Hostname: page-component-8448b6f56d-m8qmq Total loading time: 0 Render date: 2024-04-24T07:54:19.764Z Has data issue: false hasContentIssue false
  • English
  • Français

The structure of internal intermittency in turbulent flows at large Reynolds number: experiments on scale similarity

Published online by Cambridge University Press:  29 March 2006

C. W. Van Atta  and
T. T. Yeh
C. W. Van Atta
Affiliation:
Department of Applied Mechanics and Engineering Sciences, University of California, San Diego
T. T. Yeh
Affiliation:
Department of Applied Mechanics and Engineering Sciences, University of California, San Diego
Get access Rights & Permissions [Opens in a new window]

Abstract

Some of the statistical characteristics of the breakdown coefficient, defined as the ratio of averages over different spatial regions of positive variables characterizing the fine structure and internal intermittency in high Reynolds number turbulence, have been investigated using experimental data for the streamwise velocity derivative ∂u/∂t measured in an atmospheric boundary layer. The assumptions and predictions of the hypothesis of scale similarity developed by Novikov and by Gurvich & Yaglom do not adequately describe or predict the statistical characteristics of the breakdown coefficient qr,l of the square of the streamwise velocity derivative. Systematic variations in the measured probability densities and consistent variations in the measured moments show that the assumption that the probability density of the breakdown coefficient is a function only of the scale ratio is not satisfied. The small positive correlation between adjoint values of qr,l and measurements of higher moments indicate that the assumption that the probability densities for adjoint values of qr,l are statistically independent is also not satisfied. The moments of qr,l do not have the simple power-law character that is a consequence of scale similarity.

