Motile particles without inertia form caustics in vortical flows

When heavy particles in turbulent flow are centrifuged out of vortices they cluster to form singular features in the number-density called caustics [Physics of Fluids 27, 033305 (2015)]. We show that self-propelled particles (SPPs) with no 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 suspended in turbulent flow and find pronounced caustics in straining regions, for intermediate values of a non-dimensional self-propulsion velocity. The occurrence of caustics limits the applicability of continuum descriptions in active suspensions, and opens the possibility that propagating singularities might be the building block of such dynamics.