Geodesic
Linear chaotic resonance in vortex motion
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 4, pp. 639-655 
V. G. Zadorozhniy. Linear chaotic resonance in vortex motion. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 4, pp. 639-655. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_4_a10/
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     title = {Linear chaotic resonance in vortex motion},
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Voir la notice de l'article provenant de la source Math-Net.Ru

For three-dimensional vortex motion, a linear mathematical model with random coefficients is considered, and formulas for the first two moment functions of solutions are derived. The conditions are found under which a linear chaotic resonance occurs; i.e., the mean angular velocity of the motion increases. The results show that the energy of the vortex increases because of the chaotic motions present in the flow.

[1] Helmholtz H. L., “Liber Integrale der hydrodinamischen Gleihungen welhe den Wirbel-bewegungen entsprechen”, Crelles J., 1858, no. 55, 25–55 | DOI | Zbl

[2] Seffmen F. Dzh., Dinamika vikhrei, Nauchnyi Mir, M., 2000

[3] Anischenko V. S., Neiman A. B., Moss F., Shimanskii-Gaier L., “Stokhasticheskii rezonans kak indutsirovannyi shumom effekt uvelicheniya stepeni poryadka”, Uspekhi fiz. nauk, 169:1 (1999), 7–38 | DOI

[4] Zadorozhnii V. G., Khrebtova S. S., “Pervye momentnye funktsii resheniya uravneniya teploprovodnosti so sluchainymi koeffitsientami”, Zh. vychisl. matem. i matem. fiz., 49:11 (2009), 1937–1952 | MR

[5] Zadorozhnii V. G., Metody variatsionnogo analiza, RKhD, M.–Izhevsk, 2006

[6] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1968 | MR | Zbl

[7] Tikhonov V. I., “Vozdeistvie fluktuatsii na prosteishie parametricheskie sistemy”, Avtomatika i telemekhanika, 19:8 (1958), 717–723

[8] Adomian Dzh., Stokhasticheskie sistemy, Mir, M., 1987 | MR