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Instabilitäten und turbulente Strömungen

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Prandtl - Führer durch die Strömungslehre

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Das Kapitel Instabilitäten und turbulente Strömungen ist Teil des Lehrbuches und Nachschlagewerkes H. Oertel jr. (Hrsg.) Prandtl-Führer durch die Strömungslehre. Es werden ergänzend zu Prandtls Grundlagenkapitel der Dynamik zäher Flüssigkeiten das Einsetzen der Turbulenz mit der linearen Stabilitätsanalyse zwei- und dreidimensionaler Grenzschichten, der Übergangsbereich zur Turbulenz und der Bereich ausgebildeter Turbulenz mit der Klassifikation turbulenter Strömungen behandelt. Das Kapitel gibt einen Ausblick auf neue Entwicklungen und theoretische Ansätze der komplexen nicht linearen Wechselwirkungen von kleinen und großen Turbulenzstrukturen und gibt Hinweise auf mögliche Wege zur Entwicklung einer universellen Turbulenztheorie.

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Weiterführende Literatur

  • Alfredsson, P.H., Bakchinov, A.A., Kozlov, V.V., Matsubara, M.: Laminar-Turbulent transition at a high level of a free stream turbulence. In: Duck, P.W., Hall, P. (Hrsg.) Proceedings IUTAM Symposium on Nonlinear Instability and Transition in Three-Dimensional Boundary Layers, Bd. 35, S. 423–436. Kluwer, Dordrecht (1996)

    Chapter  Google Scholar 

  • Barenblatt, G.I.: Scaling laws for fully developed Turbulent Shear flows. Part 1. Basic hypothesis and analysis. J. Fluid Mech. 248, 513–520 (1993)

    Google Scholar 

  • Batchelor, G.K.: Recent developments in turbulence research. In: Levy, H. (Hrsg.) Proceedings of the 7th International Congress for Applied Mechanics, London (1948)

    Google Scholar 

  • Batchelor, G.K.: Computation of the energy spectrum in homogeneous two-dimensional turbulence. Phys. Fluids 12, II, II–233–II–239 (1969)

    Google Scholar 

  • Batchelor, G.K., Townsend, A.A.: The nature of turbulent motion at large wave numbers. In: Proceedings of the Royal Society of London A, Bd. 199, S. 238–255. Royal Society, London (1949)

    Google Scholar 

  • Boiko, A.V., Grek, G.R., Dovgal, A.V., Kozlov, V.V.: The Origin of Turbulence in Near-Wall Flows. Springer, Berlin/Heidelberg (2002)

    Book  MATH  Google Scholar 

  • Borgas, M.S.: A comparison of intermittent models in turbulence. Phys. Fluids A 4, 2055–2061 (1992)

    Article  MATH  Google Scholar 

  • Brown, F.N.M.: A combined visual and hot-wire anemometer investigation of boundary-layer transition. AIAA J. 6(1), 29–36 (1957)

    Google Scholar 

  • Carnevale, G.F., McWilliams, J.C., Pomeau, Y., Weiss, J.B., Young, W.R.: Evolution of vortex statistics in two-dimensional turbulence. Phys. Rev. Lett. 66, 2735–2737 (1991)

    Article  Google Scholar 

  • Champagne, F.H.: The fine-scale structure of the turbulent velocity field. J. Fluid Mech. 86, 67–108 (1978)

    Article  Google Scholar 

  • Chandrasekhar, S.: Hydrodynamics and Hydromagnetic Stability. Clarendon Press, Oxford (1961)

    MATH  Google Scholar 

  • Chen, S., Doolen, G.D.: Lattice Boltzmann method for fluid flow. Annu. Rev. Fluid Mech. 23, 539–600 (1991)

    Google Scholar 

  • Chorin, A.J.: Vorticity and Turbulence. Springer, Berlin/Heidelberg/New York (1994)

    Book  MATH  Google Scholar 

  • Drazin, P.G., Reid, W.H.: Hydrodynamic Stability. Cambridge University Press, Cambridge/New York (2004)

