We study low Reynolds number turbulence in a suspension of polar, extensile, self-propelled inertial swimmers. We review the bend and splay mechanisms that destabilize an ordered flock. The suspension is always unstable to bend perturbations. Using a minimal 1D model, we show that the splay-stable to splay-unstable transition occurs via a supercritical Hopf bifurcation. We perform high-resolution numerical simulations in 2D to study the varieties of turbulence present in this system transitioning from defect turbulence to concentration-wave turbulence depending on a single nondimensional number, denoting the ratio of the splay-concentration wavespeed to the swimmer motility.

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• Collective behavior
• Hydrodynamic instabilities
• Low Reynolds number flows
• Nonlinear dynamics in fluids
• Self-organized systems
• Stokesian dynamics
• Turbulence
• Living matter & active matter
• Microswimmers
• Self-propelled particles