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Fish schools are ubiquitous in marine life. Although flow interactions arethought to be beneficial for schooling, their exact effects on the speed,energetics, and stability of the group remain elusive. Recent experimentssuggest that flow interactions stabilize in-tandem formations of heaving foils.Here, we propose a minimal approach based on the vortex sheet model thatcaptures salient features of the flow interactions among flapping swimmers, andwe study the free swimming of a pair of in-line swimmers driven with identicalheaving or pitching motions. We find that, independent of the flapping mode,the follower passively stabilizes at discrete locations in the wake of theleader, consistent with the heaving foil experiments, but pitching swimmersexhibit tighter and more cohesive formations. Further, in comparison toswimming alone, pitching motions increase the energetic efficiency of the groupwhile heaving motions result in a slight increase in the swimming speed. Theseresults recapitulate that flow interactions provide a passive mechanism thatpromotes school cohesion, and provide novel insight into the role of theflapping mode in controlling the emergent properties of the school.

School cohesion, speed, and efficiency are modulated by the swimmers flapping motion