Abstract
It is revealed that the local equilibrium approximation (algebraic parametrization of triple correlations of turbulent fluctuations of a vertical velocity component) in the problem of a planar momentumless turbulent wake is a differential constraint for a third-order closure model. The results of numerical experiments that confirm the feasibility of the used known algebraic parametrization of this third-order correlation moment are presented.
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REFERENCES
A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics. Vol. I. Mechanics of Turbulence (Dover Publications, 2007).
A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics. Vol. II. Mechanics of Turbulence (Dover Publications, 2007).
N. N. Yanenko, “Compatibility Theory and Methods of Integration of Systems of Nonlinear Partial Differential Equations," inProceedings of the 4th All-Union Mathematical Congress, Leningrad, July 3–12, 1961 (Nauka. Leningradskoe Otdelenie, Leningrad, 1964) Vol. 2, pp. 247–252 [in Russian].
A. F. Sidorov, V. P. Shapeev, and N. N. Yanenko, The Method of Differential Constraints and Its Applications in Gas Dynamics (Nauka. Sib. Otd., Novosibirsk, 1988) [in Russian].
V. K. Andreev, O. V. Kaptsov, V. V. Pukhnachev, and A. A. Rodionov,Applications of Group-Theoretical Methods in Hydrodynamics (Springer Netherlands, 1998).
V. N. Grebenev and B. B. Ilyushin, “Application of Differential Constraints to the Analysis of Turbulence Models," Doklady Akademii Nauk 384 (6), 761–764 (2000) [Doklady Physics45 (10), 550–553 (2000)].
V. N. Grebenev and B. B. Ilyushin, “Method of Differential Constraints in the Problem of a Stratified Shear-Free Turbulent Mixing Layer," Doklady Akademii Nauk 382 (6), 768–771 (2002) [Doklady Physics 47 (2), 159–162 (2002)].
V. N. Grebenev, A. G. Demenkov, and G. G. Chernykh, “Analysis of the Local-Equilibrium Approximation in the Problem of Far Planar Turbulent Wake," Doklad Akademii Nauk 385 (1), 57–60 (2002) [Doklady Physics 47 (7), 518–521 (2002)].
K. Hanjalic and B. E. Launder, “A Reynolds Stress Model of Turbulence and Its Application to Thin Shear Flows," J. Fluid Mech. 52, 609–638 (1972).
O. Zeman and J. L. Lumley, “Modeling Buoyancy Driven Mixed Layer," J. Athmospher. Sci. 33, 1974–1988 (1976).
A. Chorin, “Theories of Turbulence," Lecture Notes Math.615, 36–47 (1977).
A. F. Kurbatskii, Simulating the Nonlocal Turbulent Transfer of Momentum and Heat (Nauka, Novosibirsk, 1988) [in Russian].
B. B. Ilyushin, “Model of Fourth-Order Cumulants for Description of Turbulent Transport by Large-Scale Vortex Structures," Prikl. Mekh. Tekh. Fiz. 40 (5), 106–112 (1999) [J. Appl. Mech. Tech. Phys. 40 (5), 871–876 (2015)].
Yu. M. Dmitrenko, I. I. Kovalev, N. N. Luchko, and P. Ya. Cherepanov, “Plane Turbulent Wake with Zero Excess Momentum," Inzh.-Fiz. Zhurn. 52 (5), 743–750 (1987) [J. Engng Phys. 52 (5), 536–542 (1987)].
J. M. Cimbala and W. J. Park, “An Experimental Investigation of the Turbulent Structure in a Two-Dimensional Momentumless Wake," J. Fluid Mech. 213, 479–509 (1990).
N. N. Fedorova and G. G. Chernykh, “Numerical Simulation of Planar Turbulent Wakes," Matematicheskoe Modelirovanie 6(10), 24–34 (1994) [Matem. Mod. 6 (10), 24–34 (1994)].
V. Maderich and S. Konstantinov, “Asymptotic and Numerical Analysis of Momentumless Turbulent Wakes," Fluid Dynamics Res.42, 045503 (2010). DOI: 10.1088/0169-5983/42/4/045503.
O. F. Voropaeva, B. B. Ilyushin, and G. G. Chernykh, “Numerical Simulation of the far Momentumless Turbulent Wake in a Linearly Stratified Medium," Doklady Akademii Nauk 386 (6), 756–760 (2002) [Doklady Physics 47 (10), 762–766 (2002)].
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2021, Vol. 62, No. 3, pp. 38-47.https://doi.org/10.15372/PMTF20210304.
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Grebenev, V.N., Demenkov, A.G. & Chernykh, G.G. METHOD OF DIFFERENTIAL CONSTRAINTS: LOCAL EQUILIBRIUM APPROXIMATION IN A PLANAR MOMENTUMLESS TURBULENT WAKE. J Appl Mech Tech Phy 62, 383–390 (2021). https://doi.org/10.1134/S0021894421030044
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DOI: https://doi.org/10.1134/S0021894421030044