Experimental evidence of stable schooling formations of unconstrained swimmers

Water channel experiments are presented for a pair of NACA 0012 pitching hydrofoils of aspect ratio 3. One foil is fixed, while the other is completely free to move in the horizontal plane. A side-by-side arrangement is found to be two-dimensionally stable to perturbations away from this equilibrium arrangement, and arises naturally from purely hydrodynamic forces. This provides the first experimental evidence of two-dimensional stability and supports the Lighthill conjecture, which is that hydrodynamics forces may be sculpting the structure of fish schools. This minimal schooling arrangement also increases the swimming speed by 20% compared to an isolated swimmer.  These findings are supported by force measurements, trajectory measurements, PIV measurements, and free-swimming simulations of two-dimensional pitching foils. Moreover, previously discovered one-dimensionally stable equilibria driven by wake vortex interactions are shown to be, in fact, two-dimensionally unstable, at least for an out-of-phase synchronization. These newfound schooling performance and stability characteristics suggest that fluid-mediated equilibria may play a role in the control strategies of schooling fish and fish-inspired robots.