Self-organization of multiple self-propelling flapping foils: energy saving and increased speed

The collective hydrodynamics in fish schools and bird flocks, which includes self-organization of multiple dynamic bodies, is complex and lacks sufficient exploration. In this paper, we study the performance of multiple self-propelled foils in tandem formation, whose flapping motions are asynchronous with a phase difference. It is shown that a compact formation, in which all of the foils perform like a complete anguilliform swimmer, can be spontaneously formed by multiple foils via hydrodynamic interactions. Both velocity enhancement and energy saving can be achieved by multiple foils in anguilliform-like swimming. Furthermore, such anguilliform-like swimming behaviour can be observed over a wide range of parameters, including the number of foils, the phase difference, the initial distance, the heaving amplitude and the pitching amplitude. The results obtained here may provide some light on understanding the self-organization behaviour of biological collectives.