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Analogy between predictions of Kolmogorov and Yaglom

Published online by Cambridge University Press:  10 February 1997

R. A. Antonia ,
M. Ould-Rouis ,
F. Anselmet  and
Y. Zhu
R. A. Antonia
Affiliation:
, Department of Mechanical Engineering, University of Newcastle, NSW, 2308, Australia
M. Ould-Rouis
Affiliation:
Institut de Recherche sur les Phénomènes Hors Équilibre, Université d’Aix-Marseille II, 13003 Marseille, France
F. Anselmet
Affiliation:
Institut de Recherche sur les Phénomènes Hors Équilibre, Université d’Aix-Marseille II, 13003 Marseille, France
Y. Zhu
Affiliation:
, Department of Mechanical Engineering, University of Newcastle, NSW, 2308, Australia
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Extract

The relation, first written by Kolmogorov, between the third-order moment of the longitudinal velocity increment δu 1 and the second-order moment of δu 1 is presented in a slightly more general form relating the mean value of the product δu 1(δu i)2, where (δu i)2 is the sum of the square of the three velocity increments, to the secondorder moment of δu i. In this form, the relation is similar to that derived by Yaglom for the mean value of the product δu 1(δu θ)2 where (δu θ)2 is the square of the temperature increment. Both equations reduce to a ‘four-thirds’ relation for inertialrange separations and differ only through the appearance of the molecular Prandtl number for very small separations. These results are confirmed by experiments in a turbulent wake, albeit at relatively small values of the turbulence Reynolds number.

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Type
Research Article
Information
Journal of Fluid Mechanics , Volume 332 , February 1997 , pp. 395 - 409
Copyright
Copyright © Cambridge University Press 1997

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