Hostname: page-component-8448b6f56d-qsmjn Total loading time: 0 Render date: 2024-04-17T22:26:23.287Z Has data issue: false hasContentIssue false
  • English
  • Français

Statistics of fine-scale velocity in turbulent plane and circular jets

Published online by Cambridge University Press:  20 April 2006

R. A. Antonia ,
B. R. Satyaprakash  and
A. K. M. F. Hussain
R. A. Antonia
Affiliation:
Department of Mechanical Engineering, University of Newcastle, N.S.W. 2308, Australia
B. R. Satyaprakash
Affiliation:
Department of Mechanical Engineering, University of Newcastle, N.S.W. 2308, Australia
A. K. M. F. Hussain
Affiliation:
Department of Mechanical Engineering, University of Houston, Texas 77004, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

Higher-order statistics of the streamwise velocity derivative have been measured on the centre-line of turbulent plane and circular jets. The instrumentation and sources of error are discussed to establish the accuracy of the data and convergence of statistics. The optimum setting for the low-pass filter cut-off was found to be 1·75 times the Kolmogorov frequency fK, in contrast with the majority of previous investigations where it was set equal to fK. The magnitude of the constant μ in Kolmogorov's revised hypothesis is obtained using statistics derived from the instantaneous velocity derivative or its squared value. The correlation and spectrum of fluctuations of the squared velocity derivative and the Reynolds-number variation of the skewness and flatness factors of the velocity derivative are consistent with μ ≃ 0·2, while the most popular value used is 0·5. Second-order moments of the locally averaged dissipation, assumed proportional to the squared streamwise velocity derivative, and breakdown coefficients also suggest a value of μ of about 0·2. Higher-order correlations and spectra of the dissipation are in closer agreement with the Novikov-Stewart or β-model than with Kolmogorov's lognormal model. Higher-order moments of locally averaged values of the dissipation rate are more closely represented by the lognormal than the β-model.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 119 , June 1982 , pp. 55 - 89
Copyright
© 1982 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

