Group cohesion and passive dynamics of a pair of inertial swimmers with three-dimensional hydrodynamic interactions

When swimming animals form cohesive groups, they can reap several benefits. Our understanding of collective animal motion has traditionally been driven by models based on phenomenological behavioral rules, but more recent work has highlighted the critical importance of hydrodynamic interactions among a group of inertial swimmers. To study how hydrodynamic interactions affect group cohesion, we develop a three-dimensional, inviscid, far-field model of a swimmer. In a group of two model swimmers, we observe several dynamical phases, including following, divergence, collision, and cohesion. Our results illustrate when cohesive groups can passively form through hydrodynamic interactions alone, and when other action is needed to maintain cohesion. We find that misalignment between swimmers makes passive cohesion less likely; nevertheless, it is possible for a cohesive group to form through passive hydrodynamic interactions alone. We also find that the geometry of swimmers critically affects the group dynamics due to its role in how swimmers sample the velocity gradient of the flow.