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Mixing pp 11-36 | Cite as

A Philosophical and Historical Journey through Mixing and Fully-developed Turbulence

  • Marie Farge
  • Etienne Guyon
Part of the NATO ASI Series book series (NSSB, volume 373)

Abstract

Ten years ago, the first Advanced Institute held in Cargèse considered the topic of “Mixing and Disorder” and gathered physicists, mechanicians and chemical engineers to examine common features in the manifestations and applications of mixing. A similar project motivated the organisation of a new Institute in view of recent developments, some of which were induced by the first meeting. Some subjects which were very active at the time of the first meeting, such as hydrodynamic dispersion in porous media (soils, catalytic beds), have since matured enough to be excluded from the new Institute. Other, such as chaotic advection, have emerged. The recent developments emphasize the role of dynamical features, such as coherent vortices, in promoting mixing. We acknowledge modernity of the new treatments of turbulence and mixing, but at the same time we recognize their permanence in philosophy, science and technology from the early times of humanity.

Keywords

Coherent Structure Vortex Tube Vorticity Field Inertial Range Large Reynolds Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. /Aubin 1997/.
    D. Aubin, ‘A Cultural History of Catastrophes and Chaos: around the Institut des Hautes Etudes Scientifiques from 1958 through the 80s’, PhD thesis, Princeton University, 1997 Google Scholar
  2. /Batchelor 1969/.
    G. Batchelor, ‘Computation of the Energy Spectrum in Homogeneous Two-dimensional Turbulence’, Phys. Fluid, suppl. II, 12, pp. 233–239, 1969 Google Scholar
  3. /Batchelor 1953/.
    G. Batchelor, ‘Theory of homogeneous turbulence’, Cambridge University Press, 1953 Google Scholar
  4. /Boussinesq 1877/.
    J. Boussinesq, ‘Essai sur la théorie des eaux courantes’, Mémoires de l’Acad. Sci. Paris, Tome 23,1, pp. 30–46, 1877 Google Scholar
  5. /Cafarelli 1982/.
    L. Cafarelli, R Kohn and L. Nirenberg, ‘Partial regularity of suitable weak solutions of Navier-Stokes equations’, Comm. in Pure and Applied Math., 35, pp. 771–831, 1982 ADSCrossRefGoogle Scholar
  6. /Einstein 1914/.
    A. Einstein, ‘Méthode pour la détermination de valeurs statistiques d’observations concernant des grandeurs soumises à des fluctuations irrégulières’, Archive des Sciences Physiques et Naturelle, vol. 37, pp. 254–255, 1914 ADSGoogle Scholar
  7. /Farge et al. 1990/
    M. Farge, Y. Guezennec, C. M. Ho and C. Meneveau, ‘Continuous wavelet analysis of coherent structures’, CTR Summer Program, NASA-Ames and Stanford University, pp. 331–348, 1990 Google Scholar
  8. /Farge and Holschneider 1991/.
    M. Farge and M. Holschneider, ‘Interpretation of two-dimensional turbulence spectrum in terms of singularity in the vortex core’, Europhys. Lett, 15,7, pp. 737–743, 1991 ADSCrossRefGoogle Scholar
  9. /Farge 1992/.
    M. Farge, ‘Wavelet transforms and their applications to turbulence’, Ann. Rev. Fluid Mech., 24, pp. 395–457, 1992 MathSciNetADSCrossRefGoogle Scholar
  10. /Farge, Holschneider and Philipovitch 1992/.
    M. Farge, M. Holschneider and T. Philipovitch, ‘Formation et stabilité des structures cohérentes quasi singulières en turbulence bidimensionnelle’, C. R. Acad. Sci. Paris, 315, Série II, pp. 1585–1592, 1992 Google Scholar
  11. /Farge et al. 1992/
    M. Farge, E. Goirand, Y. Meyer, F. Pascal and M. V. Wickerhauser, ‘Improved predictability of two-dimensional turbulent flows using wavelet packet compression’, Fluid Dyn. Res., 10, pp. 229–250, 1992 ADSCrossRefGoogle Scholar
