Geodesic
Turbulence as a~nonequilibrium phase transition
Teoretičeskaâ i matematičeskaâ fizika, Tome 92 (1992) no. 2, pp. 293-311

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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. 
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     author = {D. N. Zubarev and V. G. Morozov and O. V. Troshkin},
     title = {Turbulence as a~nonequilibrium phase transition},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {293--311},
     publisher = {mathdoc},
     volume = {92},
     number = {2},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1992_92_2_a7/}
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D. N. Zubarev; V. G. Morozov; O. V. Troshkin. Turbulence as a~nonequilibrium phase transition. Teoretičeskaâ i matematičeskaâ fizika, Tome 92 (1992) no. 2, pp. 293-311. http://geodesic.mathdoc.fr/item/TMF_1992_92_2_a7/