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Teoreticheskaya i Matematicheskaya Fizika, 1992, Volume 92, Number 2, Pages 293–311
(Mi tmf1504)
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This article is cited in 10 scientific papers (total in 10 papers)
Turbulence as a nonequilibrium phase transition
D. N. Zubarev, V. G. Morozov, O. V. Troshkin Steklov Mathematical Institute, Russian Academy of Sciences
Abstract:
The transition from laminar to turbulent flow is studied on the basis of an exact equation for the averaged velocity and an approximate nonlinear equation for the Reynolds stress $\tau$. The stationary state can be determined from the condition of minimum of a functional that is analogous to the Landau functional in the theory of phase transitions. The Reynolds stress plays the role of a parameter. It is shown that a nontrivial solution for $\tau$ corresponding to a steady turbulent regime exists only for Reynolds numbers $R$ that exceed a certain critical value $R_\mathrm{cr}$. The results of a numerical calculation of the profile of the averaged velocity, the friction coefficient, and the Reynolds stress in a wide range of values of $R$ agree well with experimental data for channel flow.
Received: 12.05.1992
Citation:
D. N. Zubarev, V. G. Morozov, O. V. Troshkin, “Turbulence as a nonequilibrium phase transition”, TMF, 92:2 (1992), 293–311; Theoret. and Math. Phys., 92:2 (1992), 896–908
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https://www.mathnet.ru/eng/tmf1504 https://www.mathnet.ru/eng/tmf/v92/i2/p293
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Abstract page: | 715 | Full-text PDF : | 291 | References: | 79 | First page: | 1 |
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