Active Caustics

When heavy particles in turbulent flow are centrifuged out of vortices they cluster to form singular features in the number density [Phys Fluids 27, 033305 (2015)], termed caustics for their resemblance to focal surfaces in optics. We show here that self-propelled particles (SPPs) with Reynolds number $Re= 0$ and thus no mechanical inertia display similar behaviour, thanks to the persistence of their motion in the direction of their intrinsic orientation. Using singular perturbation analysis and numerical studies we establish that SPPs form caustics at a critical distance from the origin of a point vortex. To capture the dynamics in a generic vortical flow we study SPPs advected by Navier-Stokes turbulence and find pronounced caustics in straining regions, for intermediate values of a non-dimensional self-propulsion velocity. Our work offers a route to singularly high local concentrations in a macroscopically dilute suspension of zero-Re 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.