Fish schools in a vertical diamond formation: Effect of vertical spacing on hydrodynamic interactions

Fish schooling is believed to provide benefits by allowing individuals to leverage vortices generated by nearby fish, thereby improving their performance. While prior works have characterized horizontal planar formations of fish, our comprehensive analysis of the hydrodynamics in the vertical diamond formation reveals significant interactions among vertically arranged fish. In the densest vertical diamond formation, fin-fin, body-body, wake-body, and wake-fin interactions enhance force generation and propulsive efficiency for each individual in the school. The findings of this study could guide school configurations that enhance the performance of fish-inspired bio-robotic swarms.