0
2013
Impact Factor

    Dynamics of perturbed equilateral and collinear configurations of three point vortices

    2007, Vol. 3, No. 4, pp.  379-391

    Author(s): Gudimenko A. I.

    Dynamics of perturbed stable equilateral and collinear configurations of three point vortices in an incompressible ideal fluid is studied. The asymptotics of the perturbed motion to the unperturbed one is obtained. It is shown that in the first approximation in a appropriate coordinate system the vortices rotate about their undisturbed positions in elliptical orbits. The velocity of the rotation is calculated. It is shown that the eccentricities of the orbits are coincide. The ratio of major axes of any two orbits is calculated. In case of equilateral configuration this ratio is equal to the ratio of inverse intensities of the corresponding vortices. The angle between major axes of any two orbits of the vortices is calculated. In case of equilateral configuration this angle is ±120 degrees.
    Keywords: point vortices, integrable dynamics, perturbation theory
    Citation: Gudimenko A. I., Dynamics of perturbed equilateral and collinear configurations of three point vortices, Rus. J. Nonlin. Dyn., 2007, Vol. 3, No. 4, pp.  379-391
    DOI:10.20537/nd0704001


    Download File
    PDF, 185.87 Kb




    Creative Commons License
    This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License