Hydrodynamic interaction and energy-saving mechanisms of two three-dimensional parallel swimmers with synchronous and asynchronous undulation

The hydrodynamic performance and wake structures of three-dimensional (3D) fish are distinct from those of two-dimensional (2D) models. To reveal the hydrodynamic interaction and energy-saving mechanism of 3D fish school, this study numerically simulated swimming of two 3D parallel fish, using a robust ghost cell method. The hydrodynamic benefits and wake structures were examined under different transverse spacings, Strouhal numbers, and phase differences. The results showed that the swimming efficiency at a narrow spacing was enhanced by 33.8% compared with the single-fish case. It can be further enhanced by 15.4% in the anti-phase undulation compared to the in-phase state. The critical spacing where the apparent hydrodynamic benefit occurs is wider than that obtained in 2D simulations because the vortex row induced by transverse velocity can obliquely approach that generated by the adjacent fish. The thrust enhancement can be attributed to the channeling effect in the general synchronous and asynchronous undulations. This channeling effect occurs in the wake centerline instead of in the gap between the two fish bodies in the 2D simulations. The wake is redirected downstream in the streamwise direction owing to the transverse obstruction, which strengthens the thrust. Additionally, vertical expansion with vorticity dissipation can be induced, compromising the channeling effect. Both the channeling effect and vertical expansion are more significant at narrower spacings and higher Strouhal numbers. Notably, the wall effect contributes to the thrust enhancement in the antiphase undulation. Also, the disorderly small-scale vortex contrails appearing in other phase states are not observed, further improving thrust.