Zusammenfassung
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
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)
Barenblatt, G.I.: Scaling laws for fully developed Turbulent Shear flows. Part 1. Basic hypothesis and analysis. J. Fluid Mech. 248, 513–520 (1993)
Batchelor, G.K.: Recent developments in turbulence research. In: Levy, H. (Hrsg.) Proceedings of the 7th International Congress for Applied Mechanics, London (1948)
Batchelor, G.K.: Computation of the energy spectrum in homogeneous two-dimensional turbulence. Phys. Fluids 12, II, II–233–II–239 (1969)
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)
Boiko, A.V., Grek, G.R., Dovgal, A.V., Kozlov, V.V.: The Origin of Turbulence in Near-Wall Flows. Springer, Berlin/Heidelberg (2002)
Borgas, M.S.: A comparison of intermittent models in turbulence. Phys. Fluids A 4, 2055–2061 (1992)
Brown, F.N.M.: A combined visual and hot-wire anemometer investigation of boundary-layer transition. AIAA J. 6(1), 29–36 (1957)
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)
Champagne, F.H.: The fine-scale structure of the turbulent velocity field. J. Fluid Mech. 86, 67–108 (1978)
Chandrasekhar, S.: Hydrodynamics and Hydromagnetic Stability. Clarendon Press, Oxford (1961)
Chen, S., Doolen, G.D.: Lattice Boltzmann method for fluid flow. Annu. Rev. Fluid Mech. 23, 539–600 (1991)
Chorin, A.J.: Vorticity and Turbulence. Springer, Berlin/Heidelberg/New York (1994)
Drazin, P.G., Reid, W.H.: Hydrodynamic Stability. Cambridge University Press, Cambridge/New York (2004)
Dryden, H.L.: Recent advances in the mechanics of boundary layer flow. Adv. Appl. Mech. 1, 1–40 (1948)
Emmons, H.W.: The Laminar-Turbulent transition in a boundary layer – Part I. J. Aeronaut. Sci. 18, 490–498 (1951)
Falco, R.E.: The Production of Turbulence Near a Wall. 80-1356, AIAA (1980)
Feigenbaum, M.J.: Quantitative universality for a class of nonlinear transformations. J. Stat. Phys. 19, 25 (1978)
Frisch, U.: Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press, Cambridge (1995)
Frisch, U., Vergassola, M.: A prediction of the multifractal model: the intermediate dissipation range. Europhys. Lett. 14, 439–444 (1991)
Frisch, U., Sulem, P.L.: Numerical simulation of the inverse cascade in two-dimensional turbulence. Phys. Fluids 27(8), 1921–1923 (1984)
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)
Gaster, M.: A note on the relation between temporally-increasing and spatially-increasing disturbances in hydrodynamic stability. J. Fluid Mech. 14, 222–224 (1962)
Grant, H.L., Stewart, R.W., Moilliet, A.: Turbulence spectra from a tidal channel. J. Fluid Mech. 12, 241–263 (1962)
Grossmann, S.: The onset of shear flow turbulence. Rev. Mod. Phys. 72(2), 603–618 (2000)
Heisenberg, W.: Über Stabilität und Turbulenz von Flüssigkeitsströmen. Annalen der Physik, 74 of 4, S. 577–627. Barth, Leipzig (1924)
Herbert, T., Bertolotti, F.P.: Stability analysis of nonparallel boundary layers. Bull. Am. Phys. Soc. 32, 2079–2806 (1987)
Hinze, J.O.: Turbulence. McGraw-Hill, New York (1987)
Kármán, T. von: 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)
Kida, S., Takaoka, M.: Vortex reconnection. Annu. Rev. Fluid Mech. 26, 169–189 (2004)
Klebanoff, P.S.: Characteristics of Turbulence in a Boundary Layer with Zero Pressure Gradient. Report 1247, NACA (1955)
Klebanoff, P.S., Tidstrom, K.D., Sargent, L.M.: The three-dimensional nature of boundary layer instability. J. Fluid Mech. 12, 1–34 (1962)
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)
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)
Kraichnan, R.H.: Inertial ranges in two-dimensional turbulence. Phys. Fluids 10, 1417–1423 (1967)
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)
Lesieur, M.: Turbulence in Fluids. Springer, Berlin, Heidelberg (2008)
Lesieur, M., Metais, O.: New trends in large Eddy simulation of turbulence. Annu. Rev. Fluid Mech. 28, 45–82 (1996)
Lin, C.C.: On the stability of two-dimensional parallel flows. Q. Appl. Math. 3, 117–142 (1945)
Lin, C.C.: The Theory of Hydrodynamic Stability, Bd. 5. Cambridge University Press, Cambridge (1955)
Lugt, H.J.: Vortex Flow in Nature and Technology. Wiley, New York (1983)
