Active Caustics

Abstract: Heavy particles in vortical fluid flow cluster strongly, forming singular structures termed caustics for their resemblance to focal surfaces in optics. We show here that such extreme aggregation onto low-dimensional submanifolds can arise without inertia for self-propelled particles (SPPs). We establish that a singular perturbation is at the heart of caustic formation by SPPs around a single vortex, and our numerical studies of SPPs in two-dimensional Navier-Stokes turbulence shows intense caustics in the straining regions of the flow, peaking at intermediate levels of self-propulsion. Our work offers a route to singularly high local concentrations in a macroscopically dilute suspension of zero-Reynolds number swimmers, with potentially game-changing implications for communication and sexual reproduction. An intriguing open direction is whether the active turbulence of a suspension of swimming microbes could serve to generate caustics in its own concentration.