Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-17T05:07:56.607Z Has data issue: false hasContentIssue false
  • English
  • Français

Experiments on internal intermittency and fine-structure distribution functions in fully turbulent fluid

Published online by Cambridge University Press:  29 March 2006

Albert Yi-Shuong Kuo  and
Stanley Corrsin
Albert Yi-Shuong Kuo
Affiliation:
Department of Mechanics, The Johns Hopkins University Present address: Virginia Institute of Marine Science, Gloucester Pt., Va. 23062.
Stanley Corrsin
Affiliation:
Department of Mechanics, The Johns Hopkins University
Get access Rights & Permissions [Opens in a new window]

Abstract

Spatial ‘intermittency’ in the velocity field fine-structure of fully turbulent flow regions, first observed by Batchelor & Townsend (1949), is studied further here in grid-generated nearly isotropic turbulence and on the axis of a round jet. At large enough Reynolds numbers, appropriately filtered hot-wire anemometer signals appear intermittent as the turbulent patterns are convected past the hot wire by the mean flow. Measurements show that there is a decrease in the relative fluid volume (equal to the ‘intermittency factor’) occupied by fine-structure of given size as the turbulence Reynolds number is increased. They show also that, for a fixed Reynolds number, the relative volume is smaller for smaller fine-structure. The average linear dimension of the fine-structure regions turns out to be much larger than the sizes of fine-structure therein. At Rλ, = 110, for example, the ratio ranges from 15 to 30, decreasing with decreasing ‘eddy’ size. It appears to be approaching an asymptote with increasing Rλ.

The flatness factors and probability distributions of the first derivative, the second derivative, band-passed and high-passed velocity fluctuation signals were also measured. The turbulence Reynolds numbers Rλ ranged from 12 to 830. The flatness factors of the first and the second derivatives increase monotonically with Rλ. Those of the second derivative vary with Rλ0.25 for Rλ < 100, and with Rλ0.75 for Rλ > 300. No indication of asymptotic constant values was observed for Rλ up to the order of one thousand.

The probability distributions of velocity fluctuations and large-scale signals are nearly normal, while the small-scale signals are not. The flatness factor of the filtered band-pass velocity signal increases with increasing frequency.

At the larger Reynolds numbers, the square of the signal associated with large wave-numbers may be approximated by a log-normal probability distribution for amplitudes when probabilities fall between 0·3 and 0·95, in limited agreement with the theory of Kolmogorov (1962), Oboukhov (1962), Gurvich & Yaglom (1967).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 50 , Issue 2 , 29 November 1971 , pp. 285 - 319
Copyright
© 1971 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

Batchelor, G. K. & Townsend, A. A. 1947 Proc. Roy. Soc. A 190, 534.
Batchelor, G. K. & Townsend, A. A. 1949 Proc. Roy. Soc. A 199, 238.
Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Bradshaw, P. 1967 Nat. Phys. Lab. Aero. Rep. 1220.
Champagne, F. H., Harris, V. G. & Corrsin, S. 1970 J. Fluid Mech. 41, 81.
Comte-Bellot, G. 1965 Ecoulement Turbulent Entre Deux Parois Paralleles. Paris: Publ. Sci. et Tech. du Min. de l'Air.
Comte-Bellot, G. & Corrsin, S. 1966 J. Fluid Mech. 25, 567.
Comte-Bellot, G. & Corrsin, S. 1971 J. Fluid Mech. 48, 273.
Corrsin, S. 1958 NACA Res. Memo 58B11.
Corrsin, S. 1962 Phys. Fluids, 5, 1301.
Fisher, M. J. & Davies, P. O. A. L. 1964 J. Fluid Mech. 18, 97.
Gibson, C. H., Stegen, G. R. & McConnell, S. 1970 Phys. Fluids, 13, 2448.
Gibson, C. H., Stegen, G. R. & Williams, R. B. 1970 J. Fluid Mech. 41, 153.
Gibson, M. M. 1963 J. Fluid Mech. 15, 161.
Gurvich, A. S. & Yaglom, A. M. 1967 Phys. Fluids, 10 (suppl.), 59.
Gurvich, A. S. & Zubkovskii, S. L. 1963 Izs. Acad. Sci. USSR. Geophys. Ser. 12, 1856.
Heskestad, G. 1965a J. Appl. Mech. 32, 721.
Heskestad, G. 1965b J. Appl. Mech. 32, 735.
Kennedy, D. A. & Corrsin, S. 1961 J. Fluid Mech. 10, 366.
Kohan, S. M. 1969 Ph.D. thesis, Stanford University.
Kolmogorov, A. N. 1941 C.R. Acad. Sci. (Doklady), USSR, 30, 301.
Kolmogorov, A. N. 1962 J. Fluid Mech. 13, 81.
Kovasznay, L. S. G. 1947 NACA Tech. Mem. 1130.
Kuo, A. Y.-S. 1970 Ph.D. Thesis, Johns Hopkins University.
Landau, L. D. & Lifshitz, E. 1959 Fluid Mechanics. (Trans J. B. Sykes & W. H. Reid.) Addison-Wesley. (1944, 1st Russian edn., Moscow.)
Liepmann, H. W. 1952 J. Appl. Math. Phys. 3, 321.
Lumley, J. L. 1965 Phys. Fluids, 8, 1056.
Lumley, J. L. 1970 Stochastic Tools in Turbulence. Academic.
Novikov, E. A. 1963 Prikl. Math. Mech. 27, 944.
Novikov, E. A. & Stewart, R. W. 1964 Izv. Acad. Sci. USSR. Geophys. Ser. 3, 408.
Oboukhov, A. M. 1962 J. Fluid Mech. 13, 77.
Pond, S. & Stewart, R. W. 1965 Izv. Acad. Sci. USSR, Atmos. and Oceanic Ser. 1, 914.
Rice, S. O. 1944 Bell Syst. Tech. J. 23, 282.
Rice, S. O. 1945 Bell Syst. Tech. J. 24, 46.
Rose, W. G. 1962 J. Appl. Mech. 29, 554.
Saffman, P. G. 1970 Phys. Fluids, 13, 2193.
Sandborn, V. A. 1959 J. Fluid Mech. 6, 211.
Sheih, C. M. 1969 Ph.D. thesis, Pennsylvania State University.
Sheih, C. M., Tennekes, H. & Lumley, J. L. 1971 Phys. Fluids, 14, 201.
Stewart, R. W., Wilson, J. R. & Burling, R. W. 1970 J. Fluid Mech. 41, 141.
Tennekes, H. 1968 Phys. Fluids, 11, 669.
Townsend, A. A. 1948 Aust. J. Sci. Res. A, 1, 161.
Wyngaard, J. C. 1967 Ph.D. thesis, Pennsylvania State University.
Wyngaard, J. C. & Tennekes, H. 1970 Phys. Fluids, 13, 1962.
Wygnanski, I. & Fiedler, H. E. 1970 J. Fluid Mech. 41, 327.
Yaglom, A. M. 1966 Soviet Phys. 11, 26.