McWilliams, J.C.: The vortices of two-dimensional turbulence. J. Fluid Mech. 219, 361–385 (1990)
Moin, P., Mahesh, K.: Direct numerical simulation: a tool in turbulence research. Annu. Rev. Fluid Mech. 30, 539–578 (1998)
Moffatt, H.K.: Degrees of knotedness of tangles vortex lines. J. Fluid Mech. 36, 117–129 (1969)
Monin, A.S., Yaglom, A.M.: Statistical Fluid Mechanics: Mechanics of Turbulence II. MIT, Cambridge (1975)
Narasimha, R.: The Laminar-turbulent transition zone in the boundary layer. Prog. Aerosp. Sci. 22, 29–80 (1985)
Nikuradse, J.: Gesetzmäßigkeit der turbulenten Strömung in glatten Rohren. Forschungsheft 356, VDI, Berlin (1932)
Obukhov, A.: Some specific features of atmospheric turbulence. J. Fluid Mech. 13, 77–81 (1962)
Oertel, H., Jr., Delfs, J.: Strömungsmechanische Instabilitäten. Springer, Berlin/Heidelberg (1996); Universitätsverlag, Karlsruhe (2005)
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)
Orszag, S.A.: Accurate solution of the Orr-Sommerfeld stability equation. J. Fluid Mech. 50, 684–703 (1971)
Paret, J., Tabeling, P.: Experimental observation of the two-dimensional inverse energy cascade. Phys. Rev. Lett. 79, 4162–4165 (1997)
Pope, S.B.: Turbulent Flows. Cambridge University Press, Cambridge (2000)
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)
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)
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)
Richardson, L.F.: The supply of energy from and to atmospheric Eddies. Proc. R. Soc. Lond. A 97, 354–373 (1920)
Ruelle, D., Takens, F.: On the nature of turbulence. Commun. Math. Phys. 20, 167–192 (1971)
Schubauer, G.B., Skramstad, H.K.: Laminar boundary-layer oscillations and stability of Laminar flow. J. Aeronaut. Sci. 14 (2), 69–78, (1947)
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)
Somméria, J.: Experimental study of the two-dimensional inverse energy cascade in a square box. J. Fluid Mech. 170, 139–168 (1986)
Speziale, C.G.: Analytical methods for the development of Reynolds stress closures in turbulence. Annu. Rev. Fluid Mech. 23, 107–157 (1991)
Sreenivasan, K.R.: Fractals and multifractals in fluid mechanics. Annu. Rev. Fluid Mech. 23, 539–600 (1991)
Sreenivasan, K.R.: On the universality of the Kolmogorov constant. Phys. Fluids 7, 2778–2784 (1995)
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)
Stolovitzky, G., Kailasnath, P., Sreenivasan, K.R.: Kolmogorov's refined similarity hypotheses. Phys. Rev. Lett. 69, 1178 (1992)
Stuart, J.T.: Unsteady boundary layers. In: Rosenhead, L. (Hrsg.) Laminar Boundary Layers, S. 349–408. Clarendon Press, Oxford (1963)
Tabeling, P.: Two-dimensional turbulence: a physicist's approach. Phys. Rep. 362, 1–62 (2002)
Taylor, G.I.: Stability of a viscous liquid contained between two rotating cylinders. Philos. Trans. R. Soc. Lond. A 223, 289–343 (1923)
Taylor, G.I.: Statistical theory of turbulence, Parts 1–4. Proc. R. Soc. Lond. A 151, 421–478 (1935)
Taylor, G.I.: Correlation measurements in a turbulent flow through a pipe. Proc. R. Soc. Lond. A 157, 537–546 (1936)
Tollmien, W.: Über die Entstehung der Turbulenz. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, 21–44 (1929)
Vainshtein, S.I., Sreenivasan, K.R.: Kolmogorow's refined similarity hypotheses. Phys. Rev. Lett. 73, 3085–3088 (1994)
Voth, G.A., Satyanarayanan, K., Bodenschatz, E.: Lagrangian acceleration measurements at large Reynolds numbers. Phys. Fluids 10, 2268–2280 (1998)
Yeung, P.K.: Lagrangian investigations of turbulence. Rev. Fluid Mech. 34, 115–142 (2002)
Zagarola, M.V., Smits, A.J.: Scaling of turbulent pipe flow. J. Fluid Mech. 373, 33–79 (1998)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 Springer Fachmedien Wiesbaden GmbH, ein Teil von Springer Nature
About this chapter
Cite this chapter
Sreenivasan, K.R., Oertel, H. (2022). Instabilitäten und turbulente Strömungen. In: Oertel jr., H. (eds) Prandtl - Führer durch die Strömungslehre. Springer Vieweg, Wiesbaden. https://doi.org/10.1007/978-3-658-27894-6_7
Download citation
DOI: https://doi.org/10.1007/978-3-658-27894-6_7
Published:
Publisher Name: Springer Vieweg, Wiesbaden
Print ISBN: 978-3-658-27841-0
Online ISBN: 978-3-658-27894-6
eBook Packages: Computer Science and Engineering (German Language)