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 Nelin. Dinam., 2011, Volume 7, Number 2, Pages 283–293 (Mi nd259)

The integrable and nonintegrable motion of a vortex pair embedded inside an asymmetrical deformation flow

E. A. Ryzhov

V. I. Il'ichev Pacific Oceanological Institute

Abstract: The integrable and nonintegrable motion of a vortex pair, which consists of two vortices of arbitrary intensities, embedded inside a steady and periodic external deformation flow is studied. In the general case, such an external deformation flow impacts asymmetrically on the vortex pair, which results in nonconservation of motion invariants: the linear momentum and the angular momentum. An analytical expression for the linear momentum, which gives an opportunity to reduce the initial system with 2.5 degrees of freedom to a system with 1.5 degrees of freedom, is obtained. For the steady state of a constant deformation flow the integrability of the dipole motion is shown for any initial vortices positions and intensities of vortices, and for arbitrary values of shear and rotation of the deformation flow.

Keywords: vortex pair, deformation flow, integrals of motion.

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UDC: 551.465.7
MSC: 37D45, 76F10, 76F25, 76U05
Revised: 14.06.2011

Citation: E. A. Ryzhov, “The integrable and nonintegrable motion of a vortex pair embedded inside an asymmetrical deformation flow”, Nelin. Dinam., 7:2 (2011), 283–293

Citation in format AMSBIB
\Bibitem{Ryz11} \by E.~A.~Ryzhov \paper The integrable and nonintegrable motion of a vortex pair embedded inside an asymmetrical deformation flow \jour Nelin. Dinam. \yr 2011 \vol 7 \issue 2 \pages 283--293 \mathnet{http://mi.mathnet.ru/nd259}