Flow interactions between uncoordinated flapping swimmers give rise to group cohesion

Joel W. Newbolt, Jun Zhang, Leif Ristroph

Research output: Contribution to journalArticlepeer-review


Many species of fish and birds travel in groups, yet the role of fluid-mediated interactions in schools and flocks is not fully understood. Previous fluid-dynamical models of these collective behaviors assume that all individuals flap identically, whereas animal groups involve variations across members as well as active modifications of wing or fin motions. To study the roles of flapping kinematics and flow interactions, we design a minimal robotic “school” of two hydrofoils swimming in tandem. The flapping kinematics of each foil are independently prescribed and systematically varied, while the forward swimming motions are free and result from the fluid forces. Surprisingly, a pair of uncoordinated foils with dissimilar kinematics can swim together cohesively—without separating or colliding—due to the interaction of the follower with the wake left by the leader. For equal flapping frequencies, the follower experiences stable positions in the leader’s wake, with locations that can be controlled by flapping amplitude and phase. Further, a follower with lower flapping speed can defy expectation and keep up with the leader, whereas a faster-flapping follower can be buffered from collision and oscillate in the leader’s wake. We formulate a reduced-order model which produces remarkable agreement with all experimentally observed modes by relating the follower’s thrust to its flapping speed relative to the wake flow. These results show how flapping kinematics can be used to control locomotion within wakes, and that flow interactions provide a mechanism which promotes group cohesion.

Original languageEnglish (US)
Pages (from-to)2419-2424
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number7
StatePublished - Feb 12 2019


  • Bird flocking
  • Collective locomotion
  • Fish schooling
  • Flapping flight
  • Hydrodynamic interaction

ASJC Scopus subject areas

  • General


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