Geodesic
Numerical analysis of laminar–turbulent transition by methods of chaotic dynamics
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 491 (2020), pp. 38-43

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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.
Keywords: laminar–turbulent transition, chaotic dynamics, numerical methods, bifurcation analysis, Navier–Stokes equations. 
@article{DANMA_2020_491_a6,
     author = {N. M. Evstigneev and N. A. Magnitskii},
     title = {Numerical analysis of laminar{\textendash}turbulent transition by methods of chaotic dynamics},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {38--43},
     publisher = {mathdoc},
     volume = {491},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2020_491_a6/}
}
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N. M. Evstigneev; N. A. Magnitskii. Numerical analysis of laminar–turbulent transition by methods of chaotic dynamics. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 491 (2020), pp. 38-43. http://geodesic.mathdoc.fr/item/DANMA_2020_491_a6/