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Locally axisymmetric turbulence

Published online by Cambridge University Press:  26 April 2006

William K. George  and
Hussein J. Hussein
William K. George
Affiliation:
State University of New York at Buffalo, Buffalo, NY 14260, USA
Hussein J. Hussein
Affiliation:
Vanderbilt University, Nashville, TN 37235, USA
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Abstract

The failure of local isotropy to describe the experimentally obtained derivative moments in turbulent shear flows has previously been well-documented, but is briefly reviewed. The same data are then used to evaluate the hypothesis that the turbulence is locally axisymmetric. Locally axisymmetric turbulence is defined herein as turbulence which is locally invariant to rotations about a preferred axis.

The derivative moment relations are derived from the general form of the two-point velocity correlation tensor near the origin for axisymmetric turbulence. These are used to derive relations for the rate of dissipation of kinetic energy, the mean-square vorticity, and the components of each. Almost all of the experimental derivative moment data are shown to be consistent with these equations, and thus with local axisymmetry.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 233 , December 1991 , pp. 1 - 23
Copyright
© 1991 Cambridge University Press

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References

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 temperature dissipation in a turbulent wake. J. Fluid Mech. 163, 393–405.Google Scholar
Antonia, R. A., Browne, L. W. B. & Chambers, A. J. 1984 On the spectrum of the transverse derivative of the streamwise velocity in a turbulent flow. Phys. Fluids 27, 2628–2631.Google Scholar
Antonia, R. A., Browne, W. B. & Shah, D. A. 1988 Characteristics of vorticity fluctuations in a turbulent wake. J. Fluid Mech. 189, 349–366.Google Scholar
Antonia, R. A., Rajagopalan, S., Browne, L. W. B. & Chambers, A. J. 1982 Correlations of squared velocity and temperature derivatives in a turbulent plane jet. Phys. Fluids 25, 1156–1158.Google Scholar
Balint, J. L. & Wallace, J. M. 1985 Velocity and vorticity statistical properties of a turbulent boundary layer. Bull. Am. Phys. Soc. 30, 1743.Google Scholar
Balint, J. L., Vukoslavçević, P. & Wallace, J. M. 1987 A study of the vortical structure of the turbulent boundary layer. In Advances in Turbulence (ed. G. Compte-Bellot & J. Mathieu), pp. 456–463. Springer.
Balint, J. L., Wallace, J. M. & Vukoslavçevkć, P. 1989 Vorticity spectra in turbulent flows. Bull. Am. Phys. Soc. 34, 2292.Google Scholar
Batchelor, G. K. 1946 The theory of axisymmetric turbulence.. Proc. R. Soc. Lond. A 186, 480–502.Google Scholar
Batchelor, G. K. 1953 Homogeneous Turbulence. Cambridge University Press.
Beuther, P. D. 1980 Experimental investigation of the axisymmetric buoyant plume. Ph.D. dissertation, SUNY/Buffalo.
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, 1978.Google Scholar
Champagne, F. H., Pao, Y. H. & Wygnanski, I. J. 1976 On the two-dimensional mixing region. J. Fluid Mech. 74, 209–250.Google Scholar
Chandrasekhar, S. 1950 The theory of axisymmetric turbulence.. Proc. R. Soc. Lond. A 242, 557–577.Google Scholar
Everitt, K. W. & Robins, A. G. 1978 The development and structure of turbulent plane jets. J. Fluid Mech. 88, 563–583.Google Scholar
Fabris, G. 1974 Conditionally sampled turbulent thermal and velocity fields in the wake of a warm cylinder and its interaction with an equal cool wake. Ph.D. dissertation, Illinois Institution of Technology