    Book  MATH  Google Scholar 

  • Dryden, H.L.: Recent advances in the mechanics of boundary layer flow. Adv. Appl. Mech. 1, 1–40 (1948)

    Article  MathSciNet  Google Scholar 

  • Emmons, H.W.: The Laminar-Turbulent transition in a boundary layer – Part I. J. Aeronaut. Sci. 18, 490–498 (1951)

    Article  MathSciNet  MATH  Google Scholar 

  • Falco, R.E.: The Production of Turbulence Near a Wall. 80-1356, AIAA (1980)

    Google Scholar 

  • Feigenbaum, M.J.: Quantitative universality for a class of nonlinear transformations. J. Stat. Phys. 19, 25 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  • Frisch, U.: Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press, Cambridge (1995)

    Book  MATH  Google Scholar 

  • Frisch, U., Vergassola, M.: A prediction of the multifractal model: the intermediate dissipation range. Europhys. Lett. 14, 439–444 (1991)

    Article  Google Scholar 

  • Frisch, U., Sulem, P.L.: Numerical simulation of the inverse cascade in two-dimensional turbulence. Phys. Fluids 27(8), 1921–1923 (1984)

    Article  MATH  Google Scholar 

  • Gagne, Y., Castaing, B.: Une Représentation Universelle sans Invariance Globale d'Échelle des Spectres d'Énergie en Turbulence d'Éveloppée. Comptes rendus de l'Académie des Sciences Paris 312, 441 (1991)

    Google Scholar 

  • Gaster, M.: A note on the relation between temporally-increasing and spatially-increasing disturbances in hydrodynamic stability. J. Fluid Mech. 14, 222–224 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  • Grant, H.L., Stewart, R.W., Moilliet, A.: Turbulence spectra from a tidal channel. J. Fluid Mech. 12, 241–263 (1962)

    Article  MATH  Google Scholar 

  • Grossmann, S.: The onset of shear flow turbulence. Rev. Mod. Phys. 72(2), 603–618 (2000)

    Article  Google Scholar 

  • Heisenberg, W.: Über Stabilität und Turbulenz von Flüssigkeitsströmen. Annalen der Physik, 74 of 4, S. 577–627. Barth, Leipzig (1924)

    Google Scholar 

  • Herbert, T., Bertolotti, F.P.: Stability analysis of nonparallel boundary layers. Bull. Am. Phys. Soc. 32, 2079–2806 (1987)

    Google Scholar 

  • Hinze, J.O.: Turbulence. McGraw-Hill, New York (1987)

    Google Scholar 

  • von Kármán, T.: Progress in statistical theory of turbulence. In: Proceedings of the National Academy of Sciences of the United States of America, Bd. 34, S. 530–539. Academy, Washington, DC (1948)

    Google Scholar 

  • Klebanoff, P.S.: Characteristics of Turbulence in a Boundary Layer with Zero Pressure Gradient. Report 1247, NACA (1955)

    Google Scholar 

  • Klebanoff, P.S., Tidstrom, K.D., Sargent, L.M.: The three-dimensional nature of boundary layer instability. J. Fluid Mech. 12, 1–34 (1962)

    Article  MATH  Google Scholar 

  • Kolmogorov, A.N.: Die lokale Struktur der Turbulenz in einer inkompressiblen zähen Flüssigkeit bei sehr großen Reynolds-Zahlen. Dokl. Akad. Wiss. USSR 30, 301–305 (1941)

    Google Scholar 

  • Kolmogorov, A.N.: A refinement of previous hypothesis concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds numbers. J. Fluid Mech. 13, 82–85 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  • Kraichnan, R.H.: Inertial ranges in two-dimensional turbulence. Phys. Fluids 10, 1417–1423 (1967)

    Article  Google Scholar 

  • Kurien, S., Sreenivasan, K.R.: Measures of anisotropy and the universal properties of turbulence. In: New Trends in Turbulence, Les Houches, S. 53–111 (2001)

