Bifurcation Analysis of the Problem of Two Vortices on a Finite Flat Cylinder

    Received 22 November 2023; accepted 20 December 2023; published 27 December 2023

    2024, Vol. 20, no. 1, pp.  95-111

    Author(s): Kilin A. A., Artemova E. M.

    This paper addresses the problem of the motion of two point vortices of arbitrary strengths in an ideal incompressible fluid on a finite flat cylinder. A procedure of reduction to the level set of an additional first integral is presented. It is shown that, depending on the parameter values, three types of bifurcation diagrams are possible in the system. A complete bifurcation analysis of the system is carried out for each of them. Conditions for the orbital stability of generalizations of von Kármán streets for the problem under study are obtained.
    Keywords: point vortices, ideal fluid, flat cylinder, bifurcation diagram, phase portrait, von Kármán vortex street, stability, boundary, flow in a strip
    Citation: Kilin A. A., Artemova E. M., Bifurcation Analysis of the Problem of Two Vortices on a Finite Flat Cylinder, Rus. J. Nonlin. Dyn., 2024, Vol. 20, no. 1, pp.  95-111

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