Energetic savings in fish schools using a staggered formation

It has long been hypothesized that fish can harness energy through hydrodynamic interactions when swimming collectively in schools. However, the dynamics and associated hydrodynamic interactions of the minimal school configuration—the staggered formation commonly observed between paired fish—remain quantitatively underexplored in live fish experiments. This knowledge gap hinders a comprehensive understanding of the flow physics underlying fish schooling. To address this, we conducted controlled live fish schooling experiments within a circular water channel with adjustable incoming flow speeds. High-speed cameras captured the locomotion kinematics, while individual fish positions and undulating movements were accurately tracked using a machine learning-based tool. Our statistical analysis revealed notable variability in spatial distances and synchronization patterns among fish pairs swimming in staggered formation. Approximately 66% of the observed staggered formations involved the following fish positioning themselves in close proximity to the leader, specifically maintaining a streamwise distance (S) less than 0.6 body length (BL) and a lateral distance (D) less than 0.5 BL—conditions favorable for strong constructive hydrodynamic interactions. Guided by insights from these biological experiments, we conducted high-fidelity three-dimensional simulations using an immersed-boundary-based direct numerical simulation (DNS) solver. The simulation results indicate that trailing fish achieve substantial drag reduction, up to 20%, by interacting strategically with tilted vortex rings shed by leading fish. Notably, this drag reduction effect remains stable irrespective of synchronization variations between fish pairs within the critical range of S < 0.6 BL. Furthermore, numerical findings highlight the trailing fish's ability to adjust their tail-beat phases, enhancing thrust production by up to 20% through effective extraction of energy from vortices generated by the leader.