Research on the swimming performance of two manta rays under staggered propulsion on the same frequency: When the follower is above the leader

To investigate the hydrodynamic performance of two manta rays swimming in groups under staggered formation, first, a computational model and motion equations of manta rays were established based on biological observations, and then numerical simulations were carried out based on immersed boundary method to simulate the group swimming of manta rays with the same vertical spacing but with a changing streamwise spacing. The results showed that when the streamwise spacing is small between the two manta rays, the hydrodynamic performance decreases dramatically compared to individual swimming. As the streamwise spacing increases, the hydrodynamic performance of the leader is always better than that of individual swimming, and the thrust enhancement is maximized to 10.984% and the efficiency enhancement is maximized to 3.369% when the spacing is 0.4BL. As the streamwise spacing increases, the hydrodynamic performance of the follower shows greater volatility, with a maximum thrust enhancement of 47.923% when the spacing is 0.4BL, and a maximum efficiency enhancement of 14.017% when the spacing is 0.5BL. The system's average thrust gain is maximized at 29.454% when the spacing is 0.4BL, and the system's average efficiency gain is maximized at 7.689% when the spacing is 0.5BL.