Inertia drives concentration-wave turbulence in swimmer suspensions

We discover an instability mechanism in suspensions of self-propelled particles that does not involve active stress. Instead, it is driven by a subtle interplay of inertia, swimmer motility, and concentration fluctuations, through a crucial time lag between the velocity and the concentration field. The resulting time-persistent state seen in our high-resolution numerical simulations consists of self-sustained waves of concentration and orientation, transiting from regular oscillations to wave turbulence. We analyze the statistical features of this active turbulence, including an intriguing connection to the Batchelor spectrum of passive scalars.