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Refined similarity hypotheses for passive scalars mixed by turbulence

Published online by Cambridge University Press:  26 April 2006

G. Stolovitzky ,
P. Kailasnath  and
K. R. Sreenivasan
G. Stolovitzky
Affiliation:
Mason Laboratory, Yale Univeristy, New Haven, CT 06520-8286, USA
P. Kailasnath
Affiliation:
Mason Laboratory, Yale Univeristy, New Haven, CT 06520-8286, USA
K. R. Sreenivasan
Affiliation:
Mason Laboratory, Yale Univeristy, New Haven, CT 06520-8286, USA
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Abstract

In analogy with Kolmogorov's refined similarity hypotheses for the velocity field, two hypotheses are stated for passive scalar fields mixed by high-Reynolds-number turbulence. A ‘refined’ Yaglom equation is derived under the new assumption of local isotropy in pure ensembles, which is stronger than the usual assumption of local isotropy but weaker than the isotropy of the large scale. The new theoretical result is shown to be consistent with the hypotheses of refined similarity for passive scalars. These hypotheses are approximately verified by experimental data on temperature fluctuations obtained (in air) at moderate Reynolds numbers in the wake of a heated cylinder. The fact that the refined similarity hypotheses are stated for high Reynolds (and Péclet) numbers, but verified at moderate Reynolds (and Péclet) numbers suggests that these hypotheses are not sufficiently sensitive tests of universality. It is conjectured that possible departures from universality are hidden by the process of taking conditional expectations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 297 , 25 August 1995 , pp. 275 - 291
Copyright
© 1995 Cambridge University Press

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References

Anselmet, F, Gagne, Y., Hopfinger, E. J. & Antonia, R. A. 1984 J. Fluid Mech. 140, 63.
Antonia, R. A., Chambers, A. J. & Phan-Thien, N. 1980 Boundary-Layer Met. 19, 19.
Antonia, R. A., Hopfinger, E. J., Gagne, Y. & Anselmet, F. 1984 Phys. Rev. A 30, 2704.
Antonia, R. A. & Van Atta, C. W. 1975 J. Fluid Mech. 67, 273.
Batchelor, G. K., 1959 J. Fluid Mech. 5, 113.
Batchelor, G. K., Howells, I. D & Townsend, A. A. 1959 J. Fluid Mech. 5, 134.
Batchelor, G. K. & Townsend, A. A. 1948 Proc. R. Soc. Lond. A 199, 238.
Chen, S., Doolen, G. D., Kraichnan, R. H. & She, Z.-S. 1993 Phys. Fluids A 5, 458.
Chen, S., Doolen, G. D., Kraichnan, R. H. & Wang, L.-P. 1995 Phys. Rev. Lett. 74, 1755.
Corrsin, S. 1951 J. Appl. Phys. 22, 469.
Hosokawa, I. 1993 J. Phys. Soc. Japan 62, 10.
Hosokawa, I. 1994 Phys. Rev. E 49, R4775.
Kailasnath, P. 1988a Simultaneous measurements of the velocity and temperature in a heated turbulent wake. Technical Report, Mason Laboratory, Yale University.
Kailasnath, P. 1988b Correlation between the dissipation fields of temperature and velocity in turbulent flows. Technical Report, Mason Laboratory, Yale University.
Kolmogorov, A. N. 1941a Dokl. Akad. Nauk SSSR 30, 301.
Kolmogorov, A. N. 1941b Dokl. Akad. Nauk SSSR 32, 19.
Kolmogorov, A. N. 1962 J. Fluid Mech. 13, 82.
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics. Pergamon Press.
Meneveau, C. & Sreenivasan, K. R. 1991 J. Fluid Mech. 224, 429.
Meneveau, C., Sreenivasan, K. R., Kailasnath, P. & Fan, M.S. 1990 Phys. Rev. A 41, 894.
Monin, A. S. & Yaglom, A. M. 1971 Statistical Fluid Mechanics, Vol. I. MIT Press.
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics, Vol. II. MIT Press.
Obukhov, A. M. 1949 Izv. Akad. Nauk SSSR, Ser. Geogr. i Geofiz. 13, 58.
Obukhov, A. M. 1962 J. Fluid Mech. 13, 77.
Peattie, R. 1987 J. Phys. E 20, 565.
Praskovsky, A. A. 1992 Phys. Fluids A 4, 2589.
Sreenivasan, K. R. 1991 Proc. R. Soc. Lond. A 434, 165.
Sreenivasan, K. R., Antonia, R. A. & Danh, H. Q. 1977 Phys. Fluids 20, 1238.
Sreenivasan, K. R. & Meneveau, C. 1988 Phys. Rev. A 38, 6287.
Stolovitzky, G. 1994 The statistical order of small scales in turbulence. PhD thesis, Yale University, New Haven, Connecticut.
Stolovitzky, G., Kailasnath P. & Sreenivasan, K. R. 1992 Phys. Rev. Lett. 69, 1178.
Stolovitzky, G. & Sreenivasan, K. R. 1994 Rev. Mod. Phys. 66, 229.
Thoroddsen, S. T. 1995 Phys. Fluids A 7, 691.
Thoroddsen, S. T. & Van Atta, C. W. 1992a Phys. Fluids A 4, 2592.
Thoroddsen, S. T. & Van Atta, C. W. 1992b J. Fluid Mech 244, 547.
Van Atta, C. W. 1971 Phys. Fluids 14, 1803.
Wang, L.-P., Chen, S., Brasseur, J. G. & Wyngaard, J. C. 1994 Examination of fundamental hypotheses in the Kolmogorov refined turbulence theory through high-resolution simulation. Part 1. Velocity field. J. Fluid Mech. (submitted).Google Scholar
Yaglom, A. M. 1949 Dokl. Akad. Nauk. 69, 743.