George, W. K. 1988 Self-preservation, and its relation to initial conditions, and coherent structures. In Advances in Turbulence (W. K. George & R. Arndt), pp. 39–73. Hemisphere.
George, W. K., Hussein, H. J. & Woodward, S. H. 1989 An evaluation of the effect of a fluctuating convection velocity on the validity of Taylor's hypothesis. In Proc. 10th Australasian Fluid Mechanics Conf., University of Melbourne, Dec. 11–15, 1989 (ed. A. E. Perry et al.), vol. II, pp. 11.5–11.8.
Gutmark, E. & Wygnanski, I. 1976 The planar turbulent jet. J. Fluid Mech. 73, 465–495.Google Scholar
Hinze, J. O. 1975 Turbulence. McGraw-Hill.
Hussein, H. J. 1988 Measurements of small scale turbulence in an axisymmetric jet using moving hot wires. Ph.D. dissertation SUNY/Buffalo.
Hussein, H. J. & George, W. K. 1988 The local axisymmetry of small scale turbulence in shear flows. Bull. Am. Phys. Soc. 33, 2234.Google Scholar
Hussein, H. J. & George, W. K. 1989 Measurements of small scale turbulence in an axisymmetric jet using moving hot wires. In Proc. 7th Symp. on Turbulent Shear Flows, Stanford Univ., August 14–18, 1989 (ed. W. C. Reynolds et al.), vol. II, pp. 30.2.1–30.2.6.
Hussein, H. J. & George, W. K. 1990 Spatial resolution of parallel wires In Proc. Turbulence Forum, ASME Fluids Engng Mtg, Toronto, June 5–7, 1990.
Karyakin, M. Y., Praskovsky, A. A. & Kuznetsov, V. R. 1990 Experimental verification of local isotropy assumption in high Reynolds number flows. Presentation at Second European Conf. on Turbulence, Stockholm, July 3–5, 1990.
Kolmogorov, A. A. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. C. R. Akad Sci. SSSR 30, 301–305.Google Scholar
Krishnamoorthy, L. V. & Antonia, R. A. 1987 Temperature-dissipation measurements in a turbulent boundary layer. J. Fluid Mech. 176, 265–281.Google Scholar
Laufer, J. 1954 The structure of turbulence in fully developed pipe flow. NACA Rep. 1174.Google Scholar
Launder, B. E., Reece, G. J. & Rodi, W. 1975 Progress in the development of a Reynolds stress turbulence closure. J. Fluid Mech. 68, 537–560.Google Scholar
Lawn, C. J. 1971 The determination of the rate of dissipation in turbulent pipe flow. J. Fluid Mech. 48, 477–505.Google Scholar
Lumley, J. L. 1965 Interpretation of time spectra measured in high-intensity shear flows. Phys. Fluids 8, 1056–1062.Google Scholar
Monin, A. M. & Yaglom, A. M. 1975 Statistical Fluid Mechanics, vol. II. MIT Press.
Reynolds, W. C. 1976 Computation of turbulent flows. Ann. Rev. Fluid Mech. 8, 183–208.Google Scholar
Sreenivasan, K. R., Antonia, R. A. & Danh, H. Q. 1977 Temperature dissipation fluctuations in a turbulent boundary layer. Phys. Fluids 20, 1238–1249.Google Scholar
Taulbee, D. B. 1988 Engineering turbulence models. In Advances in Turbulence (ed. W. K. George & R. Arndt), pp. 75–125. Hemisphere.
Tavoularis, S. & Corrsin, S. 1981 Experiments in nearly homogeneous turbulent shear flow with a uniform mean temperature gradient. Part 1. J. Fluid Mech. 104, 311–347.Google Scholar
Taylor, G. I. 1935 Statistical theory of turbulence.. Proc. R. Soc. Lond. A 151, 421–478.Google Scholar
Townsend, A. A. 1948 Local isotropy in the turbulent wake of a cylinder. Austral. J. Sci. Res. 1, 161–174.Google Scholar
Verollet, E. 1972 Etude d'une couche limite turbulente avec aspiration et chaufage à la paroi. Thèse Docteur dès Sciences, Université de Provence (Also Rapport CEA-R-4872 CEN Saclay).
Wygnanski, I. & Fiedler, H. 1969 Some measurements in the self-preserving jet. J. Fluid Mech. 38, 577–612.Google Scholar
Wyngaard, J. C. 1968 Measurement of small scale turbulence structure with hot-wires. J. Sci. Instrum. 1, 1105–1108.Google Scholar
Wyngaard, J. & Clifford, S. 1977 Taylor's hypothesis and high frequency turbulence spectra. J. Atmos. Sci. 34, 922–929.Google Scholar