  12. /Farge et al. 1997/
    M. Farge, K. Schneider and N. Kevlahan, ‘Coherent structure eduction in wavelet-forced two-dimensional turbulent flows’, Dynamics of Slender Vortices, ed. E. Krause, KluwerGoogle Scholar
  13. /Frisch 1995/.
    U. Frisch, ‘Turbulence, the legacy of A. N. Kolmogorov’, Cambridge University Press,p. 112, 1995 Google Scholar
  14. /Gilbert 1988/.
    A. D. Gilbert, ‘Spiral structures and spectra in two-dimensional turbulence’, J. Fluid Mech., 193, pp. 475–497 Google Scholar
  15. /Heisenberg 1948/.
    W. Heisenberg and C. F. von Weizsäcker, ‘Zur statistischen Theorie des Turbulenz’, Zeit. Für Phys., 124, pp. 628–657, 1948 zbMATHCrossRefGoogle Scholar
  16. /Kampé de Fériet 1939/.
    J. Kampé de Fériet, ‘Les fonctions aléatoires stationnaires et la théorie statistique de la turbulence homogène’, Ann. Soc. Sci. Bruxelles, 59, pp. 145–159, 1939 zbMATHGoogle Scholar
  17. /Kampé de Fériet 1956/.
    J. Kampé de Fériet, ‘La notion de moyenne en théorie de la turbulence’, Seminario Matematico e Fisico di Milano, vol. XXVII, pp. 168–207, 1956 Google Scholar
  18. /Kevlahan 1997/.
    N. Kevlahan and M. Farge, ‘Vorticity filaments in two-dimensional turbulence: creation, stability and effect’, J. Fluid Mech., 346, pp. 49–76, 1997 Google Scholar
  19. /Kolmogorov 1941/.
    A.N. Kolmogorov, ‘Local structure of turbulence in an incompressible fluid at very high Reynolds numbers’, Doklady AN SSSR, 30,4 pp. 299–303, 1941 ADSGoogle Scholar
  20. /Kolmogorov 1962/.
    A. N. Kolmogorov, ‘A refinement of previous hypotheses concerning the local structure of turbulence in viscous incompressible fluid at high Reynolds number’, J. Fluid Mech, 13, pp. 82–85, 1962 MathSciNetADSzbMATHCrossRefGoogle Scholar
  21. /Kraichnan 1967/.
    ‘Inertial-range Ranges in Two-dimensional Turbulence’, Physics of Fluids, 10, pp. I417–I423, 1967 Google Scholar
  22. A Philosophical and Historical Journey through Mixing and Turbulence 35Google Scholar
  23. /Kraichnan 1974/.
    ‘On Kolmogorov’s inertial-range theories’, JFM 62, pp. 305–330, 1974 Google Scholar
  24. /Liepmann 1962/.
    H. W. Liepmann, ‘Free turbulent flows’, Mécanique de la turbulence, ed. Favre, Masson, pp. 211–227, 1962 Google Scholar
  25. /Liepmann 1997/.
    International Workshop on ‘Dynamical Systems and Statistical Mechanics Methods for Coherent Structures in Turbulent Flows’, University of California at Santa Barbara, 12–13th February, 1997 Google Scholar
  26. /Lorentz 1896/.
    H. A. Lorentz, ‘Ein allgemeiner Satz, die Bewegung einer reibenden Flüssigkeit betreffend, nebst einigen Anwendungen desselben’, ‘A general theorem on the motion of a viscous flow near a wall’,Abhandlungen über theoretischen Physik, Leipzig, 1, pp. 43–71, 1907 Google Scholar
  27. /Lundgren 1982/.
    T. S. Lundgren,‘Strained spiral vortex model for turbulent fine structure’, Phys. Fluids, 25, pp. 2193–2203 Google Scholar
  28. /Maxwell 1877/.
    J. C. Maxwell, ‘Diffusion’, Encyclopedia Britanica, 9th edition, 1877 Google Scholar
  29. /McWilliams 1984/.
    J. C. McWilliams, ‘The emergence of isolated coherent vortices in turbulent flows’, J. Fluid Mech., 146, pp. 21–43, 1984 ADSzbMATHCrossRefGoogle Scholar
  30. /Mezic 1996/.
    I. Mezic, ‘Lévy stable distributions for velocity and velocity dofference in systems of vortex elements’, Phys. Fluids, vol. 8, 5, pp. 1169–1180, 1996 MathSciNetADSzbMATHCrossRefGoogle Scholar
  31. /Millionshchikov 1939/.
    M.D. Millionshchikov, ‘Decay of homogeneous isotropic turbulence in viscous incompressible fluids’, Doklady Akad. Nauk. SSSR, 22,5, pp. 236–240, 1939 Google Scholar
  32. /Moffatt 1993/.
