  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 violent strains 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.
