Collective behavior and hydrodynamic advantage of side-by-side self-propelled flapping foils.

Fish schools and their potential hydrodynamic advantages are intriguing problems and many underlying mechanisms are unclear due to the complexity of the system, especially for large schools. Here large schools containing four, six, and eight self-propelled foils in a side-by-side configuration are numerically studied. The effect of different combinations out of phase and in phase between two neighboring foils is studied. The results show that the multiple abreast self-propelled foils driven by synchronized harmonic flapping motions can spontaneously form stable side-by-side configurations. When compared with a single foil flapping alone, for cases in which any two neighboring foils are in an out-of-phase state, foils consume more energy with a specific cruising speed. For cases where any two neighboring foils are in an in-phase state, foils propel at a lower speed for a specific flapping frequency. Interestingly, the foils in hybrid states in which both out of phase and in phase coexist are preferred to enhance speed and save power. Further analysis indicates that the stability of the configuration and the lower cost of transport are attributed to the synchronized collaborative wake vortex structure and bow configuration formed by any three neighboring foils in a hybrid state. The collaborative vortices in the wake help the foils move forward alternatively during one flapping cycle. The bow configuration prevents the wake from spreading laterally and enhances the performance. Our paper sheds some light on understanding the self-organized collective behavior and hydrodynamic advantages of large schools.