Why Do Fish Swim in Circles? A Nonlinear Dynamical Perspective

The author recently visited the Monterey Bay Aquarium and observed that, in large circular tanks, the fish spontaneously swam collectively in a circular pattern. We present a minimal continuum theory that explains the spontaneous emergence of global rotational motion in confined fish schools. Starting from symmetry-based hydrodynamic equations for active matter, we show that confinement and nonlinear saturation generically give rise to a symmetry-breaking instability, driving a transition from a non-rotating disordered state to stable clockwise or counterclockwise rotating states. Our results demonstrate that rotational collective motion is a universal feature of confined active systems, provided that the fish-school density exceeds a critical threshold, and is largely independent of microscopic details.