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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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
@article{VUU_2010_1_a12,
     author = {I. S. Mamaev},
     title = {Method of discrete vortices in statistical vortex dynamics as a~paradigm of computer methods of analysis},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {146--155},
     year = {2010},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2010_1_a12/}
}
TY  - JOUR
AU  - I. S. Mamaev
TI  - Method of discrete vortices in statistical vortex dynamics as a paradigm of computer methods of analysis
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2010
SP  - 146
EP  - 155
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VUU_2010_1_a12/
LA  - ru
ID  - VUU_2010_1_a12
ER  - 
%0 Journal Article
%A I. S. Mamaev
%T Method of discrete vortices in statistical vortex dynamics as a paradigm of computer methods of analysis
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2010
%P 146-155
%N 1
%U http://geodesic.mathdoc.fr/item/VUU_2010_1_a12/
%G ru
%F VUU_2010_1_a12
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/

[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