A New Universal Scaling for Fully Developed Turbulence: The Distribution of Velocity Increments

  • Yves Gagne
  • Emil J. Hopfinger
  • Uriel Frisch
Part of the NATO ASI Series book series (NSSB, volume 237)


It is well known that the probability density functions (p.d.f.) of two point velocity differences measured in fully developed turbulence are non gaussian, a signature of internal intermittency. Measurements of Δu(r) = u(x) — u(x + r) were performed at high Reynolds number (Rλ = 2720). The novel results are that: (i) the functionnal behaviour of the tails of the p.d.f. can be represented by P(Δu) ∼ exp(—b(r)∣Δu/σΔu∣) and (ii) the logarithmic decrement b(r) scales as b(r) ∼ r0.15 when the separation r lies in the inertial range.


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  1. Anselmet, F., Gagne, Y., Hopfinger, E. J., and Antonia, R.A., 1978, High order velocity structure functions in turbulent shear flows, J.Fluid.Mech., 140; 63, 89.Google Scholar
  2. Castaing, B., Gunaratne, G., IIeslot, F., Kadanoff, L., Libchaber, A., Thomae, S., Wu, X., Zaleski, S., and Zanetti, G., 1988, Scaling of hard thermal turbulence in Rayleigh Bénard convection, J.Fluid.Mech., to appear.Google Scholar
  3. Frisch, U., Sulem, P.L., and Nelkin, M., 1978, A simple dynamical model of intermittent fully developed turbulence, J.Fluid.Mech., 87; 719, 736.MATHGoogle Scholar
  4. Gagne, Y., 1987, Etude expérimentale de l’intermittence et des singularités dans le plan complexe en turbulence développée, Thesis; Université de Grenoble;France.Google Scholar
  5. Kida, S., and Murakami, Y., 1988, Fluid Dynamics Res., to appear.Google Scholar
  6. Kolmogorov, A.N., 1941, Local structure in an incompressible fluid at very high Reynolds number, Dokl.Akad.Nauk., 26; 115, 118.Google Scholar
  7. Kolmogorov, A.N., 1962, A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number, J.Fluid.Mech., 13; 82, 84.MathSciNetMATHGoogle Scholar
  8. Landau, L.D., and Lifchitz, E.M., 1958, in “ Fluid Mechanics”, Addison Wesley. Métais, O., and Herring, J.R., 1988, Numerical simulations of freely evolving turbulence in stably stratified fluids, J.Fluid.Mech. in press.Google Scholar
  9. Monin, A.S., and Yaglom, A.M., 1975, in “ Statistical Fluid Mechanics”, Vol. 2, M.I.T. Press.Google Scholar
  10. Smith, L.A., Fournier, J.D., and Spiegel, E.A., 1986, Lacunarity and intermittency in turbulence, Phys. Lett., A114; 465.CrossRefGoogle Scholar
  11. Van Atta, C.W., and Park, J., 1971, Statistical self-similarity and inertial range turbulence, in “Lectures Notes in Physics”, 12;402, Springer Verlag.Google Scholar

Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • Yves Gagne
    • 1
  • Emil J. Hopfinger
    • 1
  • Uriel Frisch
    • 2
  1. 1.Institut de Mécanique de GrenobleGrenoble CedexFrance
  2. 2.Observatoire de NiceNice CedexFrance

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