Boundary Layer Analysis of Traveling Waves in Binary Convection

  • David Bensimon
  • Alain Pumir
  • Boris I. Shraiman
Part of the NATO ASI Series book series (NSSB, volume 225)


A systematic study of the phenomenon of convection in binary mixtures has revealed a rich variety of behaviors. Many interesting dynamical states have been found experimentally1–6. The situation is very different from what happens in pure fluid convection, due to the fact that the conducting state gets destabilized at a finite frequency through a Hopf bifurcation7. Propagative rolls are often observed, bifurcating subcritically when the control parameter is increased. States of confined traveling wave patterns have also been found experimentally, and their interactions induce rather complex and interesting phenomena which let one ti think that binary mixture convection might an appropriate system for testing theoretical ideas on spatio-temporal disorder and phase turbulence. Indeed, traveling waves seem to be a crucial ingredient for the understanding of many interesting and complex dynamical properties of quasi-1 dimensional systems. This paper is devoted to a thorough analysis of the emergence of nonlinear traveling waves in binary mixtures convection.


Boundary Layer Rayleigh Number Travel Wave Solution Concentration Field Critical Rayleigh 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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1).
    E. Moses and V. Steinberg, Phys. Rev. A34, 693 (1986)ADSGoogle Scholar
  2. 2).
    E. Moses, J. Fineberg and V. Steinberg, Phys. Rev. A35, 2757 (1987)ADSGoogle Scholar
  3. 3).
    R.W. Waiden, P. Kolodner, A. Passner and C. Surko, Phys. Rev. Lett. 61, 2030 (1985)Google Scholar
  4. 4).
    P. Kolodner, D. Bensimon and C. Surko, Phys. Rev. Lett. 60, 1723 (1988)ADSCrossRefGoogle Scholar
  5. 5).
    T.S. Sullivan and G. Ahlers, Phys. Rev. Lett 61, 78 (1988)ADSCrossRefGoogle Scholar
  6. 6).
    O. Lhost and J. K. Platten, these ProceedingsGoogle Scholar
  7. 7).
    D.T.J. Hurle and F. Jakeman, J. Fluid Mech. 47, 667 (1971)ADSCrossRefGoogle Scholar
  8. 8).
    B.J.A. Zielinska and H.R. Brand, Phys. Rev. A35, 4349 (1987)ADSGoogle Scholar
  9. 9).
    M.C. Cross and K. Kim, Phys. Rev. A37, 3909 (1988)MathSciNetADSGoogle Scholar
  10. 10).
    W. Barten, M. Lucke, W. Hart, M. Kamps, Phys. Rev. Lett. 63, 376 (1989)ADSCrossRefGoogle Scholar
  11. 11).
    E. Knobloch, Phys. Rev. A34, 1536 (1986)ADSGoogle Scholar
  12. 12).
    Using similar approaches, M. Proctor (J. Fluid Mech. 105, 507 (1981)) has considered the problem of steady thermohaline convectionGoogle Scholar
  13. 13).
    D. Bensimon, A. Pumir and B. Shraiman, J. Physique 50, 3039 (1989)Google Scholar
  14. 14).
    S. Chandrasekhar, Hydrodynamic and Hydromagnetic stability (Dover, New-York, 1981)Google Scholar
  15. 15).
    B.A. Malomed and M.I. Tribelsky, Physica 14D, 67 (1984),MathSciNetADSGoogle Scholar
  16. 15a).
    see also S. Douady, S. Fauve and O. Thual, Europhys. Lett. 10, 309 (1989)ADSCrossRefGoogle Scholar
  17. 15b).
    P. Coullet et al. Phys. Rev. Lett 63, 1954 (1989)ADSCrossRefGoogle Scholar
  18. 16).
    B. Shraiman, Phys. Rev. A36, 261 (1987)ADSGoogle Scholar
  19. 17).
    M.N. Rosenbluth, H.L. Berk, I. Doxas and W. Horton, Phys. Fluids 30, 2636 (1987)ADSzbMATHCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • David Bensimon
    • 1
  • Alain Pumir
    • 1
  • Boris I. Shraiman
    • 2
  1. 1.Laboratoire de Physique StatistiqueEcole Normale SupérieureParis CedexFrance
  2. 2.AT&T Bell LaboratoriesMurray HillUSA

Personalised recommendations