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High-order velocity structure functions in turbulent shear flows

Published online by Cambridge University Press:  20 April 2006

F. Anselmet ,
Y. Gagne ,
E. J. Hopfinger  and
R. A. Antonia
F. Anselmet
Affiliation:
Laboratoire Associé au CNRS, Institut de Mécanique, Université Scientifique et Médicale de Grenoble, 38402 Saint Martin d'Hères, France
Y. Gagne
Affiliation:
Laboratoire Associé au CNRS, Institut de Mécanique, Université Scientifique et Médicale de Grenoble, 38402 Saint Martin d'Hères, France
E. J. Hopfinger
Affiliation:
Laboratoire Associé au CNRS, Institut de Mécanique, Université Scientifique et Médicale de Grenoble, 38402 Saint Martin d'Hères, France
R. A. Antonia
Affiliation:
Department of Mechanical Engineering, University of Newcastle, N.S.W., 2308, Australia
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Abstract

Measurements are presented of the velocity structure function on the axis of a turbulent jet at Reynolds numbers Rλ ≤ 852 and in a turbulent duct flow at Rλ = 515. Moments of the structure function up to the eighteenth order were calculated, primarily with a view to establish accurately the dependence on the order of the inertial range power-law exponent and to draw conclusions about the distribution of energy transfer in the inertial range. Adequate definition of the probability density of the structure function was achieved only for moments of order n ≤ 10. It is shown, however, that, although the values of moments of n > 10 diverges from their true values, the dependence of the moment of the structure function on the separation r is still given to a fair accuracy for moments up to n ≈ 18. The results demonstrate that the inertial-range power-law exponent is closely approximated by a quadratic dependence on the power which for lower-order moments (n [lsim ] 12) would be consistent with a lognormal distribution. Higher-order moments diverge, however, from a lognormal distribution, which gives weight to Mandelbrot's (1971) conjecture that ‘Kolmogorov's third hypothesis’ is untenable in the strict sense. The intermittency parameter μ, appearing in the power-law exponent, has been determined from sixth-order moments 〈(δμ)6〉 ∼ r2−μ to be μ = 0.2 ± 0.05. This value coincides with that determined from non-centred dissipation correlations measured in identical conditions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 140 , March 1984 , pp. 63 - 89
Copyright
© 1984 Cambridge University Press

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References

Antonia, R. A., Satyaprakash, B. R. & Hussain, A. K. M. F. 1980 Phys. Fluids 23, 695–700.
Antonia, R. A., Satyaprakash, B. R. & Chambers, A. J. 1982a Phys. Fluids 25, 29–37.
Antonia, R. A., Satyaprakash, B. R. & Hussain, A. K. M. F. 1982b J. Fluid Mech. 119, 55–89.
Antonia, R. A. & Van Atta, C. W. 1978 Phys. Fluids 21, 1096–1099.
Chorin, A. J. 1982 Commun. Math. Phys. 83, 517–535.
Comte-Bellot, G. 1965 PST Ministère de l'Air 419, Paris.
Corrsin, S. 1962 Phys. Fluids 5, 1301–1302.
Frenkiel, F. N. & Klebanoff, P. S. 1975 Boundary-Layer Meteor. 8, 173–200.
Frenkiel, F. N., Klebanoff, P. S. & Huang, T. 1979 Phys. Fluids 22, 1606.
Frisch, U., Sulem, P-L. & Nelkin, M. 1978 J. Fluid Mech. 87, 719–736.
Fujisaka, H. & Mori, H. 1979 Prog. Theor. Phys. 62, 54.
Gagne, Y. 1980 Thèse Docteur-Ingénieur, Université Scientifique et Médicale et Institut National Polytechnique de Grenoble.
Gagne, Y. & Hopfinger, E. J. 1979 In Proc. 2nd Symp. on Turbulent Shear Flow, London.
Hentschel, H. G. E. & Procaccia, I. 1982 Phys. Rev. Lett. 49, 1158.
Kolmogorov, A. N. 1941 C.R. Acad. Sci. USSR 30, 301–305.
Kolmogorov, A. N. 1962 J. Fluid Mech. 13, 82–85.
Kraichnan, R. H. 1974 J. Fluid Mech. 72, 305–330.
Lumley, J. L. 1970 Stochastic Tools in Turbulence. Academic.
Mandelbrot, B. 1972 In Statistical Models and Turbulence. (ed. M. Rosenblatt & C. Van Atta). Lecture Notes in Physics, vol. 12, pp. 333–351. Springer.
Mandelbrot, B. 1976 In Turbulence and Navier Stokes Equations. (ed. R. Temam). Lecture Notes in Mathematics, vol. 565, pp. 121–145. Springer.
Maréchal, J. 1970 Thèse Docteur-Ingénieur, Universitè Scientifique et Médical de Grenoble.
Mathieu, J. & Comte-Bellot, G. 1958 C.R. Acad. Sci. Paris 246, 2220–2223.
Mestayer, P. 1980 Thèse Docteur ès Sciences Physiques, Université d'Aix-Marseille II.
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics: Mechanics of Turbulence, vol. 2. MIT Press.
Nelkin, M. 1981 Phys. Fluids 24, 556–557.
Nelkin, M. & Bell, T. L. 1978 Phys. Rev. A17, 363–369.
Novikov, E. A. 1971 Prikl. Math. Mekh. 35, 266–277.
Novikov, E. A. & Stewart, R. W. 1964 Izv. Geophys. 3, 408–413.
Obukhov, A. M. 1962 J. Fluid Mech. 13, 77–81.
Saffman, P. G. 1968 Lectures on Homogeneous Turbulence: Topics in Nonlinear Physics. Springer.
Schertzer, D. & Lovejoy, S. 1983 Reprints of IUTAM Symp. on Turbulence and Chaotic Phenomena in Fluids, Kyoto, p. 141.
Sreenivasan, K. R., Chambers, A. J. & Antonia, R. A. 1978 Boundary-Layer Meteor. 14, 341–359.
Tennekes, H. 1968 Phys. Fluids 11, 669–671.
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.
Tennekes, H. & Wyngaard, J. C. 1972 J. Fluid Mech. 55, 93–103.
Van Atta, C. W. & Chen, W. Y. 1970 J. Fluid Mech. 44, 145–159.
Van Atta, C. W. & Park, J. 1972 In Statistical Models and Turbulence (ed. M. Rosenblatt & C. Van Atta). Lectures Notes in Physics, vol. 12, pp. 402–426. Springer.
Vasilenko, V. M., Lyubimtsev, M. N. & Ozmidov, R. V. 1975 Izv. Atmos. Ocean. Phys. 11, 926–932.
Wygnanski, I. & Fiedler, H. 1969 J. Fluid Mech. 38, 577.
Wyngaard, J. C. & Pao, Y. H. 1972 In Statistical Models and Turbulence (ed. M. Rosenblatt & C. Van Atta). Lecture Notes in Physics, vol. 12, pp. 384–401. Springer.
Yaglom, A. M. 1966 Sov. Phys. Dokl. 11, 26–29.