Remarks on Prototypes of Turbulence, Structures in Turbulence and the Role of Chaos

  • Hassan Aref
Part of the Applied Mathematical Sciences book series (AMS, volume 58)


Turbulence is usually billed as one of the great unsolved problems in classical mechanics. It has a bit of the aura of other great classical problems, like some of the conjectures in number theory, in that the statement of the problem is much simpler than the sophistication necessary to tackle it. We are intuitively acquainted with the flow of water, even in the turbulent regime, from our daily mechanical experiences, yet the description, let alone prediction, of the properties of turbulent flow has remained elusive, continually inviting application of concepts and ideas at the forefront of physical science and mathematics.


Shear Layer Fluid Mechanic Turbulence Theory Soap Film Turbulent Behaviour 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    B.J. Cantwell, Ann. Rev. Fluid Mech. 13 (1981) 457.ADSCrossRefGoogle Scholar
  2. 2.
    E.N. Lorenz, J. Atmos. Sci. 20 (1963) 130.ADSCrossRefGoogle Scholar
  3. 3.
    H. Aret, Ann. Rev. Fluid Mech. 15 (1983) 345.ADSCrossRefGoogle Scholar
  4. 4.
    D. Rockwell, “Vortex-edge interactions” in Recent Advances in Aerodynamics and Aeroacoustics, Springer (to appear).Google Scholar
  5. 5.
    C-M. Ho and P. Huerre, Ann. Rev. Fluid Mech. 16 (1984) 365.ADSCrossRefGoogle Scholar
  6. 6.
    K.R. Sreenivasan, “Transition and turbulence in fluid flows and low-aimensional chaos” in Fundamentals of Fluid Mechanics, Springer (to appear).Google Scholar
  7. 7.
    R.H. Kraicnnan and D. Montgomery, Rep. Prog. Phys. 43 (1980) 547.ADSCrossRefGoogle Scholar
  8. 8.
    P.B. Rhines, Ann. Rev. Fluid Mech. 11, (1979) 401.ADSCrossRefGoogle Scholar
  9. 9.
    H. Aref and E.D. Siggia, J. Fluid Mech. 100 (1980) 705.ADSCrossRefGoogle Scholar
  10. 10.
    H. Aref and E.D. Siggia, J. Fluid Mech. 109 (1981) 435.ADSCrossRefGoogle Scholar
  11. 11.
    Y. Couaer and M. Rabaud, “Two-aimensional turbulence in thin liquid films,” J. Phys. Lett. (to appear).Google Scholar
  12. 12.
    D.J. Lewis, Proc. R. Soc. (London) A202 (1950) 81.ADSGoogle Scholar
  13. 13.
    R.A. Wooaing, J. Fluid Mech. 39 (1969) 477.ADSCrossRefGoogle Scholar
  14. 14.
    G.R. Baker, D.I. Meiron and S.A. Orszag, Phys. Fluids 23, (1980) 1485.ADSMATHCrossRefGoogle Scholar
  15. 15.
    G. Tryggvason and H. Aref, J. Fluid Mech. 136 (1983) 1.ADSMATHCrossRefGoogle Scholar
  16. 16.
    B.B. Mandelbrot, Fractals, Form, Chance and Dimension, Freeman (1977).MATHGoogle Scholar
  17. 17.
    J.B. Keller, Lectures at Woods Hole GFD Summer Program (1980).Google Scholar
  18. 18.
    C.D. Winant and F.K. Browana, J. Fluid Mech. 63 (1974) 237.ADSCrossRefGoogle Scholar
  19. 19.
    J.L. Lumley, Trans. ASME, J. Appl. Mech. 50 (1983) 1097.ADSCrossRefGoogle Scholar
  20. 20.
    H. Lamb, Hydroaynamics, Dover (1932).Google Scholar
  21. 21.
    J. Fora, “The statistical mechanics of classical analytic dynamics,” in Fundamental Problems in Statistical Mechanics, Nortn-Hollana (1975).Google Scholar
  22. 22.
    G. Birkhoff, Hydroaynamics, A Stuay in Logic, Fact and Similitude, Princeton University Press (1960), p. 4.Google Scholar
  23. 23.
    H. Aref, J. Fluid Mech. 143 (1984) 1.MathSciNetADSMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • Hassan Aref

There are no affiliations available

Personalised recommendations