Numerical simulations are employed to study hydrodynamic interactions between two-dimensional fish-like bodies under a traveling wavy lateral motion in high-density diamond-shaped fish schools. This study focuses on two different streamwise spacings, a dense school with 0.4 body length (BL) spacing and a sparse school with 2.0 BL spacing, respectively. An immersed-boundary-method-based incompressible Navier–Strokes flow solver is then employed to quantitatively simulate the resulting flow patterns and associated propulsive performance of the schools. The results suggest that a fish in the dense school achieves higher thrust production and higher propulsive efficiency than that in the sparse school due to a strong wall effect from neighboring fishes. In addition, results from changing the lateral spacing in the dense school have shown that the wall effect is enhanced as the lateral spacing decreases. Flow analyses have shown that the wake pattern of the fish swimming diagonally behind the leading fish in a dense diamond-shaped school transfers from 2S to 2P when the lateral spacing is smaller than 0.6 BL. As a result, an angled jet is produced behind the school and brings more momentum downstream. At the same time, the appearance of the trailing fish results in a stronger pressure region behind the leading fish and leads to a higher hydrodynamic performance of the leading fish in the dense school. The insights revealed from this study will contribute to understanding physical mechanisms in fish schools and providing a new swimming strategy for bio-inspired underwater swarm robots.

中文翻译：

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高密度鱼群中水动力相互作用的计算分析

在高密度菱形鱼群中，数值模拟被用来研究二维鱼状体在波浪状横向运动下的水动力相互作用。这项研究的重点是两个不同的水流间距，分别是0.4体长（BL）间距的密集学校和2.0 BL间距的稀疏学校。然后，使用基于浸没边界法的不可压缩Navier-Strokes流量求解器来定量模拟由此产生的流量模式和相关的学校推进性能。结果表明，由于邻近鱼的强壁效应，致密鱼群中的鱼比稀疏鱼群具有更高的推力产生和更高的推进效率。此外，密集学校中改变横向间距的结果表明，随着横向间距的减小，墙效应会增强。流动分析表明，当横向间距小于0.6 BL时，在密集的菱形学校中，对角游动在领先鱼类后面的鱼的尾迹模式从2S变为2P。结果，在学校后面产生了一个有角度的射流，并向下游带来了更多的动量。同时，拖尾鱼的出现导致领先鱼后面的压力区域更强，并导致在密集学校中领先鱼的水动力性能更高。这项研究揭示的见解将有助于理解鱼类学校的物理机制，并为受生物启发的水下群机器人提供新的游泳策略。