Effect of Formation Pattern on Schooling Energetics in Fish-Like Swimming

Abstract In the present study, an immerse-boundary-method-based in-house numerical solver is employed to investigate the effects of school pattern on energetics in fish-like swimming. Following Weihsys theory, two-dimensional diamond schools are formed for numerical simulations. The effects of the lateral distance and the longitudinal distance have been investigated to reveal the energetic saving mechanism in a fish school. It is found that the energetic performance in a narrow diamond school (2dy = 0.4) is very different from that in a wide school. In the wide school, the beneficial effect will decay gradually with the increase of longitudinal distance; however, in the narrow school, the variation of the effect is needed to divide into three phases. When the longitudinal spacing is small (2dx = 0.4 ∼ 2), the variation of power efficiency is complex. It increases sharply when 2dx changes from 0.4 to 1.2, then decrease. When the longitudinal distance is larger than two, the variation of energetics in a narrow diamond school has the same trend as that in a wide school. It is because, in the narrow school, the channeling effect is harmful to the energetics of individuals and plays an important role when the longitudinal distance is small. However, the detrimental effect will decay quickly with the increase of the longitudinal distance. Besides, when the longitudinal distance is large (2dx > 3.4), the narrow school shows a better power efficiency than the wide school. It is because, at this time, the fishes at the rear of school are still located at the instructive vortex wake produced by fishes in the front. These findings will give insight on how to form a power-efficient robotic school under water.