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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 δu1 and the second-order moment of δu1 is presented in a slightly more general form relating the mean value of the product δu1(δui)2, where (δui)2 is the sum of the square of the three velocity increments, to the secondorder moment of δui. In this form, the relation is similar to that derived by Yaglom for the mean value of the product δu1(δuθ)2 where (δuθ)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.

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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References

Anselmet, E., Gagne, Y., Hopfinger, E. J. & Antonia, R. A. 1984 High-order velocity structure functions in turbulent shear flows. J. Fluid Mech. 140, 63–89.CrossRefGoogle Scholar
Antonia, R. A., Anselmet, F. & Chambers, A. J. 1986 Assessment of local isotropy using measurements in a turbulent plane jet. J. Fluid Mech. 163, 365–391.Google Scholar
Antonia, R. A. & Browne, L. W. B. 1986 Anisotropy of the temperature dissipation in a turbulent wake. J. Fluid Mech. 163, 393–403.CrossRefGoogle Scholar
Antonia, R. A., Chambers, A. J. & Browne, L. W. B. 1983 Relations between structure functions of velocity and temperature in a turbulent jet. Exps. Fluids 1, 213–219.CrossRefGoogle Scholar
Antonia, R. A., Hopfinger, E. J., Gagne, Y. & Anselmet, F. 1984 Temperature structure functions in turbulent shear flows. Phys. Rev. A 30, 2704–2707.Google Scholar
Antonia, R. A. & Kim, J. 1994 A numerical study of local isotropy of turbulence. Phys. Fluids A 6, 834–841.CrossRefGoogle Scholar
Antonia, R. A., Satyaprakash, B. R. & Chambers, A. J. 1982 Reynolds number dependence of velocity structure functions in turbulent shear flows. Phys. Fluids 25, 29–37.CrossRefGoogle Scholar
Antonia, R. A., Satyaprakash, B. R. & Hussain, A. K. M. F. 1982 Statistics of fine scale velocity in turbulent plane and circular jets. J. Fluid Mech. 119, 55–89.Google Scholar
Antonia, R. A. & Van Atta, C. W. 1978 Structure functions of temperature fluctuations in turbulent shear flows. J. Fluid Mech. 84, 561–580.Google Scholar
Antonia, R. A., Zhu, Y., Anselmet, F. & Ould-Rouis, M. 1996 Comparison between the sum of the second-order velocity structure functions and the second-order temperature structure functions. Phys. Fluids 8, 3105–3111.Google Scholar
Batchelor, G. K. 1947 Kolmogoroff's theory of locally isotropic turbulence. Proc. Camb. Phil. Soc. 43, 553–559.Google Scholar
Batchelor, G. K. 1959 Small-scale variation of convected quantities like temperature in turbulent fluid. Part 1. General discussion and the case of small conductivity. J. Fluid Mech. 5, 113–133 Google Scholar
Batchelor, G. K. & Townsend, A. A. 1947 Decay of vorticity in isotropic turbulence. Proc. R. Soc. Lond. A 190, 543–550.Google Scholar
Beguier, C., Dekeyser, I. & LAUNDER, B. E. 1978 Ratio of scalar and velocity dissipation time scales in shear flow turbulence. Phys. Fluids 21, 307–310.Google Scholar
Browne, L. W. B., Antonia, R. A. & Shah, D. A. 1987 Turbulent energy dissipation in a wake. J. Fluid Mech. 179, 307–326.Google Scholar
Champagne, F. H. 1978 The fine-scale structure of the turbulent velocity field. J. Fluid Mech. 86, 67–108.Google Scholar
DURBIN, R A. & Speziale, C. G. 1991 Local anisotropy in strained turbulence at high Reynolds numbers. Trans. ASME J. Fluids Engng 113, 707.Google Scholar
Frisch, U. 1995 Turbulence : The Legacy of A. N. Kolmogorov. Cambridge University Press.CrossRefGoogle Scholar
Frisch, U., Sulem, P.-L. & Nelkin, M. 1978 A simple dynamical model of intermittent fully developed turbulence. J. Fluid Mech. 87, 719–736.Google Scholar
Fulachier, L. 1972 Contribution a l'etude des analogies des champs dynamique et thermique dans une couche limite turbulente — effet de l'aspiration. These Docteur es Sciences Physiques, Universite de Provence.Google Scholar
Fulachier, L. & Antonia, R. A. 1984 Spectral analogy between temperature and velocity fluctuations in several turbulent flows. Intl J. Heat Mass Transfer 27, 987–997.Google Scholar
Fulachier, L. & Dumas, R. 1976 Spectral analogy between temperature and velocity fluctuations in a turbulent boundary layer. J. Fluid Mech. 77, 257–277.Google Scholar
Hinze, J. O. 1959 Turbulence. McGraw-Hill.Google Scholar
Karman, T. VON & Howarth, L. 1938 On the statistical theory of isotropic turbulence. Proc. R. Soc. Lond. A 164, 192–215.Google Scholar
Karyakin, M. Yu., Kuznetsov, V. R. & Praskovsky, A. A. 1991 Experimental verification of the hypothesis of fine-scale isotropy of turbulence. Fluid Dyn. Res. 26, 658–670.CrossRefGoogle Scholar
Kim, J. & Antonia, R. A. 1993 Isotropy of the small scales of turbulence at low Reynolds number. J. Fluid Mech. 251, 219–238.Google Scholar
Kolmogorov, A. N. 1941 Energy dissipation in locally isotropic turbulence. Dokl. Akad. Nauk SSSR 32, 19–21.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1987 Fluid Mechanics, 2nd edn. Pergamon Press.Google Scholar
Lindborg, E. 1996 Studies in classical turbulence theory. PhD Thesis, Royal Institute of Technology, Stockholm.Google Scholar
Monin, A. S. 1959 On the theory of locally isotropic turbulence. Dokl. Akad. Nauk SSSR 125, 515–518.Google Scholar
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics. MIT Press.Google Scholar
Nelkin, M. 1994 Universality and scaling in fully developed turbulence. Adv. Phys. 43, 143–181.Google Scholar
Park, J. T. & Van Atta, C. W. 1980 Hot- and cold-wire sensitivity corrections for moments of the fine scale turbulence in heated flows. Phys. Fluids 23, 701–705.CrossRefGoogle Scholar
Saddoughi, S. G. & Veeravalli, S. F. 1994 Local isotropy in turbulent boundary layers at high Reynolds number. J. Fluid Mech. 268, 333–372.Google Scholar
Shah, D. A. & Antonia, R. A. 1986 Isotropic forms of vorticity and velocity structure function equations in several turbulent shear flows. Phys. Fluids 29, 4016–024.Google Scholar
Vainshtein, S. I. & Sreenivasan, K. R. 1994 Kolmogorov's 4/5“1 law and intermittency in turbulence. Phys. Rev. Lett. 73, 3085–3088.Google Scholar
Wyngaard, J. C. 1971 The effect of velocity sensitivity on temperature derivative statistics in isotropic turbulence. J. Fluid Mech. 48, 763–769.Google Scholar
Yaglom, A. M. 1949 On the local structure of a temperature field in a turbulent flow. Dokl. Akad. Nauk SSSR 69, 743–746.Google Scholar
Zhu, Y., Antonia, R. A. & Hosokawa, I. 1995 Refined similarity hypothesis for turbulent velocity and temperature fields. Phys. Fluids 7, 1637–1648.Google Scholar