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The fine-scale structure of the turbulent velocity field

Published online by Cambridge University Press:  12 April 2006

F. H. Champagne
F. H. Champagne
Affiliation:
Department of Applied Mechanics and Engineering Sciences, University of California, La Jolla
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Abstract

The existence of universal similarity of the fine-scale structure of turbulent velocity fields and the validity of the original Kolmogorov local similarity theory and the later reformulations were investigated. Recent studies of the fine-scale velocity field for many different flows, e.g. grid flows, wakes, jets and the atmospheric boundary layer, are shown to provide considerable evidence for the existence of Kolmogorov normalized spectral shapes which are universal in the sense that they describe the high wave-number spectral behaviour of all turbulent flow fields with a similar value of the turbulence Reynolds number Rλ. The normalized spectral shapes vary with Rλ in a manner consistent with the later reformulations. The Reynolds number dependence of the normalized spectra is demonstrated for the Rλ range from about 40 to 13 000. Expressions for the Kolmogorov normalized spectral functions are presented for three values of Rλ. Also revealed in this study is the importance of considering effects on spectra caused by deviations from Taylor's approximation in high intensity turbulent flows. Lumley's (1965) model is used to correct the high frequency portion of the measured one-dimensional spectra for these effects. An analytical solution to Lumley's expression is presented and applied to the data.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 86 , Issue 1 , 15 May 1978 , pp. 67 - 108
Copyright
© 1978 Cambridge University Press

