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We consider two problems in fluid dynamics: the collective locomotion of flying animals and the interaction of vortex rings with fluid interfaces. First, we present a model of formation flight, viewing the group as a material whose properties arise from the flow-mediated interactions among its members. This aerodynamic model explains how flapping flyers produce vortex wakes and how they are influenced by the wakes of others. Long in-line arrays show that the group behaves as a soft, excitable “crystal” with regularly ordered member “atoms” whose positioning is susceptible to deformations and dynamical instabilities. Second, we delve into the phenomenon of vortex ring reflections at water-air interfaces. Experimental observations reveal reflections analogous to total internal reflection of a light beam. We present a vortex-pair—vortex-sheet model to simulate this phenomenon, offering insights into the fundamental interactions of vortex rings with free surfaces.
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