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@article{ND_2013_9_4_a4, author = {Konstantin N. Kulik and Anatoly V. Tur and Vladimir V. Yanovskii}, title = {The evolution point dipole vortex in a domain with circular boundaries}, journal = {Russian journal of nonlinear dynamics}, pages = {659--670}, publisher = {mathdoc}, volume = {9}, number = {4}, year = {2013}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/ND_2013_9_4_a4/} }
TY - JOUR AU - Konstantin N. Kulik AU - Anatoly V. Tur AU - Vladimir V. Yanovskii TI - The evolution point dipole vortex in a domain with circular boundaries JO - Russian journal of nonlinear dynamics PY - 2013 SP - 659 EP - 670 VL - 9 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ND_2013_9_4_a4/ LA - ru ID - ND_2013_9_4_a4 ER -
%0 Journal Article %A Konstantin N. Kulik %A Anatoly V. Tur %A Vladimir V. Yanovskii %T The evolution point dipole vortex in a domain with circular boundaries %J Russian journal of nonlinear dynamics %D 2013 %P 659-670 %V 9 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/ND_2013_9_4_a4/ %G ru %F ND_2013_9_4_a4
Konstantin N. Kulik; Anatoly V. Tur; Vladimir V. Yanovskii. The evolution point dipole vortex in a domain with circular boundaries. Russian journal of nonlinear dynamics, Tome 9 (2013) no. 4, pp. 659-670. http://geodesic.mathdoc.fr/item/ND_2013_9_4_a4/
[1] Gelmgolts G., “Ob integralakh uravnenii gidrodinamiki, sootvetstvuyuschikh vikhrevym dvizheniyam”, Nelineinaya dinamika, 2:4 (2006), 473–507 ; Helmholtz H., “Über Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen”, J. Reine Angew. Math., 55 (1858), 25–55 ; Гельмгольц Г., Два исследования по гидродинамике, т. 1, О вихревом движении; т. 2, О прерывном движении жидкости, ред. С. А. Чаплыгин, Типография О. Л. Сомовой, М., 1902, 5–51; Гельмгольц Г., Основы вихревой теории, репринтное издание, Институт компьютерных исследований, М.–Ижевск, 2002, 7–40 | DOI | Zbl
[2] Greenhill A. G., “Plane vortex motion”, Quart. J. Pure Appl. Math., 15:58 (1877/78), 10–27
[3] Havelock T. H., “The stability of motion of rectilinear vortices in ring formation”, Phil. Mag., 11:70 (1931), 617–633
[4] Lin C. C., “On the motion of vortices in two dimensions. 1; 2”, Proc. Natl. Acad. Sci. USA, 27:2 (1941), 570–577 | DOI | MR | Zbl
[5] Milne-Thompson L. M., Theoretical hydrodynamics, 4th ed., Macmillan, New York, 1960, 660 pp. | MR
[6] Hardin J. C., Mason J. P., “Periodic motion of two and four vortices in a cylindrical pipe”, Phys. Fluids, 27:7 (1984), 1583–1589 | DOI | Zbl
[7] Kimura Y., “Motion of two point vortices in a circular domain”, J. Phys. Soc. Japan, 57:5 (1988), 1641–1649 | DOI | MR
[8] Kimura Y., Kusumoto Y., Hasimoto H., “Some particular solutions for symmetric motion of point vortices in a circular cylinder”, J. Phys. Soc. Japan, 53:9 (1984), 2988–2995 | DOI
[9] Simakov N. N., “Dynamics of two vortices in circular domain”, Regul. Chaotic Dyn., 3:4 (1998), 87–94 | DOI | MR | Zbl
[10] Borisov A. V., Mamaev I. S., Matematicheskie metody dinamiki vikhrevykh struktur, Institut kompyuternykh issledovanii, M.–Izhevsk, 2005, 368 pp.
