The effect of phase difference on the group hydrodynamic performance of three typical formations

The effects of group formation and phase difference on the hydrodynamic performance and vortex structure of manta rays during group swimming are investigated, where three types of formation are chosen: tandem, positive and inverted triangle, and phases (φ) are chosen as 0 and π. Morphological models and kinematic equations of manta rays were formulated from biological data and numerically simulated using the immersed boundary method. The results show that in a tandem formation, the transformation of collisional interference to absorptive fusion between individual vortex structures in the cluster can be achieved by adjusting the phase difference, realizing the system's propulsive performance gain at the full platoon spacing. In the triangular formation, anti-phase cluster swimming can effectively improve the symmetry of the far-field vortex structure of the team leader manta ray as well as the vortex structures on both sides, thus effectively improving the overall propulsive performance. This study provides new insights into the coupled roles of formation and phase in group swimming and the mechanisms of force enhancement.