Properties of Quasi One-Dimensional Rayleigh Benard Convection

  • M. Dubois
  • P. Bergé
  • A. Petrov
Part of the NATO ASI Series book series (NSSB, volume 237)


Rayleigh Bénard convection1 is a well known phenomenon which develops striking spatial periodic structures in a fluid layer submitted to a destabilizing temperature gradient. In a rectangular container of horizontal extensions L x and L y large compared to the depth d, nice straight parallel rolls can be observed under some particular conditions2 near the critical Rayleigh number Ra c . When the convection is achieved with a high Prandtl number fluid, an increase of Ra beyond a well defined value RaII (about 10 Ra c ) generates a new set of rolls superimposed on the critical roll pattern. The axes of the two sets are mutually perpendicular. In both cases, the convection is stationary. The velocity field associated with the simple critical rolls (below RaII) is two-dimensional while, in the case of the two perpendicular sets of rolls a three-dimensional velocity field is excited. As far as the horizontal planeform is concerned (meaning that we disregard the vertical dependence of the velocity) the spatial properties only depend on one coordinate, say X, in the case of the rolls below Ra II; in this context we speak of one-dimensional convection, while above Ra II, where the two sets of rolls coexist, we speak of two-dimensional convection.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    P. Bergé, M. Dubois, Contemporary Physics, 25, 535 (1984)CrossRefGoogle Scholar
  2. 2.
    A. Pocheau, V. Croquette, J. de Phys., 45, 35 (1984)Google Scholar
  3. 3.
    P. Bergé, “Chaos and Order in Nature”, Elmau 1981, ed. By H. Haken (Springer-Verlag), P.14.Google Scholar
  4. 4.
    M.S. Heutmaker, P.N. Fraenkel, J.P. Gollub, Phys. Rev. Lett., 54, 1369 (1985)CrossRefGoogle Scholar
  5. 5.
    A. Pocheau, V. Croquette, P. le Gal, Phys. Rev. Letters, 55, 1094 (1985)CrossRefGoogle Scholar
  6. 6.
    Le Chaos. Théorie et experiences, ed. by P. Bergé. Eyrolles Paris (1988)Google Scholar
  7. 7.
    J.P. Gollub, S.V. Benson, J. of Fluid Mech., 100, 449 (1980)CrossRefGoogle Scholar
  8. 8.
    A. Libchaber, S. Fauve, C. Laroche, Physica 7D, 73 (1983)Google Scholar
  9. 9.
    M. Dubois, P. Bergé, Physica Scripta, 33, 159 (1986)CrossRefGoogle Scholar
  10. 10.
    J.N. Koster, U. Müller, J. Fluid Mech., 125, 429 (1982)CrossRefGoogle Scholar
  11. 11.
    O Kvenvold, Int. J. Heat Mass Transfer, 22 395 (1979)Google Scholar
  12. 12.
    K. Stork, U. Müller, J. Fluid Mech., 71, 231 (1975)CrossRefGoogle Scholar
  13. 13.
    F. Daviaud, P. Bergé, M. Dubois, J. de Phys. Colloques “Non linear coherent structures in Physics, Mechanics and Biological Systems”, Paris (1988) to appear.Google Scholar
  14. 14.
    M. Dubois, R. Da Silva, F. Daviaud, P. Bergé, A. Petrov, Europhysics Letters.To appear.Google Scholar
  15. 15.
    F. Daviaud et al, to be publishedGoogle Scholar
  16. 16.
    S. Ciliberto, P. Bigazzi, Phys. Rev. Lett., 60, 286 (1988)CrossRefGoogle Scholar
  17. 17.
    P. Bergé, M. Dubois, P. Manneville, Y. Pomeau, J. de Phys. Lettres, 41, L341 (1980)CrossRefGoogle Scholar
  18. 18.
    H. Chaté and Manneville, Phys. Rev. Lett., 58, 112 (1987)CrossRefGoogle Scholar
  19. 19.
    B. Nicolaenko, H. Chaté, these proceedingsGoogle Scholar

Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • M. Dubois
    • 1
  • P. Bergé
    • 1
  • A. Petrov
    • 1
  1. 1.Service de Physique du Solide et de Résonance MagnétiqueC.E.N.-SaclayGif-sur-Yvette, CedexFrance

Personalised recommendations