Cooperative propulsion in multi-scale V-shaped fish schools

Multi-scale biomimetic fish propulsion CFD models were established to investigate how formation arrangement affects propulsive efficiency and energy transfer. Inspired by avian V-shaped formations, several representative configurations were designed, and dynamic mesh techniques were used to simulate upstream swimming under incoming-flow conditions. By varying individual arrangement, the analysis was extended from single-fish to collective propulsion, examining how hydrodynamic interactions affect vorticity, force characteristics, power consumption, and efficiency. Asymmetric (G3) and symmetric formations (G4) were compared in terms of pressure distribution, velocity field, and vortex structures, while a larger symmetric formation (G5) was analyzed to assess school-size effects. Results show that the symmetric formation generates a stable energy-transfer pathway, improving overall propulsive efficiency by approximately 25% compared with the asymmetric formation. Increasing school size under symmetric conditions enhances the hydrodynamic advantages of symmetry but introduces additional energy.