[11] A. V. Borisov, I. S. Mamaev, M. A. Sokolovskii (red.), Fundamentalnye i prikladnye problemy teorii vikhrei, Sb. st., Institut kompyuternykh issledovanii, M.–Izhevsk, 2003, 704 pp.
[12] Tur A. V., Yanovskii V. V., Gidrodinamicheskie vikhrevye struktury, Institut monokristallov NAN Ukrainy, Kharkov, 2012, 294 pp.
[13] Borisov A. V., Pavlov A. E., “Dynamics and statics of vortices on a plane and a sphere, 1”, Regul. Chaotic Dyn., 3:1 (1998), 28–38 | DOI | MR | Zbl
[14] Borisov A. V., Lebedev V. G., “Dynamics of three vortices on a plane and a sphere. 2: General compact case”, Regul. Chaotic Dyn., 3:2 (1998), 99–114 | DOI | MR | Zbl
[15] Borisov A. V., Lebedev V. G., “Dynamics of three vortices on a plane and a sphere. 3: Noncompact case. Problems of collaps and scattering”, Regul. Chaotic Dyn., 3:4 (1998), 74–86 | DOI | MR | Zbl
[16] Borisov A. V., Kilin A. A., Mamaev I. S., “Reduktsiya i khaoticheskoe povedenie tochechnykh vikhrei na ploskosti i sfere”, Nelineinaya dinamika, 1:2 (2005), 233–246 | Zbl
[17] Montaldi J., Soulière A., Tokieda T., “Vortex dynamics of a cylinder”, SIAM J. Appl. Dyn. Sys., 2:3 (2003), 417–430 | DOI | MR | Zbl
[18] Tkachenko V. K., “Ustoichivost vikhrevykh reshetok”, ZhETF, 50:6 (1966), 1573–1585
[19] O'Neil K. A., “On the Hamiltonian dynamics of vortex lattices”, J. Math. Phys., 30:6 (1989), 1373–1372 | DOI | MR
[20] Yanovsky V. V., Tur A. V., Kulik K. N., “Singularities motion equations in $2$-dimensional ideal hydrodynamics of incompressible fluid”, Phys. Lett. A, 373:29 (2009), 2484–2487 | DOI | Zbl
[21] Gröbli W., “Specialle Probleme über Bewegung geradliniger paralleler Wirbelfäden”, Vierteljahresschr. Naturforsch. Ges. Zürich, 22 (1877), 37–81
[22] Novikov E. A., “Dinamika i statistika sistemy vikhrei”, ZhETF, 68:5 (1975), 1868–1882
[23] Aref H., “Motion of three vortices”, Phys. Fluids, 31:6 (1988), 1392–1409 | DOI | MR
[24] Kulik K. N., Tur A. V., Yanovskii V. V., “Vzaimodeistvie tochechnogo i dipolnogo vikhrei v neszhimaemoi zhidkosti”, TMF, 162:3 (2010), 459–480 | DOI | MR | Zbl
[25] Tur A., Yanovsky V., Kulik K., “Vortex structures with complex points singularities in the two-dimensional Euler equation: New exact solutions”, Phys. D, 240:13 (2011), 1069–1079 | DOI | MR | Zbl
[26] Llewellyn Smith S. G., How do singularities move in potential flow?, Phys. D, 240:20 (2011), 1644–1651 | DOI | MR | Zbl
[27] Tur A. V., Yanovsky V. V., Interaction of a dipole point vortex with flat boundary, 20 Apr. 2012, arXiv: 1204.4557v1
[28] Lewis T. C., “Some cases of vortex motion”, Messenger of Math., 9 (1879), 93–95
[29] Milne-Thomson L. M., Theoretical aerodynamics, Dover, New York, 1966, 430 pp.
[30] Landau L. D., Lifshits E. M., Teoreticheskaya fizika, V 10 tt., v. 1, Mekhanika, 4-e izd., Nauka, M., 1988, 216 pp.