Various and orderly formations in the hydrodynamic schooling of multiple flapping swimmers

Abstract

The fluid mechanics underlying the collective motion of fish schools and bird flocks still lack full understanding. In this paper, the collective motion of multiple asynchronous flapping foils is numerically studied. It is found that various and orderly formations are achieved by multiple foils only via hydrodynamic interactions. Three distinct states have been verified according to the equilibrium distance between adjacent foils, i.e., the sparse state, the compact state, and the combined state. The “head goose effect” is found in the combined state, and the significant speed enhancement can be observed in both the compact and combined states, except when the first subgroup of the combined group is isolated. The obvious energy savings can be observed in most cases examined in the current work, no matter which state occurs. Moreover, for a given phase difference, the compact group has the highest propulsive efficiency, while the sparse group has the lowest. In addition, the fluid mechanics by which the multiple-foil system achieves speed enhancement and energy savings are analyzed. The results obtained here may shed some light on understanding the collective motion of fish schools and bird flocks.