Skip to main content Accessibility help
×
Hostname: page-component-5c6d5d7d68-thh2z Total loading time: 0 Render date: 2024-08-20T01:02:19.738Z Has data issue: false hasContentIssue false

13 - Epilogue: a turbulence timeline

Published online by Cambridge University Press:  07 October 2011

Peter A. Davidson
Affiliation:
University of Cambridge
Yukio Kaneda
Affiliation:
Nagoya University
Keith Moffatt
Affiliation:
University of Cambridge
Peter A. Davidson
Affiliation:
University of Cambridge
Yukio Kaneda
Affiliation:
Nagoya University, Japan
Keith Moffatt
Affiliation:
University of Cambridge
Katepalli R. Sreenivasan
Affiliation:
New York University
Get access

Summary

To supplement the foregoing chapters, we offer below a table listing some key developments in turbulence research over the period covered by this book, i.e. roughly up to mid-1970s. Later developments involving massive computations, low-dimensional dynamics, the renormalization group, turbulence control, modern instrumentation, and so on, are not included; nor do we include such closely related areas as turbulent thermal convection, combustion, wave turbulence, or the vast field of applications in geophysics, astrophysics and plasma physics. Moreover, the table is ‘internal’ to the subject, in that we make no attempt to relate the events to developments in other scientific fields or to the wider historical context. Despite these limitations, it is our hope that the table, necessarily subjective to some extent, will provide a useful point of reference for the reader. We thank the authors of this book for their comments on the table, especially Professor R. Narasimha for the inspiration he provided.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Arnold, V.I. 1963. Proof of a theorem by A.N. Kolmogorov on the invariance of quasi-periodic motions under small perturbations of the Hamiltonian. Usp. Math. Nauk 18, 13–40.Google Scholar
Barenblatt, G.I. 2003. Scaling. Cambridge University Press. This book is a summary and accessible account of many years of work of the author with Ya.B. Zeldovich.CrossRefGoogle Scholar
Batchelor, G.K. 1953. The Theory of Homogeneous Turbulence. Cambridge University Press. Besides systematizing the then-available statistical theory of turbulence, the book brought Kolmogorov's work to the attention of the Western world. For a fuller account of Batchelor's contributions, see the accompanying article by H.K. Moffatt.Google Scholar
Batchelor, G.K. 1959. Small-scale variation of convected quantities like temperature in turbulent fluid. Part 1. General discussion and the case of small conductivity. J. Fluid Mech. 5, 113–33.CrossRefGoogle Scholar
Batchelor, G.K. 1969. Computation of the energy spectrum in homogeneous two-dimensional turbulence. Phys. Fluids Suppl. 11 233–239.Google Scholar
Batchelor, G.K. & Proudman, I. 1956. The large-scale structure of homogeneous turbulence. Phil. Trans. Roy. Soc. Lond. A 248, 369–405.CrossRefGoogle Scholar
Batchelor, G.K. & Townsend, A.A. 1949. The nature of turbulent motion at large wave-numbers. Proc. Roy. Soc. Lond. A 199, 238–55.CrossRefGoogle Scholar
Blasius, H. 1913. Das Ähnlichkeitsgesetz bei Reibúngsvorgängen in Flüssigkeiten. Forschungsarbeiten auf dem Gebiete des Ingenieurwesens no. 131, Berlin.
Boussinesq, J. 1870. Essai théorique sur les lois trouvées expérimentalement par M. Bazin pour l'écoulment unifrome de l'eau dans les canaux découverts. C.R. Acad. Sci. Paris 71, 389–393.Google Scholar
Brown, G.L. & Roshko, A. 1974. Density effect and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775–816.CrossRefGoogle Scholar
Burgers, J.M. 1948. A mathematical model illustrating the theory of turbulence. Adv. Appl. Mech. 1, 171–199. For a brief description of Burgers' work, see the accompanying article by K.R. Sreenivasan.CrossRefGoogle Scholar
Corrsin, S. 1951. On the spectrum of isotropic temperature fluctuations in isotropic turbulence. J. Appl. Phys. 22, 469–473. For a fuller account of Corrsin's contributions, see the accompanying article by C., Meneveau & J.J., Riley.CrossRefGoogle Scholar
Corrsin, S. & Kistler, A.L. 1955. The free-stream boundaries of turbulent flows. NASA Tech. Rep. 1244.
