Geodesic
Turbulent boundary layers at very large Reynolds numbers
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 59 (2004) no. 1, pp. 47-64 Cet article a éte moissonné depuis la source Math-Net.Ru

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Andrei Nikolaevich Kolmogorov firmly believed that in the absence of a rigorous self-contained theory of turbulent fluids and gases one must use hypotheses obtained by processing experimental data. This paper begins with a discussion of the hypothesis of complete self-similarity used in the proof of the widely known (Reynolds-number independent) von Kármán–Prandtl logarithmic law for the distribution of velocity in a turbulent shear flow. It is shown that this hypothesis has not been confirmed experimentally. Instead, a hypothesis of incomplete self-similarity is proposed which leads to a power-law dependence on the Reynolds number. It is shown that this law agrees well with experiments for the most important classes of turbulent shear flows (for flows in pipes and boundary layers). 
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G. I. Barenblatt. Turbulent boundary layers at very large Reynolds numbers. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 59 (2004) no. 1, pp. 47-64. http://geodesic.mathdoc.fr/item/RM_2004_59_1_a4/

[1] Th. von Kármán, “Mechanische Ähnlichkeit und Turbulenz”, Proceedings of the Third International Congress on Applied Mechanics, v. 1 (Stockholm, 1930), eds. C. W. Oseen and W. Weibull, AB Sveriges Lifografska Tryckenier, 1931, 85–93 | Zbl

[2] L. Prandtl, “Zur turbulenten Strömung in Röhren und längs Platten”, Ergeb. Aerodyn. Versuchsanst. Göttingen, 4 (1932), 18–29 | Zbl

[3] A. N. Kolmogorov, “Lokalnaya struktura turbulentnosti v neszhimaemoi vyazkoi zhidkosti pri ochen bolshikh chislakh Reinoldsa”, Dokl. AN SSSR, 30:4 (1941), 299–303

[4] A. M. Obukhov, “O raspredelenii energii v spektre turbulentnogo potoka”, Dokl. AN SSSR, 32:1 (1941), 22–24 | MR

[5] A. N. Kolmogorov, Izbrannye trudy. Matematika i mekhanika, Nauka, M., 1985 | MR

[6] G. I. Barenblatt, A. J. Chorin, V. M. Prostokishin, “Scaling laws in fully developed turbulent pipe flow”, Appl. Mech. Rev., 50 (1997), 413–429 | DOI | MR

[7] A. J. Chorin, “New perspectives in turbulence”, Quart. Appl. Math., 56:4 (1998), 767–785 | MR | Zbl

[8] G. I. Barenblatt, “Scaling laws for turbulent wall-bounded shear flows at very large Reynolds numbers”, J. Engrg. Math., 36:4 (1999), 361–384 | DOI | MR | Zbl

[9] G. I. Barenblatt, A. J. Chorin, V. M. Prostokishin, “Self-similar intermediate structures in turbulent boundary layers at large Reynolds numbers”, J. Fluid Mech., 410 (2000), 263–283 | DOI | MR | Zbl

[10] L. D. Landau, E. M. Lifshits, Teoreticheskaya fizika. T. 6: Gidrodinamika, Nauka, M., 1986

[11] A. S. Monin, A. M. Yaglom, Statisticheskaya gidromekhanika. T. 1: Mekhanika turbulentnosti, Nauka, M., 1965

[12] M. V. Zagarola, Mean flow scaling in turbulent pipe flow, PhD Thesis, Princeton Univ. Press, Princeton, 1996

[13] G. I. Barenblatt, Scaling, Self-Similarity, and Intermediate Asymptotics, Cambridge Univ. Press, Cambridge, 1996 | MR | Zbl

[14] H. Schlichting, Boundary Layer Theory, McGraw-Hill, New York, 1968 | MR

[15] J. Nikuradse, “Gesetzmässigkeiten der turbulenten Strömung in glatten Röhren”, VDI Forschungscheftg vool 356, 1932 | Zbl

[16] S. J. Kline, W. C. Reynolds, F. A. Schraub, P. W. Rundstadtler, “The structure of turbulent boundary layers”, J. Fluid Mech., 30:4 (1967), 741–774 | DOI

[17] A. Izakson, “Formula for the velocity distribution near a wall”, J. Exp. Theor. Physics, 7 (1937), 919–924

[18] C. B. Millikan, “A critical discussion of turbulent flows in channels and circular tubes”, Proceedings of the Fifth International Congress on Applied Mechanics (Cambridge, 1938), eds. J. P. den Hartog and H. Peters, Wiley/Chapman Hall, New York/London, 1939, 386–392

[19] R. von Mises, “Some remarks on the laws of turbulent motion in tubes”, Th. von Kármán, Anniversary Volume, CalTech Press, Pasadena, 1941, 317–327 | MR | Zbl

[20] L. P. Erm, P. N. Joubert, “Low Reynolds-number turbulent boundary layers”, J. Fluid Mech., 230 (1991), 1–44 | DOI

[21] P.-Å. Krogstad, R. A. Antonia, “Surface roughness effects in turbulent boundary layers”, Exp. in Fluids, 27 (1999), 450–460 | DOI

[22] H. H. Fernholz, P. J. Finley, “The incompressible zero-pressure gradient turbulent boundary layer: an assessment of the data”, Progr. Aeros. Sci., 32 (1996), 245–311 | DOI

[23] G. I. Barenblatt, A. J. Chorin, V. M. Prostokishin, “Characteristic length scale of the intermediate structure in zero-pressure-gradient boundary layer flow”, Proc. Natl. Acad. Sci. USA, 97:8 (2000), 3799–3802 | DOI | MR | Zbl

[24] I. Marušić, A. E. Perry, “A wall-wake model for the turbulence structure of boundary layers. Part 2. Further experimental support”, J. Fluid Mech., 298 (1995), 389–407; http://www.mame.mu.oz.au/ivan | DOI

[25] G. I. Barenblatt, A. J. Chorin, V. M. Prostokishin, “A model of a turbulent boundary layer with a nonzero pressure gradient”, Proc. Natl. Acad. Sci. USA, 99:9 (2002), 5772–5776 | DOI | MR | Zbl

[26] F. H. Clauser, “The turbulent boundary layer”, Adv. Appl. Mech., 4 (1956), 2–52

[27] D. E. Coles, “The law of the wake in the turbulent boundary layer”, J. Fluid Mech., 1:3 (1956), 191–226 | DOI | MR | Zbl