Hydrodynamically coupled rigid bodies

This paper considers a finite number of rigid bodies moving in potential flow. The dynamics of the solid-fluid system is described in terms of the solid variables only using Kirchhoff potentials. The equations of motion are first derived for the problem of two submerged bodies where one is forced into periodic oscillations. The hydrodynamic coupling causes the free body to drift away from or towards the oscillating body. The method of multiple scales is used to separate the slow drift from the fast response. Interestingly, the free body, when attracted towards the forced one, starts to drift away after it reaches certain separation distance. This suggests that the hydrodynamic coupling helps in preventing collisions. The fluid's role in collision avoidance and motion coordination is examined further through examples. In particular, we show that a free body can coordinate its motion with that of its neighbours, which may be relevant to understanding the coordinated motion in fish schooling.