    H. K. Moffatt, ‘Spiral structures in turbulent flow’, Wavelets, Fractals and Fourier Transforms, ed. Farge, Hunt and Vassilicos, Clarendon, pp. 317–324, 1993 Google Scholar
  33. /Monin and Yaglom 1965/.
    Monin and Yaglom, Statistical Fluid Mechanics, The MIT Press, 1965/Google Scholar
  34. /Obukhov 1941/.
    A. M. Obukhov, ‘Energy distribution in the spectrum of a turbulent flow’, Izvestiya AN SSSR, 4-5, pp. 453–466, 1941 Google Scholar
  35. /Onsager 1945/.
    L. Onsager, ‘The distribution of energy in turbulence’, Phys. Rev., 68, p. 286, 1945 Google Scholar
  36. /Onsager 1949/.
    L. Onsager, ‘The distribution of energy in turbulence’, Phys. Rev., 68, pp. 286, 1945,’ Statistical hydrodynamics’, Suppl. Nuovo Cimento, suppl. vol. 6, pp. 279-287, 1949 Google Scholar
  37. /Reynolds 1883/.
    O. Reynolds, ‘An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and the law of resistance in parallel channels’, Phil. Trans. Roy. Soc, p. 51, 1883 Google Scholar
  38. /Reynolds 1894/.
    O. Reynolds, ‘On the dynamical theory of incompressible viscous fluids and the determination of the criterion’, Phil. Trans. Roy. Soc. London, vol. 186, pp. 123–164, 1894 ADSGoogle Scholar
  39. /Richardson 1922/.
    L. F. Richardson, ‘Weather prediction by numerical process’,Cambridge University Press, 1922 Google Scholar
  40. /Richardson and Gaunt 1930/.
    L. F. Richarson and A. Gaunt, ‘Diffusion regarded as a compensation for smoothing’, Memoirs of the Royal Meteorological Society, vol. 3,30, pp. 111–115, 1930 Google Scholar
  41. /Saffman 1971/.
    P. G. Saffman, ’A note on the spectrum and decay of random two-dimensional vorticity distribution’ Stud. Appl. Math., vol. 50, pp. 311–383, 1911 Google Scholar
  42. /Schneider, Kevlahan and Farge 1997/.
    K. Schneider, N. Kevlahan and M. Farge, ‘Comparison of and adaptive wavelet method and nonlinear filtered pseudospectral methods for two-dimensional turbulence’, Theoretic. Comput. Fluid Dynamics, 9, pp. 191–206, 1991 ADSCrossRefGoogle Scholar
  43. /Spinoza/.
    B. Spinoza, ‘Ethics, 1, Appendix’ Penguin Classics, pp. 29–30, 1996 Google Scholar
  44. /Taylor 1921/.
    G. I. Taylor, ‘Diffusion by continuous movements’, Proc. London Math. Soc, 20, pp. 196–211, 1921 zbMATHCrossRefGoogle Scholar
  45. /Taylor 1935/.
    G. I. Taylor, ‘Statistical Theory of Turbulence’, Proc. Roy. Soc. London A, vol. 151, pp. 421–418, 1935 ADSzbMATHCrossRefGoogle Scholar
  46. /Taylor 1938/.
    G. I. Taylor, ‘The Spectrum of Turbulence’, Proc. R. Soc. London A, 164, PP-416–490, 1938 Google Scholar
  47. /Theodorsen 1955/.
    Theodorsen, ‘The Structure of Turbulence’, 50 Jahre Gren-zschichtforsung, 1955 Google Scholar
  48. /Townsend 1951/.
    A. A. Townsend, ‘On the fine-scale structure of turbulence’, Proc. Royal Soc, A 208, pp. 534–542, 1951 ADSzbMATHCrossRefGoogle Scholar
  49. /Van den Water 1993/.
    W. Van den Water, ‘Experimental study of scaling in fully developed turbulence’, Turbulence in spatially extended systems, ed. Benzi et al., pp. 189–213, 1993 Google Scholar
  50. /Weiss and Me Williams 1991/.
    J. B. Weiss and J. C. McWilliams, ‘Nonergodicity of point vortices’, Phys. Fluids, A3, 835, 1991 Google Scholar
  51. /Wiener 1933/.
    The Fourier Integral’, 1933 Google Scholar
  52. Yaglom A. M., ‘Einstein’s Work on Methods for Processing Fluctuating Series of Observations and the Role of these Methods in Meteorology’, Izvestia, Atmospheric and Oceanic Physics, vol. 22,1, pp. 18–82, 1986 Google Scholar

Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Marie Farge
    • 1
  • Etienne Guyon
    • 1
  1. 1.Ecole Normale SupérieureParisFrance

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