Abstract:
This paper is concerned with the dynamics of vortex sources in a deformation flow. The case of two vortex sources is shown to be integrable by quadratures. In addition, the relative equilibria (of the reduced system) are examined in detail and it is shown that in this case the trajectory of vortex sources is an ellipse.
The work of I. A. Bizyaev (Section 3) was carried out within the framework of the state assignment for institutions of higher education and partially supported by the Dynasty Foundation. The work of A. V. Borisov (Sections 1, 2) was supported by the Russian Science Foundation (project No. 15-12-20035). The work of I. S. Mamaev (Sections 4, 5) was supported by the RFBR grants Nos. 14-01-00395-a and 15-38-20879 mol_a_ved.
Citation:
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Dynamics of Vortex Sources in a Deformation Flow”, Regul. Chaotic Dyn., 21:3 (2016), 367–376
\Bibitem{BizBorMam16}
\by Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev
\paper The Dynamics of Vortex Sources in a Deformation Flow
\jour Regul. Chaotic Dyn.
\yr 2016
\vol 21
\issue 3
\pages 367--376
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\crossref{https://doi.org/10.1134/S1560354716030084}
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Linking options:
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Elizaveta M. Artemova, Evgeny V. Vetchanin, “The Motion of an Unbalanced Circular Disk
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Armand Vic, Xavier Carton, Jonathan Gula, “The Interaction of Two Unsteady Point Vortex Sources
in a Deformation Field in 2D Incompressible Flows”, Regul. Chaotic Dyn., 26:6 (2021), 618–646
E. M. Artemova, E. V. Vetchanin, “Control of the motion of a circular cylinder in an ideal fluid using a source”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 30:4 (2020), 604–617
J. Koiller, “Getting into the vortex: on the contributions of James Montaldi”, J. Geom. Mech., 12:3 (2020), 507–523
A. Kazakov, “Merger of a Henon-like attractor with a Henon-like repeller in a model of vortex dynamics”, Chaos, 30:1 (2020), 011105
Alexey V. Borisov, Ivan S. Mamaev, Ivan A. Bizyaev, “Three Vortices in Spaces of Constant Curvature: Reduction, Poisson Geometry, and Stability”, Regul. Chaotic Dyn., 23:5 (2018), 613–636
Evgeny V. Vetchanin, Ivan S. Mamaev, “Dynamics of Two Point Vortices in an External Compressible Shear Flow”, Regul. Chaotic Dyn., 22:8 (2017), 893–908
Sergei V. Sokolov, Pavel E. Ryabov, “Bifurcation Analysis of the Dynamics of Two Vortices in a Bose – Einstein Condensate. The Case of Intensities of Opposite Signs”, Regul. Chaotic Dyn., 22:8 (2017), 976–995
Yu. M. Grishin, M. Long, “Numerical simulation of the argon-hydrogen plasma flow in the channel of RF inductively coupled plasma torch”, International Conference Problems of Thermal Physics and Power Engineering (PTPPE-2017), Journal of Physics Conference Series, 891, IOP Publishing Ltd, 2017, UNSP 012302
Eugene A. Ryzhov, Konstantin V. Koshel, “Parametric Instability of a Many Point-vortex System in a Multi-layer Flow Under Linear Deformation”, Regul. Chaotic Dyn., 21:3 (2016), 254–266
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