Flow interactions stabilize flapping swimmers at positions that favor power saving

There is growing evidence that schooling fish benefit from flow interactions with their neighbors. Experiments with pairs of robotic flappers indicate that followers obtain hydrodynamic benefits by matching their tailbeat motion with the flow velocity induced by leader's wake, a strategy that freely-swimming goldfish were found to exhibit. However, it is not clear if fish actively seek this strategy or whether it is a passive outcome of the hydrodynamic interactions. Meanwhile, pairs of hydrofoils, positioned in tandem with no means of adjusting their motions, were shown to swim together cohesively due to interactions with the wake of the leader. Are the same hydrodynamic mechanisms at play in these distinct arrangements? To answer this question, we employed a vortex sheet model to capture the flow interactions among flapping swimmers, and we analyzed the free swimming of a pair of in-line and laterally-displaced flapping swimmers. We found that flow interactions stabilize formations of swimmers at positions that favor power saving for any flapping phase and lateral position of the follower. Our results suggest that fish do not need to actively match their tailbeat phase with the local vorticity to save energy and that passive hydrodynamics alone could create these energetically favorable formations.