Hydrodynamic analysis of fish schools arranged in the vertical plane

Schools of fish can provide individuals with hydrodynamic advantages, thereby improving the swimming efficiency. Fish schools in nature are mostly spatial configurations, not just limited to the horizontal plane. Through three-dimensional numerical simulations, this paper discusses the hydrodynamic characteristics and flow field structure of fish schools in various vertical patterns. The results show that a school of fish arranged vertically can improve the thrust and swimming efficiency of individuals as well as those arranged horizontally. There are two ways to significantly enhance hydrodynamic advantages. One is to maximize the channeling effect in multiple planes. In a vertical circular pattern, the fish school forms multiple coupled channels, which hinder the free expansion of flow in both vertical and horizontal planes, thereby obtaining higher energy-saving benefits. The other is the combined exploitation of the channeling effect and wake energy, which is illustrated in the vertical rectangular pattern. The following fish can use the channeling effect to increase the thrust due to the presence of parallel companion. Meanwhile, the high speed region of the following fish can merge with the jet flows of the preceding fish, thereby capturing the wake energy and further improving swimming efficiency.