Passive hydrodynamic interactions in minimal fish schools

It is a long-held perception that schooling swimming of fish can provide individuals in a group with additional hydrodynamic benefits. However how fish maintain a stable schooling formation, and the underlying interaction bases, are still unknown. This study aims to investigate effects of pure passive hydrodynamic interactions on schooling swimming and deal with whether fish can solely rely on the interactions to maintain a stable formation. The study is a pure numerical investigation based on a two-dimensional 3-DoF self-propelled model. Three two-fish formations, namely, tandem, side-by-side, and staggered formation, are investigated to explore the effects of the interactions. The study presents that the passive interactions do bring performance benefits to individuals, but swimmers cannot maintain the benefits for a long time when only relying on the pure passive interactions. The work also discusses different effects induced by the hydrodynamic interactions in some detail, including effects of deflection, wake, phase, attraction and repulsion. Essentially the hydrodynamic effects can be explained by considering time-varying pressure field. Due to the effects, a small disturbance or unbalanced moment may cause a large difference in the swimming directions of individuals in a group. The findings could offer some insights into understanding the schooling swimming mechanism.