Spatial Organization and Cohesion of Large Collectives of Inertial Swimmers

Fish are known to arrange in formations that endow collective benefits. A key aspect of this is to maintain a cohesive group, which raises the question: are such groups stable? Using a three-dimensional far-field model of freely moving inertial swimmers, we examine whether passive hydrodynamic interactions alone can generate such cohesion. We study groups of various initial structures with O(10⁴) individuals. Spherical groups of swimmers maintain overall shape despite a small fraction of swimmers diverging. For three-dimensional diamond lattices of swimmers, the outer shell of swimmers diverges from an inner core that remains intact for extended durations. These findings suggest that maintaining cohesion in large groups may require controlling only select elements---either the few divergent swimmers in disordered groups or the outer shell in ordered configurations---rather than managing each individual within the school.