia, caustics form near trajectories with specific fluid-velocity gradient histories, differing from large inertia cases.

Contribution

The study introduces a new theory explaining caustic formation at small particle inertia through optimal paths involving specific fluid-velocity gradient conditions.

Findings

Caustics form near trajectories with low vorticity and high strain.

Caustic formation at small inertia differs from the large inertia case.

A theoretical framework based on optimal paths explains the formation process.

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.