Dhawan, S. 1952. Direct measurement of skin friction. NASA Tech. Note 2567. For a fuller account of Dhawan's contributions, see the accompanying article by R., Narasimha.
Eiffel, G. 1912. Sur la résistance des sphéres dans l'air en mouvement. Compt. Rend. 155, 1587–1599.Google Scholar
Emmons, H.W. 1951. The laminar turbulent transition in a boundary layer. J. Aero Sci. 18, 490–498.CrossRefGoogle Scholar
Favre, A., 1965. Equations des gaz turbulents compressibles. J. de Mécanique 4, 361–390.Google Scholar
Feynman, R.P. 1955. Application of quantum mechanics to liquid helium. Prog. Low Temp. Phys. 1, 17–53.CrossRefGoogle Scholar
Grant, H.L., Stewart, R.W. & Moilliet, A. 1962. Turbulence spectra from a tidal channel. J. Fluid Mech., 12, 263–272. Obukhov verified the equivalent result of the 2/3 power for the second-order structure function in 1949, using the data of K. Gödecke, obtained in 1935.CrossRefGoogle Scholar
Hagen, G. 1939. Über die Bewegnung des Wassers in engen zylindrichen Röhren. Pogg. Ann. 46, 423–442.Google Scholar
Hinze, J.O. 1959. Turbulence. An Introduction to its Mechanisms and Theory.McGraw Hill Co.New York.Google Scholar
Hopf, E. 1948. A mathematical example displaying the features of turbulence. Commun. Pure Appl. Math. 1, 303–322.CrossRefGoogle Scholar
Kármán, Th. von 1930. Mechanische Ahnlichkeit und Turbulenz. Nach. Ges. Wiss. Göttingen, Math.-Phys. Kl, 58–76. For various nuances of shared credit for the log-law between Kármán and Prandtl, see the accompanying article by A., Leonard & N., Peters on Kármán and that on Prandtl by E., Bodenschatz & M., Eckert in this volume.Google Scholar
Kármán, Th. von & Howarth, L. 1938. On the statistical theory of isotropic turbulence. Proc. Roy. Soc. Lond. A164, 192–215. For scientific exchanges between Kármán and Taylor on this problem, see the accompanying article by A., Leonard & N., Peters on Kármán and that on Taylor by K.R., Sreenivasan in this volume.CrossRefGoogle Scholar
Keller, L.V. & Friedman, A.A. 1924. Differentialgleichung für die turbulente Bewegung einer kompressiblen Flüssigkeit. Proc. 1st Intern. Cong. Appl. Mech.Delft, pp. 395–405.Google Scholar
Kelvin, Lord. 1887. On the propagation of laminar motion through a turbulently moving inviscid liquid. Phil. Mag. 24, 342–353.Google Scholar
King, L.V. 1914. On the convection of heat from small cylinders in a stream of fluid: determination of the convection constants of small platinum wires, with applications to hot-wire anemometry. Proc. Roy. Soc. 90, 563–570.CrossRefGoogle Scholar
Kline, S.J., Reynolds, W.C., Schraub, F.A. & Runstadler, P.W. 1967. The structure of turbulent boundary layers. J. Fluid Mech. 30, 741–773.CrossRefGoogle Scholar
Kolmogorov, A.N. 1941. The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 9–13. (reprinted in Proc. Roy. Soc. Lond.A434, 9–13). The main results were rederived independently by Onsager: ‘The distribution of energy in turbulence’. Phys. Rev.68, 286 (1945); by Heisenberg: ‘Zur statistichen Theorie der Turbulenz’. Z. Phys.124, 628–657 (1948) and Proc. Roy. Soc. Lond. A.195, 402–406 (1948); and by von Weizsäcker: ‘Das Spektrum der Turbulenz bei grossen Reynoldschen Zahlen’. Zeit. f. Phys.124, 614–627 (1948). Kolmogorov followed up this seminal paper of his by two others on different aspects of the same topic: they appeared in the same journal. For a more complete list of references, and for a discussion of further contributions by Kolmogorov, see the accompanying article by G., Falkovich.Google Scholar
Kolmogorov, A.N. 1942. Equations of turbulent motion of an incompressible fluid. Izv. AN SSSR. Ser. Fiz. 6, 56–58.
