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Eurasian Journal of Mathematical and Computer Applications, 2019, том 7, выпуск 2, страницы 20–61 (Mi ejmca102)  

On hydrodynamic instabilities qua nonequilibrium (Cahn–Pillard) phase transitions

E. V. Radkevicha, O. A. Vasil'evab, E. A. Lukashevc

a Moscow State University, Faculty of Mechanics and Mathematics Russia, 119899, Moscow, Vorob’evy gory
b Moscow State University of Civil Engineering Russia, 129337, Moscow, Yaroslavskoe shosse, 26
c Geodeziya Scientific Research Institute Russia, 41292, Moscow oblast’, Krasnoarmeysk sity, Ispitateley shosse, 14

Аннотация: For the laminar–turbulent transition, we construct a model of reconstruction of the initial stage of instability qua a nonequilibrium transition with diffusion separation mechanism. It is shown that the free Gibbs energy of departure from the homogeneous state (withrespect to the instability under consideration) is an analogue of the Ginzburg–Landau potential. Numerical experiments for self-excitation of the homogeneous state with control of the boundary condition of velocity increase were carried out, which showed the appearance of the laminar–turbulent transition and its development from regular forms (the so-called dissipative structures) with subsequent transition to irregular flows via chaotization of the process. An external action (an increase in velocity) results in a transition to chaos in terms of period-doubling bifurcations similarly to the Feigenbaum cascade of period-doubling bifurcations. The chaotization of the process transforms regular forms (dissipative structures) into the two-velocity regime (the regime of two shock waves), which was called the Riemann–Hugoniot catastrophe by Prigogine and Nicolis. This transformation depends substantially on gravitation. The perturbation is shown to be nonlocal, which indications that the classical perturbation theory is inapplicable in this case.

Ключевые слова: the laminar–turbulent transition, nonequilibrium phase transitions, the Kahn Hillard model, diffusion fibration, the Ginzburg-Landau potential, Gibbs free energy.

DOI: https://doi.org/10.32523/2306-6172-2019-7-2-20-61

Полный текст: PDF файл (6891 kB)

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Тип публикации: Статья
MSC: 76E09, 76F35, 82C26
Поступила в редакцию: 05.01.2019
Принята в печать:05.02.2019
Язык публикации: английский

Образец цитирования: E. V. Radkevich, O. A. Vasil'eva, E. A. Lukashev, “On hydrodynamic instabilities qua nonequilibrium (Cahn–Pillard) phase transitions”, Eurasian Journal of Mathematical and Computer Applications, 7:2 (2019), 20–61

Цитирование в формате AMSBIB
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\by E.~V.~Radkevich, O.~A.~Vasil'eva, E.~A.~Lukashev
\paper On hydrodynamic instabilities qua nonequilibrium (Cahn–Pillard) phase transitions
\jour Eurasian Journal of Mathematical and Computer Applications
\yr 2019
\vol 7
\issue 2
\pages 20--61
\mathnet{http://mi.mathnet.ru/ejmca102}
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