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Fish schools are ubiquitous in marine life. Although flow interactions are thought to be beneficial for schooling, their exact effects on the speed, energetics and stability of the group remain elusive. Recent numerical simulations and experimental models suggest that flow interactions stabilize in-tandem formations of flapping foils. Here, we employ a minimal vortex sheet model that captures salient features of the flow interactions among flapping swimmers, and we study the free swimming of a pair of in-line swimmers driven with identical heaving or pitching motions. We find that, independent of the flapping mode, heaving or pitching, the follower passively stabilizes at discrete locations in the wake of the leader, consistent with the heaving foil experiments, but pitching swimmers exhibit tighter and more cohesive formations. Further, in comparison to swimming alone, pitching motions increase the energetic efficiency of the group while heaving motions result in a slight increase in the swimming speed. A deeper analysis of the wake of a single swimmer sheds light on the hydrodynamic mechanisms underlying pairwise formations. These results recapitulate that flow interactions provide a passive mechanism that promotes school cohesion, and afford novel insights into the role of the flapping mode in controlling the emergent properties of the school.
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Flow interactions between uncoordinated flapping swimmers give rise to group cohesion
Significance Fish and birds moving in groups are thought to benefit from hydrodynamic or aerodynamic interactions between individuals. To better understand these effects, we devise a robotic “school” of flapping swimmers whose formations and motions come about from flow interactions. Surprisingly, we find that the flows naturally generated during swimming can also prevent collisions and separations, allowing even uncoordinated individuals with different flapping motions to travel together. Other benefits include freeloading by a “lazy” follower who keeps up with a faster-flapping leader by surfing on its wake. More generally, our study provides complete maps linking flapping motions to group locomotion, which is needed to test whether flow interactions are also exploited by animals.
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- Award ID(s):
- 1847955
- PAR ID:
- 10515491
- Publisher / Repository:
- Proceedings of the National Academy of Sciences
- Date Published:
- Journal Name:
- Proceedings of the National Academy of Sciences
- Volume:
- 116
- Issue:
- 7
- ISSN:
- 0027-8424
- Page Range / eLocation ID:
- 2419 to 2424
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1073/pnas.1816098116
