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Active caustics

Rahul Chajwa1,2, C. Rajarshi2, Rama Govindarajan2, and Sriram Ramaswamy3,2

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Phys. Rev. Fluids 11, 033104 – Published 20 March, 2026

DOI: https://doi.org/10.1103/m3v2-bdvj

Abstract

Inertial particles (IPs) in vortical fluid flow cluster strongly, forming singular structures termed caustics for their resemblance to focal surfaces in optics. Here we show that such extreme aggregation onto low-dimensional submanifolds can arise without mechanical inertia for self-propelled particles (SPPs), through a formal correspondence between the dynamics of IPs and SPPs in a generic background flow. We establish that a singular perturbation underlies caustics formation by SPPs around a single vortex, and numerical studies of SPPs in two-dimensional Navier-Stokes turbulence reveal intense caustics in 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. Caustics generate burstlike encounters through large relative velocities between neighboring swimmers, with potentially significant 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.

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Phys. Rev. Fluids 11, 033104– Published 20 March, 2026
  • Received 17 March 2024
  • Accepted 11 February 2026
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