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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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