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Russia Izhevsk
Year
2020
Volume
30
Issue
4
Pages
618-627
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Section Mechanics
Title Dynamics of a pair of point vortices and a foil with parametric excitation in an ideal fluid
Author(-s) Bizyaev I.A.a, Mamaev I.S.b
Affiliations Udmurt State Universitya, Izhevsk State Technical Universityb
Abstract In this paper we obtain equations of motion for a vortex pair and a circular foil with parametric excitation due to the periodic motion of a material point. Undoubtedly, such problems are, on the one hand, model problems and cannot be used for an exact quantitative description of real trajectories of the system. On the other hand, in many cases such 2D models provide a sufficiently accurate qualitative picture of the dynamics and, due to their simplicity, an estimate of the influence of different parameters. We describe relative equilibria that generalize Föppl solutions and collinear configurations when the material point does not move. We show that a stochastic layer forms in the neighborhood of relative equilibria in the case of periodic motion of the foil's center of mass.
Keywords point vortices, ideal fluid, Poincaré map, foil in a fluid, 2D hydrodynamics
UDC 531.011
MSC 76B47
DOI 10.35634/vm200406
Received 20 September 2020
Language Russian
Citation Bizyaev I.A., Mamaev I.S. Dynamics of a pair of point vortices and a foil with parametric excitation in an ideal fluid, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2020, vol. 30, issue 4, pp. 618-627.
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