Advertisement

A Galerkin Approximation for Convection in Binary Mixtures with Realistic Concentration Boundary Conditions

  • S. J. Linz
  • M. Lücke
Part of the Springer Series in Synergetics book series (SSSYN, volume 41)

Abstract

We discuss linear and nonlinear properties of a generalized Lorenz model previously derived by the authors to describe convection in binary fluid mixtures with free slip, impermeable boundary conditions.

Keywords

Nusselt Number Rayleigh Number Hopf Bifurcation Travel Wave Solution Conductive State 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    For a review see: J.K. Platten, J.C. Legros: Convection in Fluids (Springer, 1984); and references cited therein.CrossRefGoogle Scholar
  2. 2.
    G. Ahlers and I. Rehberg: Phys.Rev.Lett. 56, 1373 (1986).CrossRefADSMathSciNetGoogle Scholar
  3. 3.
    P. Kolodner, A. Passner, C.M. Surko, and R. Walden: Phys.Rev.Lett. 56, 2621 (1986)CrossRefADSGoogle Scholar
  4. C.M. Surko, P. Kolodner, A. Passner and R. Walden: Physica 23D, 220 (1986)ADSGoogle Scholar
  5. C.M. Surko, P. Kolodner: Phys.Rev.Lett. 58, 2055 (1987).CrossRefADSGoogle Scholar
  6. 4.
    E. Moses and V. Steinberg: Phys.Rev.A 34. 693 (1986); Phys.Rev.Lett. 57, 2018 (1986).CrossRefADSGoogle Scholar
  7. 5.
    E. Moses, J. Feinberg, and V. Steinberg: Phys.Rev.A 35, 2757 (1987).ADSGoogle Scholar
  8. 6.
    R Heinrichs, G. Ahlers, and D.S. Cannell: Phys.Rev.A 35, 2761 (1987).ADSGoogle Scholar
  9. 7.
    H. Gao and RP. Behringer: Phys.Rev.A 34, 697 (1986); Phys.Rev.A 35, 3993 (1987).ADSGoogle Scholar
  10. 8.
    D.T. J. Hurle and E. Jakeman: J.Fluid Mech. 47, 667 (1971).CrossRefADSGoogle Scholar
  11. 9.
    D. Gutkowicz-Krusin, M.A. Collins, and J. Ross: Phys.Fluids 22, 1443, 1451 (1979).CrossRefzbMATHADSGoogle Scholar
  12. 10.
    B.J.A. Zielinska and H.R. Brand: Phys.Rev.A 35, 4349 (1987).CrossRefADSGoogle Scholar
  13. 11.
    H.R. Brand, P.C. Hohenberg, and V. Steinberg: Phys.Rev.A 30, 2548 (1984); and references cited therein.CrossRefADSGoogle Scholar
  14. 12.
    M. Cross: Phys.Lett.119A, 21 (1986).ADSGoogle Scholar
  15. 13.
    G. Ahlers and M. Lücke: Phys.Rev.A 35, 470 (1987).CrossRefADSGoogle Scholar
  16. 14.
    E. Knobloch: Phys.Rev.A 34, 1538 (1986).CrossRefADSGoogle Scholar
  17. 15.
    S.J. Linz and M. Lücke: Phys.Rev.A 35, 3997 (1987); (E) A 36, 2486 (1987).CrossRefADSGoogle Scholar
  18. 16.
    S.J. Linz and M. Lücke: Phys.Rev.A 36, 3505 (1987).CrossRefADSGoogle Scholar
  19. 17.
    In the past, numerous five—mode FSP Lorenz models have been studied. See, e.g., G. Veronis: J.Mar.Res. 23, 1 (1965)Google Scholar
  20. J.K. Platten and G. Chavepeyer: Int.J.Heat Mass Transfer 18, 1071 (1975)CrossRefzbMATHGoogle Scholar
  21. M.G. Velarde and J.C. Antoranz: Phys.Lett. 72A, 123 (1979)ADSGoogle Scholar
  22. L.N. da Costa, E. Knobloch, and N.O. Weiss: J.Fluid Mech. 109, 25 (1981).CrossRefzbMATHADSMathSciNetGoogle Scholar
  23. 18.
    P.M. Gresho and R.L. Sani: J.Fluid Mech. 40, 783 (1970)CrossRefzbMATHADSGoogle Scholar
  24. G. Ahlers, P.C. Hohenberg, and M. Lücke: Phys.Rev.A 32, 3493 (1985)ADSGoogle Scholar
  25. J. Niederländer: Diploma thesis, Universität Saarbrücken (1986)Google Scholar
  26. H. Kuhlmann: Phys.Rev.A 32, 1703 (1985).CrossRefADSGoogle Scholar
  27. 19.
    E.N. Lorenz: J.Atmos.Sci. 20, 190 (1963).Google Scholar
  28. 20.
    M.C. Cross: private communication.Google Scholar
  29. 21.
    S.J. Linz, M.Lücke, H.W. Müller, and J. Niederländer: to be published.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • S. J. Linz
    • 1
  • M. Lücke
    • 1
  1. 1.Institut für Theoretische PhysikUniversität des SaarlandesSaarbrückenFed. Rep. of Germany

Personalised recommendations