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Laser Doppler Study of the Onset of Turbulent Convection at Low Prandtl Number

  • J P Gollub
  • S L Hulbert
  • G M Dolny
  • H L Swinney
Part of the Nato Advanced Study Institutes Series book series (NSSB, volume 23)

Abstract

The transition to turbulence by a sequence of instabilities, although extensively studied both theoretically and experimentally,1 is not well understood at this time. In particular, it is not known whether there are some features of the process that are universal, in the sense of characterizing the onset of turbulence in all systems that show a sequence of instabilities. (We exclude from consideration those situations in which turbulence occurs catastrophically with no intermediate periodic states, such as boundary layers and pipe flow.) Unfortunately, the term “turbulence” implies different degrees of disorder to different workers, and this ambiguity interferes with the possibility of making clear distinctions between turbulent and non-turbulent regimes. Consequently, we concentrate on a well-defined problem, namely the onset of aperiodic motion, which can be detected by the absence of sharp peaks in the power spectrum of the velocity field, or by the decay of the autocorrelation function of the velocity field.

Keywords

Power Spectrum Autocorrelation Function Prandtl Number Rayleigh Number Broadband Noise 
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.

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References

  1. 1.
    J.A. Whitehead, in Fluctuations, Instabilities and Phase Transitions, ed. by T. Riste (Plenum Press, New York 1975), p. 153.CrossRefGoogle Scholar
  2. 2.
    However, the probe may disturb the flow even in open systems, since pressure disturbances can propagate upstream.Google Scholar
  3. 3.
    R.M. Clever and F.H. Busse, J. Fluid Mech. 65, 625 1974.ADSMATHCrossRefGoogle Scholar
  4. 4.
    J.B. McLaughlin and P.C. Martin, Phys. Rev. A 12, 186 1975.ADSCrossRefGoogle Scholar
  5. 5.
    G. Ahlers, Phys. Rev. Lett. 33, 1185 1974.ADSCrossRefGoogle Scholar
  6. 6.
    B.J. Daly, J. Fluid Mech. 64, 129 1974.ADSMATHCrossRefGoogle Scholar
  7. 7.
    G.E. Willis and J.W. Deardorff, Phys. Fluids 8, 2225 1965.ADSCrossRefGoogle Scholar
  8. G.E. Willis and J.W. Deardorff, Phys. Fluids 10, 931 1967.ADSCrossRefGoogle Scholar
  9. G.E. Willis and J.W. Deardorff, J. Fluid Mech. 44, 661 1970.ADSCrossRefGoogle Scholar
  10. 8.
    W.V.R. Malkus, Proc. Roy. Soc. A225, 185 1954.MathSciNetADSGoogle Scholar
  11. W.V.R. Malkus, Proc. Roy. Soc. A225, 196 1954.MathSciNetADSGoogle Scholar
  12. 9.
    R. Krishnamurti, J. Fluid Mech. 42, 309 1970.ADSCrossRefGoogle Scholar
  13. R. Krishnamurti, J. Fluid Mech. 42, 295 (1970).ADSCrossRefGoogle Scholar
  14. R. Krishnamurti, J. Fluid Mech. 60, 285 (1973).ADSCrossRefGoogle Scholar
  15. 10.
    F.H. Busse and J.A. Whitehead, J. Fluid Mech. 66, 67 1974.ADSCrossRefGoogle Scholar
  16. 11.
    H.T. Rossby, J. Fluid Mech. 36, 309 1969.ADSCrossRefGoogle Scholar
  17. 12.
    P. Bergé and M. Dubois, Phys. Rev. Lett. 32, 1041 1974.ADSCrossRefGoogle Scholar
  18. P. Bergé, in Fluctuations, Instabilities and Phase Transitions, ed. by T. Riste (Plenum Press, New York, 1975), p. 323; and P. Berge and M. Dubois, to appear.CrossRefGoogle Scholar
  19. 13.
    P. Bergé and M. Dubois, to appear.Google Scholar
  20. 14.
    Handbook of Chemistry and Physics, 52nd ed. (Chemical Rubber Co., Cleveland, Ohio 1971).Google Scholar
  21. 15.
    R.K. Otnes and L. Enochson, Digital Time Series Analysis (Wiley, New York, 1972).MATHGoogle Scholar
  22. 16.
    W.W. Fowlis and R. Hide, J. Atmos. Sci. 22, 541 1965 and references therein.ADSCrossRefGoogle Scholar
  23. 17.
    D. Fultz, R.R. Long, G.V. Owens, W. Bohan, R. Kaylor, and J. Weil, Meteor. Monog. 4, 21 1959 and.Google Scholar
  24. D. Fultz, R.R. Long, G.V. Owens, W. Bohan, R. Kaylor, and J. Weil, Advances in Geophysics 7, 1 1961.ADSCrossRefGoogle Scholar
  25. 18.
    E.N. Lorenz, J. Atmos. Sci. 20, 130 1963.ADSCrossRefGoogle Scholar
  26. 19.
    J.E. Hart, J. Atmos. Sci. 30, 1017 1973 and.ADSCrossRefGoogle Scholar
  27. J.E. Hart, Geophys. Fluid Dyn. 3, 181 1972.ADSCrossRefGoogle Scholar
  28. 20.
    D. Ruelle and F. Takens, Commun. Math. Phys. 20, 167 1971.MathSciNetADSMATHCrossRefGoogle Scholar
  29. 21.
    J.P. Gollub and H. Swinney, Phys. Rev. Lett. 35, 927 1975.ADSCrossRefGoogle Scholar
  30. 22.
    T.B. Benjamin, Proc. Roy. Soc. A299, 59 1967.ADSGoogle Scholar
  31. 23.
    T.B. Benjamin and J.E. Feir, J. Fluid Mech. 27, 417 1976.ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1977

Authors and Affiliations

  • J P Gollub
    • 1
  • S L Hulbert
    • 1
  • G M Dolny
    • 1
  • H L Swinney
    • 2
  1. 1.Haverford CollageHaverfordUSA
  2. 2.Physics DepartmentCity College of the City University of New YorkNew YorkUSA

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