Paths to caustic formation in turbulent aerosols

The dynamics of identical, small, and heavy particles in a turbulent flow has singularities, so-called caustics. At a caustic, local particle neighbourhoods collapse as the phase-space manifold folds over configuration space and particle-velocity gradients diverge. The formation of caustics has been studied in detail in the white-noise limit where caustic formation is essentially Kramers' escape. A different picture is that of the sling effect, where caustics form as the inertial particles are expelled from vortices in the turbulent flow. Here we reconcile these two distinct perspectives by computing an optimal escape path for the matrix of particle-velocity gradients in a persistent-flow model that accounts for persistent vortices in the flow. Whether caustics form by Kramers' escape or according to the sling effect depends on the degree of particle inertia. We compare our predictions with statistical-model simulations, and with results based on direct numerical simulations of two-dimensional turbulence.