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Teoreticheskaya i Matematicheskaya Fizika, 2009, Volume 158, Number 2, Pages 292–311
DOI: https://doi.org/10.4213/tmf6315 (Mi tmf6315) 		 
This article is cited in 9 scientific papers (total in 9 papers)

The question of the realizability of the Landau scenario for the development of turbulence

S. D. Glyzina, A. Yu. Kolesova, N. Kh. Rozovb

a P. G. Demidov Yaroslavl State University
b M. V. Lomonosov Moscow State University
Full-text PDF (601 kB) Citations (9)
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DOI: https://doi.org/10.4213/tmf6315
Abstract: We suggest a phenomenological model for the development of turbulence in the form of the nonlinear Klein–Gordon equation perturbed by nonconservative disturbances. Combining analytic and numerical methods, we establish that the transition to turbulence in this equation can follow both the Landau and the Landau–Sell scenarios. As is known, the first scenario is related to a cascade of bifurcations of stable invariant tori of increasing dimensions. The other scenario is related to a chaotic attractor whose Lyapunov dimension increases indefinitely under variation of a certain control parameter.
Keywords: Landau scenario, invariant torus, bifurcation, turbulent attractor, chaos.
Received: 14.03.2008
English version:
Theoretical and Mathematical Physics, 2009, Volume 158, Issue 2, Pages 246–261
DOI: https://doi.org/10.1007/s11232-009-0020-8
Bibliographic databases:
Language: Russian
Citation: S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “The question of the realizability of the Landau scenario for the development of turbulence”, TMF, 158:2 (2009), 292–311; Theoret. and Math. Phys., 158:2 (2009), 246–261
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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