Hydrodynamic force induced by vortex–body interactions in orderly formations of flapping tandem flexible plates

Abstract

The mechanism behind stable aggregations of active swimmers is not fully understood. In particular, the in-depth quantitative explanations are notably lacking. To address this, a vorticity-based force expression is proposed to study the collective behaviors of two two-dimensional tandem flapping plates. The hydrodynamic force is directly related to the generation of vorticity on the plate and viscous forces resulting from its subsequent evolution. For the first time, the physical process by which the interactions between the rear plate and the wake vortices of the leader affects the hydrodynamic force is quantitatively elucidated and not based on simplified theory. The wake vortices of the leader influence the hydrodynamic force on the rear plate indirectly by inducing an additional oncoming flow. The flow affects the generation of vorticity, which mainly occurs on the head of the rear plate. The results show that, if the trajectory of the rear plate passes through the vortex cores, vorticity generation on the rear plate is suppressed and the thrust effect is weakened. If the rear plate slaloms between the vortices, the vorticity generation and the thrust effect are enhanced. We also found that the wake vortices of the leader has a certain ability to trap the rear plate into orderly configurations—no matter the rear plate has a dissimilar flapping amplitude or is applied an external horizontal loading—by adjusting the equilibrium position of the rear plate in it. The findings may shed some light on the understanding of collective behaviors in swimming animals.