Phase Turbulence and Mean Flow Effects in Rayleigh-Bénard Convection

  • A. Pocheau
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 41)

Abstract

Hydrodynamical experiments have been widely used to study the transition to turbulence, especially when they could provide closed flows, well controlled and without external disturbances. Two famous examples of such situations are provided by the Rayleigh-Bénard and the Couette Taylor flow instabilities, but we will focus on the first one here. This instability arises when a fluid is heated from below and cooled from above, beyond a temperature difference threshold. Convective motions then set in and organize themselves in patches of counterrotating rolls. The convective features are governed by the Rayleigh number Ra, proportional to this difference, and by the Prandtl number Pr of the fluid (at threshold the Rayleigh number is written Rac). When the roll pattern is so confined by the sidewalls that only two or three rolls are present, the transition to turbulence recovers the various scenarios inherent to the systems of a few degrees of freedom /1/. However, we will concentrate here on the opposite case of extended systems, containing a large number of rolls.

Keywords

Combustion Convection Argon Covariance Helium 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J.P.Eckmann, Rev.Mod.Phys., 53, 643 (1981)CrossRefMATHADSMathSciNetGoogle Scholar
  2. 2.
    F.H.Busse.Rep.Prog.Phys., 41, 1929 (1978)CrossRefADSGoogle Scholar
  3. H.Busse and R.M.Clever, J.Fluid.Mech., 102, 61 (1981)CrossRefMATHADSGoogle Scholar
  4. 3.
    G.Ahlers and R.P. Behringer. Phys.Rev.Lett., 40, 712 (1978)CrossRefADSGoogle Scholar
  5. 4.
    A.Pocheau, V.Croquette, and P.Le Gal, Phys.Rev.Lett., 55, 10 (1985)CrossRefGoogle Scholar
  6. 5.
    A.Pocheau, Thése d’Etat, Université Paris VII, March 1987Google Scholar
  7. 6.
    A.Pocheau and CPoitou, future publicationGoogle Scholar
  8. 7.
    E.D.Siggia and A.Zippelius, Phys.Rev. A., 1036 (1981)Google Scholar
  9. 8.
    V.Croquette, P.Le Gal, A.Pocheau and R.Guglielmetti, Europhys.Lett., 18, 393 (1986)CrossRefADSGoogle Scholar
  10. 9.
    A.Pocheau, V.Croquette, P.Le Gal, and C.Poitou, Europhys.Lett., 8, 915 (1987); Due to a typographic error, the modified phase equation does not contain the mean flow amplitude U.CrossRefADSGoogle Scholar
  11. 10.
    Y.Pomeau and P.Manneville, J.Phys.Lett., 40, 609 (1979)CrossRefMathSciNetGoogle Scholar
  12. 11.
    P.Coullet and S.Fauve, Phys.Rev.Lett., 55, 2857 (1985)CrossRefADSGoogle Scholar
  13. 12.
    K.Kawasaki and H.Brand, Annals of Physics, 160, 420 (1985)CrossRefADSMathSciNetGoogle Scholar
  14. 13.
    P.Clavin, this volumeGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • A. Pocheau
    • 1
    • 2
  1. 1.DPh-G, SRM, Orme des Merisiers, CEN SaclayGif-sur-Yvette CedexFrance
  2. 2.Laboratoire de Recherche en Combustion, Service 252Université de Provence, Centre de St. JérômeMarseilleFrance

Personalised recommendations