Paths to caustic formation in turbulent aerosols

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, characterized 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.

Automated summary

In the dynamics of small, heavy identical particles in turbulence, the formation of singularities known as caustics leads to significant fluctuations in spatial particle-number density and collision velocities. While caustic formation for particles with large inertia is akin to Kramers escape, for particles with small inertia, caustics tend to form near trajectories with specific histories of fluid-velocity gradients characterized by low vorticity and violent strain surpassing a certain threshold. A theory is developed to explain these findings in terms of an optimal path to caustic formation in the small inertia limit.