Flow-coupled swimmers self-organize into energetically cooperative or greedy spatial patterns

Schooling fish interact, in addition to socially, physically through the fluid medium. Cooperative versus greedy group dynamics are often associated with social interactions, whereas flow interactions are thought to enable individuals to derive energetic benefits when swimming in groups. Here, using fluid-structure interactions models, we corroborate previous findings that flapping swimmers self-organize into stable and energy-efficient formations with only flow-interaction. Furthermore, in these stable formations, the separation distance between pairs of swimmers and the difference in flapping phase follows a universal linear relationship. Importantly, we demonstrate in larger groups that flow interactions are sufficient create versatile spatial patterns, ranging from cooperative “phalanx" patterns that favor egalitarian distribution of energy savings among group members to greedy “inline" patterns where few members get maximal benefit, leaving trailing swimmers with diminished opportunities for maintaining group coherence and gaining energetic advantage. These findings emphasize the role of flow physics in the emergence of cooperative and competitive group dynamics and hint at an intriguing prospect that, unless challenged to cooperate, fish dynamically position themselves within the school to compete over energetically favorable positions.