    Google Scholar 

  • Lesieur, M.: Turbulence in Fluids. Springer, Berlin, Heidelberg (2008)

    Book  MATH  Google Scholar 

  • Lesieur, M., Metais, O.: New trends in large Eddy simulation of turbulence. Annu. Rev. Fluid Mech. 28, 45–82 (1996)

    Article  MathSciNet  Google Scholar 

  • Lin, C.C.: On the stability of two-dimensional parallel flows. Q. Appl. Math. 3, 117–142 (1945)

    Article  MathSciNet  MATH  Google Scholar 

  • Lin, C.C.: The Theory of Hydrodynamic Stability, Bd. 5. Cambridge University Press, Cambridge (1955)

    MATH  Google Scholar 

  • Lugt, H.J.: Vortex Flow in Nature and Technology. Wiley, New York (1983)

    Google Scholar 

  • McWilliams, J.C.: The vortices of two-dimensional turbulence. J. Fluid Mech. 219, 361–385 (1990)

    Article  Google Scholar 

  • Moin, P., Mahesh, K.: Direct numerical simulation: a tool in turbulence research. Annu. Rev. Fluid Mech. 30, 539–578 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  • Moffatt, H.K.: Degrees of knotedness of tangles vortex lines. J. Fluid Mech. 36, 117–129 (1969)

    Article  MATH  Google Scholar 

  • Monin, A.S., Yaglom, A.M.: Statistical Fluid Mechanics: Mechanics of Turbulence II. MIT, Cambridge (1975)

    Google Scholar 

  • Narasimha, R.: The Laminar-turbulent transition zone in the boundary layer. Prog. Aerosp. Sci. 22, 29–80 (1985)

    Article  Google Scholar 

  • Nikuradse, J.: Gesetzmäßigkeit der turbulenten Strömung in glatten Rohren. Forschungsheft 356, VDI, Berlin (1932)

    Google Scholar 

  • Obukhov, A.: Some specific features of atmospheric turbulence. J. Fluid Mech. 13, 77–81 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  • Oertel, H., Jr., Delfs, J.: Strömungsmechanische Instabilitäten. Springer, Berlin/Heidelberg (1996); Universitätsverlag, Karlsruhe (2005)

    Google Scholar 

  • Orr, W.M.F.: The stability or instability of the steady motions of a perfect liquid and a viscous liquid. Proc. R. Ir. Acad. A 27, 69–138 (1907)

    MATH  Google Scholar 

  • Orszag, S.A.: Accurate solution of the Orr-Sommerfeld stability equation. J. Fluid Mech. 50, 684–703 (1971)

    Article  MATH  Google Scholar 

  • Paret, J., Tabeling, P.: Experimental observation of the two-dimensional inverse energy cascade. Phys. Rev. Lett. 79, 4162–4165 (1997)

    Article  Google Scholar 

  • Pope, S.B.: Turbulent Flows. Cambridge University Press, Cambridge (2000)

    Book  MATH  Google Scholar 

  • Rayleigh, J.W.S.: On convection currents in a horizontal layer of fluid, when the higher temperature is on the under side. Philos. Mag. Ser. 32 (6), 529–546 (1916)

    Article  MATH  Google Scholar 

  • Reynolds, O.: An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels. Philos. Trans. R. Soc. Lond. 174, 935–982 (1883)

    MATH  Google Scholar 

  • Reynolds, O.: On the dynamic theory of incompressible viscous fluids and the determination of the criterion. Philos. Trans. R. Soc. Lond. 186, 123–164 (1894)

    Google Scholar 

  • Richardson, L.F.: The supply of energy from and to atmospheric Eddies. Proc. R. Soc. Lond. A 97, 354–373 (1920)

    Article  Google Scholar 

  • Ruelle, D., Takens, F.: On the nature of turbulence. Commun. Math. Phys. 20, 167–192 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  • Schubauer, G.B., Skramstad, H.K.: Laminar boundary-layer oscillations and stability of Laminar flow. J. Aeronaut. Sci. 14 (2), 69–78, (1947)

