A New Universal Scaling for Fully Developed Turbulence: The Distribution of Velocity Increments
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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- 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
- 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
- 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
- Kida, S., and Murakami, Y., 1988, Fluid Dynamics Res., to appear.Google Scholar
- Kolmogorov, A.N., 1941, Local structure in an incompressible fluid at very high Reynolds number, Dokl.Akad.Nauk., 26; 115, 118.Google Scholar
- 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
- Monin, A.S., and Yaglom, A.M., 1975, in “ Statistical Fluid Mechanics”, Vol. 2, M.I.T. Press.Google Scholar
- 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