Kolmogorov, A.N. 1954. On the conservation of conditionally periodic motions for a small change in Hamilton's function. Dokl. Akad. Nauk SSSR 98, 525–530.Google Scholar
Kolmogorov, A.N. 1962. A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. J. Fluid Mech. 13, 82–85.CrossRefGoogle Scholar
Kovasznay, L.S.G., Kibens, V. & Blackwelder, R.F. 1970. Large scale motion in the intermittent region of a turbulent boundary layer. J. Fluid Mech. 41, 283–325.CrossRefGoogle Scholar
Kraichnan, R.H. 1959. The structure of isotropic turbulence at very high Reynolds numbers. J. Fluid Mech. 5, 497–543. For a fuller account of Kraichnan's work, including his passive scalar work not included here, see the accompanying article by G.L., Eynik & U., Frisch.CrossRefGoogle Scholar
Kraichnan, R.H. 1965. Lagrangian-history closure approximation for turbulence. Phys. Fluids 8, 575–598.CrossRefGoogle Scholar
Kraichnan, R.H. 1967. Inertial ranges in two-dimensional turbulence. Phys. Fluids 10, 1417–1423.CrossRefGoogle Scholar
Landau, L.D. 1944. On the problem of turbulence. Akad. Nauk. 44 339–342.Google Scholar
Landau, L.D. & Lifschitz, E.M. 1944. Fluid Mechanics (published in English by Pergamon Press in 1963). The book contains other important contributions to turbulence, not touched upon here.
Leray, J. 1934. Sur le mouvement d'un liquide visqueux emplissant l'espace. Acta Math. 63, 193–248. The work on weak solutions was extended by W. Hopf in 1951 and O.A. Ladyzhenskaya in late 1950s. The latter has summarized the essentials in 2003 as: ‘Sixth problem of the millennium: Navier–Stokes equations, existence and smoothness’, Usp. Mat. Nauk58, 45–78.CrossRefGoogle Scholar
Lighthill, M.J. 1952. On sound generated aerodynamically. Proc. Roy. Soc. Lond. A 211, 564–587. Subsequent papers of Lighthill on this topic followed in the same journal.CrossRefGoogle Scholar
Lilly, D.K., 1967. The representation of small-scale turbulence in numerical simulation experiments. Proc. of the IBM Sci. Comp. Symp. on Env. Sci., IBM-Form No. 320–1951.
Lorenz, E.N. 1963. Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130–141.2.0.CO;2>CrossRefGoogle Scholar
Mandelbrot, B.B. 1974. Intermittent turbulence in self-similar cascades; divergence of high moments and dimension of the carrier. J. Fluid Mech. 62, 331–358. Mandelbrot (1983) contains a vivid description of his work on turbulence.CrossRefGoogle Scholar
Mandelbrot, B.B. 1983. The Fractal Geometry of Nature. W.H. Freeman and Co.New York.Google Scholar
Millionshchikov, M.D. 1939. Decay of homogeneous isotropic turbulence in viscous incompressible fluids. Dokl. AN SSSR, 22, 236–240.Google Scholar
Moffatt, H.K. 1969. The degree of knottedness of tangled vortex lines. J. Fluid Mech. 35, 117–129.CrossRefGoogle Scholar
Monin, A.S. & Yaglom, A.M. 1971. Statistical Fluid Mech., vol. I. MIT Press (Russian edition 1965)Google Scholar
Monin, A.S. & Yaglom, A.M. 1975. Statistical Fluid Mech., vol. II. MIT Press (Russian edition 1965). The two volumes made a valiant effort to bring together much of the knowledge available at that time.Google Scholar
Moreau, J.-J. 1961. Constants d'un ilôt tourbillonaire en fluide parfait barotrope. Comptes Rendus, Acad. des Sciences 252, 2810–2813.Google Scholar
Moser, J.K. 1962. On invariant curves of area-preserving mappings of an annulus. Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II. 1, 1–20.Google Scholar
Nikuradse, J. 1932. Gesetzmässigkeiten der turbulenten Strömung in glatten Röhren. VDI-Forschungsheft no. 356. The work on rough pipes appeared in 1933 as: Strömungs gesetze in rauhen Röhren, in VDI-Forschungsheft no. 361.Google Scholar
