The regular and chaotic dynamics of structures in fluid flows

M.I. Rabinovich, M.M. Sushchik
Federal Research Center A.V. Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences, ul. Ulyanova 46, Nizhny Novgorod, 603000, Russian Federation

``Order in chaos'' is not an abstraction. It is a characteristic of real disordered processes and can be formulated quantitatively. In application to turbulence the term "order in chaos" means the existence of localized metastable states–structures. In this review experiments demonstrating that the nonlinear dynamics of these structures can be both regular and chaotic are discussed. Models on the basis of which it is possible to construct a theory of spatial-temporal chaos in an ensemble of structures and thereby to discuss turbulence with small and moderate values of the critical parameter (relative Reynolds number) are studied.

PACS: 47.52.+j, 47.27.ed, 47.27.Jv, 47.32.−y (all)
DOI: 10.1070/PU1990v033n01ABEH002403
URL: https://ufn.ru/en/articles/1990/1/a/
Citation: Rabinovich M I, Sushchik M M "The regular and chaotic dynamics of structures in fluid flows" Sov. Phys. Usp. 33 (1) 1–35 (1990)

BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Рабинович М И, Сущик М М «Регулярная и хаотическая динамика структур в течениях жидкости» УФН 160 (1) 3–64 (1990); DOI: 10.3367/UFNr.0160.199001a.0003

References (245) Cited by (60) Similar articles (20) ↓

A.V. Getling “Formation of spatial structures in Rayleigh—Bénard convection” Sov. Phys. Usp. 34 (9) 737–776 (1991)
V.V. Zosimov, L.M. Lyamshev “Fractals in wave processes” Phys. Usp. 38 347–384 (1995)
A. Loskutov “Fascination of chaos” Phys. Usp. 53 1257–1280 (2010)
A.I. Olemskoi, A.Ya. Flat “Application of fractals in condensed-matter physics” Phys. Usp. 36 (12) 1087–1128 (1993)
H.D. Abarbanel, M.I. Rabinovich et al “Synchronisation in neural networks” Phys. Usp. 39 337–362 (1996)
M.I. Rabinovich “Stochastic self-oscillations and turbulence” Sov. Phys. Usp. 21 443–469 (1978)
V.S. Anishchenko, T.E. Vadivasova et al “Statistical properties of dynamical chaos” Phys. Usp. 48 151–166 (2005)
M.I. Rabinovich, A.L. Fabrikant, L.Sh. Tsimring “Finite-dimensional spatial disorder” Sov. Phys. Usp. 35 (8) 629–649 (1992)
M.I. Rabinovich, M.K. Muezzinoglu “Nonlinear dynamics of the brain: emotion and cognition” Phys. Usp. 53 357–372 (2010)
B.S. Kerner, V.V. Osipov “Self-organization in active distributed media: scenarios for the spontaneous formation and evolution of dissipative structures” Sov. Phys. Usp. 33 (9) 679–719 (1990)
K.V. Koshel, S.V. Prants “Chaotic advection in the ocean” Phys. Usp. 49 1151–1178 (2006)
V.S. Anishchenko, A.B. Neiman et al “Stochastic resonance: noise-enhanced order” Phys. Usp. 42 7–36 (1999)
V.F. Kop’ev, S.A. Chernyshev “Vortex ring oscillations, the development of turbulence in vortex rings and generation of sound” Phys. Usp. 43 663–690 (2000)
S.P. Kuznetsov “Dynamical chaos and uniformly hyperbolic attractors: from mathematics to physics” Phys. Usp. 54 119–144 (2011)
F.V. Dolzhanskii, V.A. Krymov, D.Yu. Manin “Stability and vortex structures of quasi-two-dimensional shear flows” Sov. Phys. Usp. 33 (7) 495–520 (1990)
G.R. Ivanitskii, A.B. Medvinskii, M.A. Tsyganov “From the dynamics of population autowaves generated by living cells to neuroinformatics” Phys. Usp. 37 961–989 (1994)
B.N. Belintsev “Dissipative structures and the problem of biological pattern formation” Sov. Phys. Usp. 26 775–800 (1983)
A.S. Monin “On the nature of turbulence” Sov. Phys. Usp. 21 429–442 (1978)
K.P. Zybin, V.A. Sirota “Stretching vortex filaments model and the grounds of statistical theory of turbulence” Phys. Usp. 58 556–573 (2015)
Ya.B. Zel’dovich, S.A. Molchanov et al “Intermittency in random media” Sov. Phys. Usp. 30 353–369 (1987)

The list is formed automatically.