Generalization of waving‐plate theory to multiple interacting swimmers
Generalization of waving‐plate theory to multiple interacting swimmers
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DOI：
10.1002/cpa.22113
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发表时间：
2021-06
影响因子：
3
通讯作者：
Peter J. Baddoo;Nicholas J. Moore;Anand U. Oza;D. Crowdy
中科院分区：
文献类型：
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作者：
Peter J. Baddoo;Nicholas J. Moore;Anand U. Oza;D. Crowdy
空气动力学和生物推进的早期研究是由Theodorsen、von Kármán、Wu和其他人的解析解极大地推进的。虽然这些经典的解决方案只适用于孤立的游泳者，多个游泳者之间的流动相互作用是相关的许多实际应用，包括学校和群集的动物集体。在这项工作中，我们得到了一类解决方案，描述了任意数量的游泳者在二维无粘流体之间的流体动力学相互作用。我们的方法植根于多连通复分析，并利用了最近的几个结果。具体地说，超越（Schottky-Klein）素函数作为基本构建块来构造适当的共形映射和前缘吸力函数，这使我们能够解决出现的修改的施瓦茨问题。因此，我们的解决方案将经典的薄翼型理论，特别是吴的波板分析，推广到多个游泳者的情况。对于一对相互作用的游泳者的情况下，我们开发了一个有效的数值实现，允许每个游泳者的力的快速计算。我们研究了流动介导的平衡，并发现我们的新解决方案和以前报道的实验结果之间非常一致。我们的解决方案恢复和统一不同的结果在文献中，从而打开大门，为未来的研究多个游泳者之间的相互作用。
Early research in aerodynamics and biological propulsion was dramatically advanced by the analytical solutions of Theodorsen, von Kármán, Wu and others. While these classical solutions apply only to isolated swimmers, the flow interactions between multiple swimmers are relevant to many practical applications, including the schooling and flocking of animal collectives. In this work, we derive a class of solutions that describe the hydrodynamic interactions between an arbitrary number of swimmers in a two‐dimensional inviscid fluid. Our approach is rooted in multiply‐connected complex analysis and exploits several recent results. Specifically, the transcendental (Schottky–Klein) prime function serves as the basic building block to construct the appropriate conformal maps and leading‐edge‐suction functions, which allows us to solve the modified Schwarz problem that arises. As such, our solutions generalize classical thin aerofoil theory, specifically Wu's waving‐plate analysis, to the case of multiple swimmers. For the case of a pair of interacting swimmers, we develop an efficient numerical implementation that allows rapid computations of the forces on each swimmer. We investigate flow‐mediated equilibria and find excellent agreement between our new solutions and previously reported experimental results. Our solutions recover and unify disparate results in the literature, thereby opening the door for future studies into the interactions between multiple swimmers.