Obukhov, A.M. 1941. Energy distribution in the spectrum of a turbulent flow. Izv. AN SSSR Ser. Geogr. Geofiz. 5, 453–466.Google Scholar
Obukhov, A.M. 1949. Structure of temperature fields in a turbulent flow. Izv. AN SSSR Ser. Geogr. Geofiz. 13, 58–69.Google Scholar
Obukhov, A.M. 1962. Some specific features of atmospheric turbulence. J. Fluid Mech. 13, 77–81.CrossRefGoogle Scholar
Onsager, L. 1949. Statistical hydrodynamics. Neuvo Cimento 6, Suppl. no. 2, 279–287. This article is about both the statistical equilibria of point vortices in two dimensions and the energy spectrum in three-dimensional turbulence. For a fuller account of Onsager's turbulence work, see G.L., Eyink, & K.R., Sreenivasan ‘Onsager and the theory of hydrodynamic turbulence’. Rev. Mod. Phys.78, 87–135 (2006).CrossRefGoogle Scholar
Orr, W.M. 1907. The stability or instability of the steady motions of a perfect liquid and of a viscous liquid. Proc. Roy. Irish Acad. A 27, 9–68; 69–138.Google Scholar
Orszag, S.A. 1970. Analytical theories of turbulence. J. Fluid Mech. 41, 363–386.CrossRefGoogle Scholar
Prandtl, L. 1904. Über Flüssigkeitsbewegnung bei sehr kleiner Reibung. In Verhandlungen des dritten Internationalen Mathematiker-Kongresses in Heidelberg 1904, edited by A., Krazer, Teubner, , Leipzig, (1905), 574–584. (English translation in Early Developments of Modern Aerodynamics, edited by Ackroyd, J.A.K., B.P., Axcell & A.I., Ruban, Butterworth–Heinemann, Oxford, UK (2001), pp. 77–87.) For several other lasting contributions to turbulence by Prandtl and his school, see the accompanying article by E., Bodenschatz & M., Eckert, this volume.Google Scholar
Prandtl, L. 1914. Der Luftwiderstand von Kugelin. Nachrichten der Gesselschaft der Wissenschaften zu Göttingen, Math.-Phys. Klasse, 177–190.
Prandtl, L., 1925. Bericht uber Untersuchungen zur ausgebildeten Turbulenz. ZAMM 5, 136–139.Google Scholar
Prandtl, L. 1932. Zur turbulenten Strömung in Rohren und längs Platten. Ergebnisse der Aerodynamischen Versuchsanstalt zu Göttingen. 4, 18–29.Google Scholar
Prandtl, L. 1945 Über die Rolle der Zähigkeit im Mechanismus der ausgebildete Turbulenz (The role of viscosity in the mechanism of developed turbulence). Göttinger Archiv des DLR, Göttingen 3712.
Proudman, I. & Reid, W.H. 1954. On the decay of a normally distributed and homogeneous turbulent velocity field. Phil. Trans. Roy. Soc. Lond. A 247, 163–189.CrossRefGoogle Scholar
Rao, K.N., Narasimha, R. & Badri Narayanan, M.A. 1971. The ‘bursting’ phenomenon in a turbulent boundary layer. J. Fluid Mech. 48, 339–352.CrossRefGoogle Scholar
Rayleigh, Lord. 1892. On the question of stability of the flow of fluids. Phil. Mag. 34, 59–70.CrossRefGoogle Scholar
Reynolds, O. 1874. On the extent and action of the heating surface for steam boilers. Proc. Manchester Lit. Phil. Soc. 14, 7–12. For Reynolds' contributions to turbulence and his place in history, see the article by B.E., Launder & J.D., Jackson, this volume.Google Scholar
Reynolds, O. 1883. 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. Phil. Trans. Roy. Soc. Lond. 174, 935–982.CrossRefGoogle Scholar
Reynolds, O. 1895. On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Phil. Tran. Roy. Soc. Lond. 86, 123–164.CrossRefGoogle Scholar
Richardson, L.F. 1922. Weather Prediction by Numerical Methods.Cambridge University Press. For Richardson's other contributions to turbulence and his eclectic work, see the article by R., Benzi, this volume.Google Scholar
Richardson, L.F. 1926, Atmospheric diffusion shown on a distance–neighbour graph. Proc. Roy. Soc. Lond. A 110, 709–737.CrossRefGoogle Scholar
Ruelle, D. & Takens, F. 1971. On the nature of turbulence. Commun. Math. Phys. 20, 167–192.CrossRefGoogle Scholar
