Hydrodynamic Efficiency and Wake Interactions in Fish School Swimming

The mechanism by which fish enhance hydrodynamic performance through collective swimming is a research hotspot in the field of underwater bionic robots. This study employs the Immersed Boundary-Lattice Boltzmann Method (IB-LBM) to conduct numerical simulations on a two-dimensional, single-degree-of-freedom (1-DOF) autonomous propulsion bionic fish swarm. It systematically investigates the effects of swarm size and inter-individual spacing on swimming speed and cost of transport (CoT) under two typical configurations: series and parallel arrangements. Findings reveal that hydrodynamic benefits are highly dependent on the spatiotemporal evolution of flow field structures. In the series configuration, an optimal spacing range of 1.5 L to 2.0 L exists within the school, where the "wake capture" effect is pronounced. Trailing fish achieve a maximum speed increase of approximately 41.1% while significantly reducing energy consumption. However, as spacing increases to 2.5 L, the cooperative gain for front and middle-row individuals rapidly diminishes, and the lead fish even experiences significant performance loss. Uniquely, the trailing fish in the four-fish formation exhibits distinct flow field reorganization and performance recovery at the 4.5 L trailing position. In the parallel formation, the "channel effect" and "blocking effect" of the fluid dominate. The study identifies 0.4 L laterally as the critical instability spacing under the investigated kinematic regime, where strong destructive interference causes a sharp deterioration in individual swimming performance. Additionally, the parallel formation exhibits pronounced positional differentiation. Central individuals, constrained by dual lateral flow fields, experience restricted lateral wake expansion and accelerated energy dissipation, resulting in significantly weaker escape capabilities from low-speed conditions compared to marginal individuals. The vortex-dynamic mechanism revealed herein provides theoretical foundations for formation control in multi-fish biomimetic cooperative systems.