As the scale ratio l/r changes, the probability density of qr,l evolves from a sharply peaked, highly negatively skewed density for large values of the scale ratio to a very symmetrical distribution when the scale ratio is equal to two, and then to a highly positively skewed density as the scale ratio approaches one. There is a considerable effect of heterogeneity on the values of the higher moments, and a small but measurable effect on the mean value. The moments are roughly symmetrical functions of the displacement of the shorter segment from the centre of the larger one, with a minimum value when the shorter segment is centrally located within the larger one.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 59 , Issue 3 , 17 July 1973 , pp. 537 - 559
Copyright
© 1973 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Chen, W. Y. 1971 Lognormality of small-scale structure of turbulence Phys. Fluids, 14, 1639.Google Scholar
Frenkiel, F. N. & Klebanoff, P. S. 1971 Statistical properties of velocity derivatives in a turbulent field J. Fluid Mech. 48, 183.Google Scholar
Gibson, C. H. & Masiello, P. 1972 Observations of the variability of dissipation rates of turbulent velocity and temperature fields, in statistical models and turbulence. Lecture Notes in Physics, vol. 12 (ed. M. Rosenblatt and C. Van Atta). Springer.
Gibson, C. H., Stegen, G. R. & Williams, R. B. 1970 Statistics of the fine structure of turbulent velocity and temperature fields measured at high Reynolds number J. Fluid Mech. 41, 153.Google Scholar
Gurvich, A. S. 1966 On the probability distribution of the square of the difference of velocities in a turbulent flow Izv. Akad. Nauk SSSR, Physics of the Atmosphere and Ocean, 2, no. 10.Google Scholar
Gurvich, A. S. 1967 On the probability distribution of the square of the temperature difference between two points of a turbulent stream Dokl. Akad. Nauk SSSR, 172, no. 3.Google Scholar
Gurvich, A. S. & Yaglom, A. M. 1967 Breakdown of eddies and probability distributions for small-scale turbulence Phys. Fluids Suppl. 10, S59.Google Scholar
Haugen, D. A., Kaimal, J. C. & Bradley, E. F. 1971 An experimental study of Reynolds stress and heat flux in the atmospheric boundary layer Quart. J. Roy. Met. Soc. 97, 168.Google Scholar
Hekestad, G. 1965 A generalized Taylor hypothesis with application for high Reynolds number turbulent shear flows J. Appl. Mech. 32, 735.Google Scholar
Kholmyansky, M. Z. 1970 Investigations of the micro-pulsations of the velocity gradient of the wind in the atmospheric layer near the ground Izv. Akad. Nauk. SSSR, Physics of the Atmosphere and Ocean, 6, no. 4.Google Scholar
Kolmogorov, A. N. 1941 The local structure of turbulence in an incompressible fluid for very large Reynolds numbers Dokl. Akad. Nauk SSSR, 30, 301.Google Scholar
Kolmogorov, A. N. 1962 A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number J. Fluid Mech. 13, 82.Google Scholar
Kuo, A. Y. & Corrsin, S. 1971 Experiments on internal intermittency and fine-structure distribution functions in fully turbulent fluid J. Fluid Mech. 50, 285.Google Scholar
Novikov, E. A. 1965 On higher-order correlations in a turbulent flow Izv. Akad. Nauk SSSR, Ser. Geofiz. 1, 788.Google Scholar
Novikov, E. A. 1969 Similarity of scale for stochastic fields Dokl. Akad. Nauk SSSR, 184, no. 5.Google Scholar
Novikov, E. A. 1971 Intermittency and scale similarity in the structure of a turbulent flow Prikl. Math. Mech. 35, 266.Google Scholar
Novikov, E. A. & Stewart, R. W. 1964 Turbulent intermittency and the spectrum of fluctuations of energy dissipation. Izv. Akad. Nauk SSSR, Ser. Geophys. no. 3.Google Scholar
Obukhov, A. M. 1941 On the distribution of energy in the spectrum of turbulent flow Dokl. Akad. Nauk SSSR, 32, 19.Google Scholar
Obukhov, A. M. 1962 Some specific features of atmospheric turbulence J. Fluid Mech. 13, 77.Google Scholar
Onsager, L. 1949 The distribution of energy in turbulence Nuovo Cimento Suppl. 6, no. 2, 277.Google Scholar
Orszag, S. A. 1970 Indeterminacy of the moment problem for intermittent turbulence Phys. Fluids, 13, 2211.Google Scholar
Prohorov, J. V. & Rozanov, J. A. 1967 Probability Theory. Moscow: Nauka.
Saffman, P. G. 1970 Dependence on Reynolds number of high-order moments of velocity derivatives in isotropic turbulence Phys. Fluids, 13, 2193.Google Scholar
Stewart, R. W., Wilson, J. R. & Burling, R. W. 1970 Some statistical properties of small-scale turbulence in an atmospheric boundary layer J. Fluid Mech. 41, 141.Google Scholar
Taylor, G. I. 1938 The spectrum of turbulence. Proc. Roy. Soc. A 164, 476.Google Scholar
Tennekes, H. & Wyngaard, J. C. 1972 The intermittent small-scale structure of turbulence: data-processing hazards. J. Fluid Mech. 55, 93.Google Scholar
Van Atta, C. W. & Chen, W. Y. 1970 Structure functions of turbulence in the atmospheric boundary layer over the ocean J. Fluid Mech. 44, 145.Google Scholar
Wyngaard, J. C. & Lumley, J. L. 1967 A sharp cutoff spectral differentiator J. Appl. Meteorol. 6, 952.Google Scholar
Wyngaard, J. C. & Pao, Y. H. 1972 Some measurements of the fine structure of large Reynolds number turbulence, in statistical models and turbulence. Lecture Notes in Physics, vol. 12 (ed. M. Rosenblatt & C. Van Atta). Springer.
Wyngaard, J. C. & Tennekes, H. 1970 Measurements of the small-scale structure of turbulence at moderate Reynolds numbers. Phys. Fluids, 13, 1962.Google Scholar
Yaglom, A. M. 1966 On the influence of fluctuations in energy dissipation on the form of turbulence characteristics in the inertial range Dokl. Akad. Nauk SSSR, 166, 49.Google Scholar