Saffman, P.G. 1967. The large-scale structure of homogeneous turbulence. J. Fluid Mech. 27, 581–593. For Saffman's other contributions to turbulence, see the article by D.I., Pullin & D.I., Meiron, this volume.CrossRefGoogle Scholar
Saint-Venant, A.J.C. 1850. Mémoire sur des formulaes nouvelles pour la solution des problémes relatifs aux eaux courantes. C. R. Acad. Sci. Paris 31, 283–286.Google Scholar
Schubauer, G.B. & Skramstad, H.K. 1947. Laminar boundary-layer oscillations and stability of laminar flow. J. Aero. Sci. 14, 69–76.CrossRefGoogle Scholar
Smagorinsky, J. 1963. General circulation experiments with the primitive equations, I. The basic experiment. Monthly Weather Rev. 91, 99–164.2.3.CO;2>CrossRefGoogle Scholar
Sommerfeld, A. 1908. Ein Beitrag zur hydrodynamischen Erklärung der turbulenten Flüssigkeitsbewegungen. Proc. 4th Internat. Cong. Math. Rome, 3, 116–124.Google Scholar
Steenbeck, M., Krause, F. & Radler, K.-H. 1966. Berechnung der mittleren LorentzFeldstarke fur ein elektrisch leitendes Medium in turbulenter, durch CoriolisKrafte beeinflusster Bewegung. 2. Naturf. 21a, 369–376.Google Scholar
Tatsumi, T. 1957. The theory of decay process of incompressible isotropic turbulence. Proc. Roy. Soc. Lond. A 239, 16–45.CrossRefGoogle Scholar
Taylor, G.I. 1915. Eddy motion in the atmosphere. Phil. Trans. Roy. Soc. Lond. A 215, 1–26.CrossRefGoogle Scholar
Taylor, G.I. 1921. Diffusion by continuous movements. Proc. Lond. Math. Soc. 20, 196–212.Google Scholar
Taylor, G.I. 1923. Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. Roy. Soc. Lond. A 223, 289–343.CrossRefGoogle Scholar
Taylor, G.I. 1935. Statistical theory of turbulence. I. Proc. Roy. Soc. Lond. A 151, 421–444. Subsequent parts II–V on this topic appeared in the same journal. For a full list of references and a more complete description of Taylor's contributions, see the article in this volume by K.R., Sreenivasan.CrossRefGoogle Scholar
Taylor, G.I. 1937. Flow in pipes and between parallel planes. Proc. Roy. Soc. Lond. A 159, 496–506.CrossRefGoogle Scholar
Taylor, G.I. 1938. The spectrum of turbulence. Proc. Roy. Soc. Lond. A 164, 476–481.CrossRefGoogle Scholar
Townsend, A.A. 1956. The Structure of Turbulent Shear Flow. Cambridge University Press. Townsend's book emphasized the presence of structure within statistical description. See the article by I., Marusic & T., Nichols, this volume, for an elaboration of this aspect and the other work of Townsend. Similar recognitions of the importance of flow structures were made by others, e.g., T., Theodorsen, ‘Mechanism of turbulence’, in Proc. Second Midwestern Conf. on Fluid Mech. Ohio State University, Columbus, Ohio, pp. 1–19 (1952). Townsend initiated the modeling of small scales through vortex sheets and tubes in ‘On the fine-scale structure of turbulence’, Proc. Roy. Soc. A, 208, 534–642 (1951).Google Scholar
Tollmien, W. 1929. Über die Entstehung der Turbulenz. Nachr. Ges. Wiss. Göttingen Math-Phys. Kl, II, 21–44Google Scholar
Ueda, Y. 1970. In 1961, Ueda posed a mathematical model on an analog computer that displayed chaotic dynamics. However, this work was not published until 1970; see Y., Ueda, C., Hayashi, N., Akamatsu, & H., Itakura, On the behavior of self-oscillatory systems with external force. Electronics & Communication in Japan 53, 31–39 (1970).Google Scholar
Yaglom, A.M. 1949. Local structure of the temperature field in a turbulent flow. Dokl. Akad. Nauk. SSSR 69, 743–746.Google Scholar
Yeh, Y. & Cummins, H.Z. 1964. Localized fluid flow measurements with an He–Ne laser spectrometer. Appl. Phys. Lett. 4, 176–178.CrossRefGoogle Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×