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References

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Boston, N. E. J. & Burling, R. W. 1972 J. Fluid Mech. 55, 473.
Bradshaw, P. 1966 Nat. Phys. Lab. Aero. Rep. no. 1124.
Bradshaw, P. 1967 Nat. Phys. Lab. Aero. Rep. no. 1220.
Busch, N. E. 1973 Boundary-Layer Met. 4, 213.
Champagne, F. H., Friehe, C. A., Larue, J. C. & Wyngaard, J. 1977 J. Atmos. Sci. 34, 515.
Champagne, F. H., Harris, V. G. & Corrsin, S. 1970 J. Fluid Mech. 41, 81.
Champagne, F. H., Sleicher, C. A. & Wehrmann, O. H. 1967 J. Fluid Mech. 28, 153.
Champagne, F. H., Wygnanski, I. & Pao, Y. H. 1976 J. Fluid Mech. 74, 209.
Comte-Bellot, G. 1965 Publ. Sci. Tech. Min. Air (France) Notes Tech. no. 419.
Comte-Bellot, G. & Corrsin, S. 1971 J. Fluid Mech. 48, 273.
Corrsin, S. 1957 Proc. 1st Naval Hydro. Symp., Nat. Acad. Sci. Math. Res. Counc. publ. 515, p. 373.
Corrsin, S. 1959 J. Geophys. Res. 64, 2134.
Elderkin, C. E. 1966 Ph.D. thesis, Dept. of Atmospheric Sciences, University of Washington, Seattle.
Favre, A. J. 1965 J. Appl. Mech. 87, 241.
Fisher, M. J. & Davies, P. O. A. L. 1964 J. Fluid Mech. 18, 97.
Gibson, C. H. & Masiello, P. 1972 Proc. Symp. Statistical Models and Turbulence. Lecture Notes in Physics, vol. 12. Springer.
Gibson, C. H. & Schwarz, W. H. 1963 J. Fluid Mech. 16, 365.
Gibson, C. H., Stegen, G. R. & Williams, R. B. 1970 J. Fluid Mech. 41, 153.
Gibson, M. M. 1963 J. Fluid Mech. 15, 161.
Grant, H. L., Stewart, R. W. & Moilliet, A. 1962 J. Fluid Mech. 12, 241.
Gurvich, A. S. & Yaglom, A. M. 1967 Phys. Fluids Suppl. 10, S 59.
Heskestad, G. 1965 J. Appl. Mech. 87, 735.
Kaimal, J. C., Wyngaard, J. C., Isumi, Y. & COTÉ, O. R. 1972 Quart. J. Roy. Met. Soc. 98, 563.
KÁrmÁn, Th. Von & Howarth, L. 1938 Proc. Roy. Soc. A 164, 192.
Kholmyanskiy, M. Z. 1972 Izv. Atmos. Ocean. Phys. 8, 472.
Kistler, A. L. & Vrebalovich, T. 1966 J. Fluid Mech. 26, 37.
Kolmogorov, A. N. 1941 Dokl. Akad. Nauk SSSR 30, 301.
Kolmogorov, A. N. 1962 J. Fluid Mech. 13, 82.
Kuo, A. 1970 Ph.D. thesis, Dept. of Mechanics, Johns Hopkins University.
Kuo, A. & Corrsin, S. 1972 J. Fluid Mech. 56, 447.
Laufer, J. 1954 N.A.C.A. Rep. no. 1174.
Lumley, J. L. 1964 J. Atmos. Sci. 21, 99.
Lumley, J. L. 1965 Phys. Fluids 8, 1056.
Mestayer, P. G. 1975 Thèse de Docteur-Ingénieur, Institut de Mécanique Statistique de la Turbulence, Université de Marseille, France.
Oboukhov, A. M. 1962 J. Fluid Mech. 13, 77.
Panchev, S. 1971 Random Functions and Turbulence. Pergamon.
Pao, Y. H. 1965 Phys. Fluids 8, 1063.
Pao, Y. H., Hansen, S. D. & Macgregor, G. R. 1969 Boeing Sci. Res. Lab. Doc. D1-82-0863.
Pond, S., Smith, S. D., Hamblin, P. F. & Burling, R. W. 1966 J. Atmos. Sci. 23, 376.
Pond, S., Stewart, R. W. & Burling, R. W. 1963 J. Atmos. Sci. 20, 319.
Robertson, H. P. 1940 Proc. Camb. Phil. Soc. 36, 209.
Roshko, A. 1960 J. Fluid Mech. 10, 348.
Sheih, C. M., Tennekes, H. & Lumley, J. L. 1971 Phys. Fluids 14, 201.
Stegen, G. R., Gibson, C. H. & Friehe, C. A. 1973 J. Phys. Ocean. 3, 86.
Stewart, R. W. & Townsend, A. A. 1951 Phil. Trans. Roy. Soc. A 243, 359.
Stewart, R. W., Wilson, J. R. & Burling, R. W. 1970 J. Fluid Mech. 41, 141.
Taylor, G. I. 1938 Proc. Roy. Soc. A 164, 476.
Taylor, R. J. 1955 Austr. J. Phys. 8, 535.
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.
Tennekes, H. & Wyngaard, J. C. 1972 J. Fluid Mech. 55, 93.
Uberoi, M. S. & Freymuth, P. 1969 Phys. Fluids 12, 1359.
Weiler, H. S. & Burling, R. W. 1967 J. Atmos. Sci. 24, 653.
Williams, R. M. 1974 Ph.D. thesis, Oregon State University, Corvallis.
Wills, J. A. B. 1964 J. Fluid Mech. 20, 417.
Wygnanski, I. & Fiedler, H. 1969 J. Fluid Mech. 38, 577.
Wyngaard, J. C. 1968 J. Sci. Instrum. 1, 1105.
Wyngaard, J. C. 1969 J. Sci. Instrum. 2, 983.
Wyngaard, J. C. 1971 J. Fluid Mech. 48, 763.
Wyngaard, J. C. & Pao, Y. H. 1972 Proc. Symp. Statistical Models and Turbulence. Lecture Notes in Physics, vol. 12. Springer.
Wyngaard, J. C. & Tennekes, H. 1970 Phys. Fluids 13, 1962.
Yaglom, A. M. 1966 Dokl. Akad. Nauk SSSR 166, 49.