Abstract
This paper summarizes the results of studies of the laminar–turbulent transition in some fluid and gas dynamics problems obtained by applying numerical methods and methods of chaotic dynamics. The following problems are analyzed: 2D and 3D Kolmogorov problems in a periodic domain, 3D Rayleigh–Benard convection in rectangular domains, 3D backward-facing step flow, and development of 3D Rayleigh–Taylor and Kelvin–Helmholtz instabilities in viscous compressible flows. An analysis confirms that instabilities develop via cascades of subcritical or supercritical bifurcations. In all systems, a universal scenario of the transition to chaos (Feigenbaum–Sharkovskii–Magnitskii scenario) is found along with other scenarios of chaotization of dynamical systems.
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Notes
The projection of the phase space, the Poincaré section, and the corresponding physical solution are shown in Figs. 1 and 2.
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Funding
This work was supported by the Russian Foundation for Basic Research, grant nos. 18-29-10008 mk and 20-07-00066.
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Translated by I. Ruzanova
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Evstigneev, N.M., Magnitskii, N.A. Numerical Analysis of Laminar–Turbulent Transition by Methods of Chaotic Dynamics. Dokl. Math. 101, 110–114 (2020). https://doi.org/10.1134/S1064562420020118
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DOI: https://doi.org/10.1134/S1064562420020118