    Article  Google Scholar 

  • Sommerfeld, A.: Ein Beitrag zur hydrodynamischen Erklärung der turbulenten Flüssigkeitsbewegung. In: Castelnuovo, G. (Hrsg.) Atti del IV Congresso internazionale dei matematici, Roma, S. 116–124 (1908)

    Google Scholar 

  • Somméria, J.: Experimental study of the two-dimensional inverse energy cascade in a square box. J. Fluid Mech. 170, 139–168 (1986)

    Article  Google Scholar 

  • Speziale, C.G.: Analytical methods for the development of Reynolds stress closures in turbulence. Annu. Rev. Fluid Mech. 23, 107–157 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  • Sreenivasan, K.R.: Fractals and multifractals in fluid mechanics. Annu. Rev. Fluid Mech. 23, 539–600 (1991)

    Article  Google Scholar 

  • Sreenivasan, K.R.: On the universality of the Kolmogorov constant. Phys. Fluids 7, 2778–2784 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  • Sreenivasan, K.R., Donnelly, R.J.: Role of cryogenic helium in classical fluid dynamics: basic research and model testing. Adv. Appl. Mech. 37, 239–275 (2000)

    Article  Google Scholar 

  • Stolovitzky, G., Kailasnath, P., Sreenivasan, K.R.: Kolmogorov's refined similarity hypotheses. Phys. Rev. Lett. 69, 1178 (1992)

    Google Scholar 

  • Stuart, J.T.: Unsteady boundary layers. In: Rosenhead, L. (Hrsg.) Laminar Boundary Layers, S. 349–408. Clarendon Press, Oxford (1963)

    Google Scholar 

  • Tabeling, P.: Two-dimensional turbulence: a physicist's approach. Phys. Rep. 362, 1–62 (2002)

    Google Scholar 

  • Taylor, G.I.: Stability of a viscous liquid contained between two rotating cylinders. Philos. Trans. R. Soc. Lond. A 223, 289–343 (1923)

    Article  MATH  Google Scholar 

  • Taylor, G.I.: Statistical theory of turbulence, Parts 1–4. Proc. R. Soc. Lond. A 151, 421–478 (1935)

    Article  MATH  Google Scholar 

  • Taylor, G.I.: Correlation measurements in a turbulent flow through a pipe. Proc. R. Soc. Lond. A 157, 537–546 (1936)

    Article  Google Scholar 

  • Tollmien, W.: Über die Entstehung der Turbulenz. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, 21–44 (1929)

    Google Scholar 

  • Voth, G.A., Satyanarayanan, K., Bodenschatz, E.: Lagrangian acceleration measurements at large Reynolds numbers. Phys. Fluids 10, 2268–2280 (1998)

    Article  Google Scholar 

  • Yeung, P.K.: Lagrangian investigations of turbulence. Rev. Fluid Mech. 34, 115–142 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  • Zagarola, M.V., Smits, A.J.: Scaling of turbulent pipe flow. J. Fluid Mech. 373, 33–79 (1998)

    Article  MATH  Google Scholar 

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Sreenivasan, K.R., Oertel, H. (2021). Instabilitäten und turbulente Strömungen. In: Oertel jr., H. (eds) Prandtl - Führer durch die Strömungslehre. Springer Reference Technik . Springer Vieweg, Wiesbaden. https://doi.org/10.1007/978-3-658-08933-7_7-2

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  • DOI: https://doi.org/10.1007/978-3-658-08933-7_7-2

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Chapter history

  1. Latest

    Instabilitäten und turbulente Strömungen
    Published:
    04 January 2022

    DOI: https://doi.org/10.1007/978-3-658-08933-7_7-2

  2. Original

    Instabilitäten und turbulente Strömungen
    Published:
    22 April 2016

    DOI: https://doi.org/10.1007/978-3-658-08933-7_7-1