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TMF, 2010, Volume 162, Number 3, Pages 459–480 (Mi tmf6482)  

This article is cited in 12 scientific papers (total in 12 papers)

Interaction of point and dipole vortices in an incompressible liquid

K. N. Kulika, A. V. Turab, V. V. Yanovskiia

a Institute for Monocrystals, National Academy of Sciences of Ukraine, Kharkov, Ukraine
b Center D'etude Spatiale Des Rayonnements, Toulouse, France

Abstract: We discuss the interaction between point vortices and point dipole vortices in two-dimensional ideal hydrodynamics and show that the equations of motion of the interacting point and point dipole vortices are exactly integrable. We find exact solutions for all possible parameter values characterizing the vortices and for arbitrary initial conditions and establish the regimes of vortex motion.

Keywords: two-dimensional ideal hydrodynamics, Hamiltonian formalism, point vortex, point dipole vortex, exact solution, regime of motion


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English version:
Theoretical and Mathematical Physics, 2010, 162:3, 383–400

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Received: 13.07.2009

Citation: K. N. Kulik, A. V. Tur, V. V. Yanovskii, “Interaction of point and dipole vortices in an incompressible liquid”, TMF, 162:3 (2010), 459–480; Theoret. and Math. Phys., 162:3 (2010), 383–400

Citation in format AMSBIB
\by K.~N.~Kulik, A.~V.~Tur, V.~V.~Yanovskii
\paper Interaction of point and dipole vortices in an~incompressible liquid
\jour TMF
\yr 2010
\vol 162
\issue 3
\pages 459--480
\jour Theoret. and Math. Phys.
\yr 2010
\vol 162
\issue 3
\pages 383--400

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    This publication is cited in the following articles:
    1. E. A. Ryzhov, “Integriruemoe i neintegriruemoe dvizhenie vikhrevoi pary v nesimmetrichnom deformatsionnom potoke”, Nelineinaya dinam., 7:2 (2011), 283–293  mathnet
    2. Smith S.G.L., “How do singularities move in potential flow?”, Phys. D, 240:20 (2011), 1644–1651  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. Tur A., Yanovsky V., Kulik K., “Vortex structures with complex points singularities in two-dimensional Euler equations. New exact solutions”, Phys. D, 240:13 (2011), 1069–1079  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. Tchieu A.A., Kanso E., Newton P.K., “The finite-dipole dynamical system”, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 468:2146 (2012), 3006–3026  crossref  mathscinet  zmath  adsnasa  isi  scopus
    5. K. N. Kulik, A. V. Tur, V. V. Yanovskii, “Evolyutsiya tochechnogo vikhrya dipolnogo tipa v krugovoi oblasti”, Nelineinaya dinam., 9:4 (2013), 659–670  mathnet
    6. Tsang Alan Cheng Hou, Kanso E., “Dipole Interactions in Doubly Periodic Domains”, J. Nonlinear Sci., 23:6 (2013), 971–991  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. Kanso E., Tsang Alan Cheng Hou, “Dipole Models of Self-Propelled Bodies”, Fluid Dyn. Res., 46:6 (2014), 061407  crossref  adsnasa  isi  scopus
    8. Matsumoto Yu., Ueno K., “A Dynamical System of Interacting Dipoles in Two-Dimensional Flows”, Fluid Dyn. Res., 46:3 (2014), 031413  crossref  mathscinet  zmath  adsnasa  isi  scopus
    9. Kanso E., Tsang Alan Cheng Hou, “Pursuit and Synchronization in Hydrodynamic Dipoles”, J. Nonlinear Sci., 25:5, SI (2015), 1141–1152  crossref  mathscinet  zmath  adsnasa  isi  scopus
    10. 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  mathnet  crossref  mathscinet
    11. Tur A., Yanovsky V., “Dynamics of Point Vortex Singularities”: Tur, A Yanovsky, V, Coherent Vortex Structures in Fluids and Plasmas, Springer Series in Synergetics, Springer International Publishing Ag, 2017, 15–74  crossref  isi
    12. Tur A., Yanovsky V., “Nontrivial Stationary Vortex Configurations”: Tur, A Yanovsky, V, Coherent Vortex Structures in Fluids and Plasmas, Springer Series in Synergetics, Springer International Publishing Ag, 2017, 129–174  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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