Skip to main content

Part of the book series: NATO Advanced Study Institutes Series ((NSSB,volume 77))

Abstract

This is a limited excursion in the field of hydrodynamical instabilities, in itself an infinite domain of research. It is first restricted to a Rayleigh Benard experiment, and we will study the case of a small Prandtl number fluid (0.4 < P < 1). To simplify the problem some more we shall restrict ourselves to the geometry of a small rectangular box with two or three convective rolls present. This somewhat artificial case allows us to truncate the degrees of freedom of the system and thus to define some simple bifurcations to turbulence.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G. Ahlers, R.W. Waiden, Phys. Rev. Lett., 44:445 (1980).

    Article  ADS  Google Scholar 

  2. J. Wesfreid, V. Croquette, Phys. Rev. Lett., 45:634 (1980).

    Article  ADS  Google Scholar 

  3. A. Libchaber, J. Maurer, Journal Phys. Lettres, 39:369 (1978).

    Article  Google Scholar 

  4. K. Stork, U. Müller, J. Fluid Mech., 71:231 (1975), 54:599 (1972).

    Article  ADS  Google Scholar 

  5. R.D. Mc Carthy, Thermophysical Properties of 4He, Bur. Stand. Tech. Note n° 631 (1972).

    Google Scholar 

  6. F.H. Busse, Report Progr. Physics 41:1929 (1978).

    Article  ADS  Google Scholar 

  7. M. Velarde, C. Normand, Scientific American, 243:78 (July 1980).

    Article  Google Scholar 

  8. E.L. Koschmieder, Adv. Chemical Physics, 26:177 (1974).

    Article  Google Scholar 

  9. M.E. Cross, P.G. Daniels, P.C. Hohenberg, E. Siggia, Phys. Rev. Lett., 45:898 (1980).

    Article  ADS  Google Scholar 

  10. Y. Pomeau, S. Zaleski, C. R. Acad. Sc. Paris, 290 (série B):505 (1980).

    MathSciNet  ADS  Google Scholar 

  11. J. Maurer, A. Libchaber, J. Physique Lettres, 40:419 (1979).

    Article  Google Scholar 

  12. B.H. Busse, R.M. Clever, J. Fluid Mech., 91:319 (1979).

    Article  ADS  Google Scholar 

  13. J. Maurer, A. Libchaber, J. Phys. Lettres, 41:515 (1980).

    Article  Google Scholar 

  14. E. Siggia, A. Zippelius, “Dynamics of Defects in Rayleigh-Benard Convection”, preprint.

    Google Scholar 

  15. A. Libchaber, J. Maurer, J. de Physique, Coll. C3, 41:51 (1980).

    Google Scholar 

  16. A. Adler, Proc. I.R.E., 34:351 (1946).

    Article  Google Scholar 

  17. G. Iooss, Math. Studies, 36, New York (1979).

    Google Scholar 

  18. G. Iooss, W.F. Langford, Annals of the New York Academy of Sciences, Vol. 327 (1980).

    Google Scholar 

  19. R.L. Stratonovich, Topics in the Theory of Random Noise, Gordon and Breach (1967).

    MATH  Google Scholar 

  20. W.E. Lamb Jr., Phys. Rev., 134:429 (1964).

    Article  ADS  Google Scholar 

  21. B. Van der Pol, Phil. Mag., 3:65 (1927).

    Google Scholar 

  22. J.E. Flaherty, F.C. Hoppensteadt, Study Appl. Math., 58:5 (1978).

    MathSciNet  Google Scholar 

  23. J.P. Gollub, E.J. Romer, J.E. Socolar, Journ. Stat. Phys., 23:321 (1980).

    Article  MathSciNet  ADS  Google Scholar 

  24. J.P. Gollub, S.V. Benson, J. Fluid Mech., 100:449 (1980).

    Article  ADS  Google Scholar 

  25. M. Dubois, Colloque Pierre Curie, Paris (1980).

    Google Scholar 

  26. M. Dubois, P. Berge, J. Physique, 42:167 (1981).

    Google Scholar 

  27. G. Ahlers, R.L. Behringer, Phys. Rev. Lett., 40:712 (1978).

    Article  ADS  Google Scholar 

  28. L. Landau, E. Lifshitz, Fluid Mechanics, Chapt. 3, Pergamon, Oxford (1959).

    Google Scholar 

  29. D. Ruelle, F. Takens, Coram. Math. Phys., 20:167 (1971).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. E.N. Lorenz, J. Atmos. Sci., 20:130 (1978).

    Article  MathSciNet  ADS  Google Scholar 

  31. M.J. Feigenbaum, Phys. Lett., 74A:375 (1979); Coram. Math. Phys., 77:65 (1980).

    MathSciNet  ADS  Google Scholar 

  32. P. Coullet, C. Tresser, A. Arneodo, Phys. Lett., 72A:268 (1979).

    MathSciNet  ADS  Google Scholar 

  33. J. Collet, J.P. Eckmann, “Iterated Maps of the Interval as Dynamical Systems”, Birkhaiiser (1980).

    Google Scholar 

  34. Lord Rayleigh, “The Theory of Sound”, Vol. I, Chapt. 3, Dover (1945).

    MATH  Google Scholar 

  35. C. Bender, S. Orzag, “Advanced Math. Methods for Scientists”, McGraw Hill (1978).

    Google Scholar 

  36. M. Nauenberg, J. Rüdnick, “University and the Power Spectrum at the Onset of Chaos”, preprint.

    Google Scholar 

  37. M. Giglio, S. Musazzi, U. Perini, “Transition to Chaos via a Well Defined Ordered Sequence of Period Doubling”, preprint.

    Google Scholar 

  38. S. Grossmann, S. Thomae, Z. Naturforsch., 32a:1353 (1977).

    MathSciNet  ADS  Google Scholar 

  39. S. Thomae, S. Grossman, “Correlations and Spectra of Periodic Chaos Generated by the Logistic Parabola”, preprint.

    Google Scholar 

  40. A. Wolf, J. Swift, “Universal Power Spectra for the Reverse Bifurcation Sequence”, preprint.

    Google Scholar 

  41. B. Huberman, A. Zisook, Phys. Rev. Lett., 46:626 (1981).

    Article  MathSciNet  ADS  Google Scholar 

  42. P. Manneville, Y. Pomeau, Phys. Lett., 75A:1 (1979).

    MathSciNet  ADS  Google Scholar 

  43. Y. Pomeau, P. Manneville, Physica, D1:219 (1980).

    MathSciNet  ADS  Google Scholar 

  44. P. Bergé, M. Dubois, P. Manneville, Y. Pomeau, J. Phys. Lettres, 41:341 (1980).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1982 Plenum Press, New York

About this chapter

Cite this chapter

Libchaber, A., Maurer, J. (1982). A Rayleigh Bénard Experiment: Helium in a Small Box. In: Riste, T. (eds) Nonlinear Phenomena at Phase Transitions and Instabilities. NATO Advanced Study Institutes Series, vol 77. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-4127-7_15

Download citation

  • DOI: https://doi.org/10.1007/978-1-4684-4127-7_15

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-4129-1

  • Online ISBN: 978-1-4684-4127-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics