Geodesic
Method of discrete vortices in statistical vortex dynamics as a paradigm of computer methods of analysis
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2010), pp. 146-155

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With the help of mathematical modelling, we study the dynamics of many point vortices system on the plane. For this system, we consider the following cases: vortex rings with outer radius $r=1$ and variable inner radius $r_0$, vortex ellipses with semiaxes $a$, $b$.
Keywords: vortex dynamics, hydrodynamics, asymptotic behavior.
Mots-clés : point vortex 
I. S. Mamaev. Method of discrete vortices in statistical vortex dynamics as a paradigm of computer methods of analysis. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2010), pp. 146-155. http://geodesic.mathdoc.fr/item/VUU_2010_1_a12/
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[1] Onsager L., “Statistical hydrodynamics”, Nuovo Cimento, 6 (1949), 279–287 | DOI | MR

[2] Montgomery D., Joyce G., “Statistical mechanics of negative temperature states”, Phys. Fluids, 17:6 (1974), 1139–1145 | DOI | MR

[3] Kozlov V. V., “Uravnenie vikhrya 2D-gidrodinamiki, statsionarnoe kineticheskoe uravnenie Vlasova i razvitaya turbulentnost”, Nelineinaya dinamika, 2:4 (2006), 425–434

[4] Helmholtz H., “Über Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen”, J. Reine Angew. Math., 55 (1858), 25–55 | DOI | Zbl

[5] Kirchhoff G., Vorlesungen über mathematische Physik, Mechanik, Leipzig, 1874

[6] Strett Dzh. V. (lord Relei), Teoriya zvuka, v. II, GITTL, M., 1955, 476 pp.

[7] Drazin F., Vvedenie v teoriyu gidrodinamicheskoi ustoichivosti, Fizmatlit, M., 2005, 288 pp.

[8] Love A. E. H., “On the stability of certain vortex motions”, Proc. London Math. Soc., 25 (1894), 18–42 | DOI | MR

[9] Bühler O., “Statistical mechanics of strong and weak point vortices in a cylinder”, Phys. Fluids, 14:7 (2002), 2139–2149 | DOI | MR

[10] Pavlov V., Buisine D., and Goncharov V., “Formation of vortex clusters on a sphere”, Nonlinear Proc. Geophys., 8 (2001), 9–19 | DOI

[11] Yatsuyanagi Yu., Kiwamoto Ya., Tomita H., Sano M. M., Yoshida T., and Ebisuzaki T., “Dynamics of two-sign point vortices in positive and negative temperature state”, Phys. Rev. Lett., 94 (2005), 054502, 4 pp. | DOI

[12] Yoshida T., Sano M. M., “Numerical simulation of vortex crystals and merging in $N$-point vortex systems with circular boundary”, J. Phys. Soc. Japan, 74 (2005), 587–598 | DOI | Zbl

[13] Chavanis P. H., Lemou M., “Kinetic theory of point vortices in two dimensions: Analytical results and numerical simulations”, Eur. Phys. J. B, 59:2 (2007), 217–247 | DOI | MR | Zbl

[14] Borisov A. V., Mamaev I. S., Matematicheskie metody dinamiki vikhrevykh struktur, Inst. kompyutern. issled., M., Izhevsk, 2005, 368 pp. | MR

[15] Weiss J. B., McWilliams J. C., “Nonergodicity of point vortices”, Phys. Fluids, 3:5 (1991), 835–844 | DOI | MR | Zbl

[16] Kizner Z., Khvoles R., “The tripole vortex: Experimental evidence and explicit solutions”, Phys. Rev. E, 70 (2004), 016307, 4 pp. | DOI | MR

[17] Mitchell T. B., Rossi L. F., “The evolution of Kirchhoff elliptic vortices”, Phys. Fluids, 20:5 (2008), 054103, 12 pp. | DOI | Zbl