Antonia, R. A., Chambers, A. J. & Satyaprakash, B. R. 1981 Univ. Newcastle, N.S.W., Dept. Mech. Engng Rep. TN-FM 52.
Antonia, R. A., Phan-thien, N. & Chambers, A. J. 1980 J. Fluid Mech. 100, 193.
Antonia, R. A., Phan-Thien, N. & Satyaprakash, B. R. 1981 Phys. Fluids 24, 554.
Antonia, R. A., Satyaprakash, B. R. & Hussain, A. K. M. F. 1980 Phys. Fluids 23, 695.
Antonia, R. A. & Sreenivasan, K. R. 1977 Phys. Fluids 20, 1800.
Antonia, R. A. & Van Atta, C. W. 1978 Phys. Fluids 21, 1096.
Batchelor, G. K. & Townsend, A. A. 1947 Proc. R. Soc. Lond. A 190, 534.
Batchelor, G. K. & Townsend, A. A. 1949 Proc. R. Soc. Lond. A 199, 238.
Bradshaw, P. 1971 An Introduction to Turbulence and its Measurement. Pergamon.
Champagne, F. H. 1978 J. Fluid Mech. 86, 67.
Champagne, F. H., Pao, Y. H. & Wygnanski, I. J. 1976 J. Fluid Mech. 74, 209.
Champagne, F. H., Sleicher, C. A. & Wehrmann, O. H. 1967 J. Fluid Mech. 28, 153.
Chock, D. P. 1978 Boundary-layer Met. 14, 397.
Comte-Bellot, G. 1963 Ph.D. thesis, University of Grenoble (English transl. (1969) by P. Bradshaw, ARC 31609, FM 41202).
Corrsin, S. 1962 Phys. Fluids 5, 1301.
Elena, M. 1977 Int. J. Heat Mass Transfer 20, 935.
Frenkiel, F. M. & Klebanoff, P. S. 1975 Boundary-layer Met. 8, 173.
Frenkiel, F. M., Klebanoff, P. S. & Huang, T. 1979 Phys. Fluids 22, 1606.
Friehe, C. A., Van Atta, C. W. & Gibson, C. H. 1971 In Proc. AGARD Special Meeting on Turbulent Shear Flows, London, 18.1.
Frisch, U., Sulem, P.-L. & Nelkin, M. 1978 J. Fluid Mech. 87, 719.
Gagne, Y. & Hopfinger, E. J. 1979 In Proc. 2nd Int. Turbulent Shear Flow Conf., Imperial Coll., London, 11.7.
Gagne, Y., Hopfinger, E. J. & Marechal, J. 1979 In Proc. Dynamic Flow Conf., 1978, Marseille and Baltimore (Ed. L. S. G. Kovasznay, A. Favre, P. Buchhave, L. Fulachier & B. W. Hansen).
Gibson, C. H. & Masiello, P. J. 1972 In Statistical Models and Turbulence (Ed. M. Rosenblatt & C. W. Van Atta), Lecture Notes in Physics, vol. 12, p. 427. Springer.
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.
Gurvich, A. S. & Yaglom, A. M. 1967 Phys. Fluids 10, S59.
Gutmark, E. & Wygnanski, I. 1976 J. Fluid Mech. 73, 465.
Heskestad, G. 1965 Trans. A.S.M.E. E, J. Appl. Mech. 87, 735.
Husain, Z. D. & Hussain, A. K. M. F. 1979 A.I.A.A. J. 17, 48.
Hussain, A. K. M. F. 1980 Lecture Notes in Physics, vol. 136, p. 252. Springer.
Hussain, A. K. M. F. & Clark, A. R. 1977 Phys. Fluids 20, 1416.
Hussain, A. K. M. F. & Ramjee, V. 1976 J. Fluids Engng 98, 58.
Hussain, A. K. M. F. & Zedan, M. F. 1978 Phys. Fluids 21, 1100.
Keffer, J. F., Budny, R. S. & Kawall, J. G. 1978 Rev. Sci. Instrum. 49, 1343.
Kholmyanskiy, M. Z. 1972 Izv. Atmos. & Oceanic Phys. 8, 818.
Kholmyanskiy, M. Z. 1973 Izv. Atmos. & Oceanic Phys. 9, 453.
Kolmogorov, A. N. 1941 Dokl. Akad. Nauk SSSR 30, 301.
Kolmogorov, A. N. 1962 J. Fluid Mech. 13, 82.
Kraichnan, R. H. 1974 J. Fluid Mech. 62, 305.
Kuo, A. Y. & Corrsin, S. 1971 J. Fluid Mech. 50, 285.
Landau, L. D. & Lifschitz, E. 1959 Fluid Mechanics. Addison-Wesley.
Lumley, J. L. 1965 Phys. Fluids 8, 1056.
Lumley, J. L. 1970 Stochastic Tools in Turbulence, p. 72. Academic.
Mcconnell, S. O. 1976 Ph.D. thesis, Univ. California, San Diego.
Mandelbrot, B. 1974 J. Fluid Mech. 62, 331.
Mandelbrot, B. 1976 In Lecture Notes in Mathematics: Turbulence and Navier Stokes Equation. Orsay.
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics: Mechanics of Turbulence, vol. 2. M.I.T. Press.
Nelkin, M. 1981 Phys. Fluids 24, 556.
Nelkin, M. & Bell, T. L. 1978 Phys. Rev. A 17, 363.
Novikov, E. A. 1965 Izv. Atmos. & Oceanic Phys. 1, 788.
Novikov, E. A. 1971 Prikl. Math. Mech. 35, 266.
Novikov, E. A. & Stewart, R. W. 1964 Izv. Akad. Nauk Ser. Geophys. 3, 408.
Obukhov, A. M. 1941 Izv. Nauk SSSR, Ser. Geogr.: Geofiz. 5, 453.
Obukhov, A. M. 1962 J. Fluid Mech. 13, 77.
Pao, Y. H. 1965 Phys. Fluids 8, 1063.
Park, J. T. 1976 Ph.D. thesis, Univ. California, San Diego.
Saffman, P. G. 1970 Phys. Fluids 13, 2193.
Saffman, P. G. 1978 In Structure and Mechanics of Turbulence II (ed. H. Fiedler), Lecture Notes in Physics, vol. 76, p. 273. Springer.
Schedvin, J., Stegen, G. R. & Gibson, C. G. 1974 J. Fluid Mech. 65, 561.
Sreenivasan, K. R., Antonia, R. A. & Danh, H. Q. 1977 Phys. Fluids 20, 1238.
Sreenivasan, K. R., Chambers, A. J. & Antonia, R. A. 1978 Boundary-Layer Met. 14, 341.
Stewart, R. W. 1951 Proc. Comb. Phil. Soc. 47, 146.
Tennekes, H. 1968 Phys. Fluids 11, 669.
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. M.I.T. Press.
Tennekes, H. & Wyngaard, J. C. 1972 J. Fluid Mech. 55, 93.
Townsend, A. A. 1951 Proc. R. Soc. Lond. A 208, 534.
Van Atta, C. W. & Antonia, R. A. 1980 Phys. Fluids 23, 252.
Van Atta, C. W. & Yeh, T. T. 1973 J. Fluid Mech. 59, 537.
Williams, R. M. & Paulson, C. A. 1977 J. Fluid Mech. 83, 547.
Wyngaard, J. C. 1968 J. Sci. Instrum. 1, 1105.
Wyngaard, J. C. 1973 In Workshop on Micrometeorology (ed. D. A. Haugen), p. 101. Am. Met. Soc.
Wyngaard, J. C. & Pao, Y. H. 1972 In Statistical Models and Turbulence (ed. M. Rosenblath & C. Van Atta). Lecture Notes in Physics, vol. 12, p. 384. Springer.
Wyngaard, J. C. & Tennekes, H. 1970 Phys. Fluids 13, 1962.
Yaglom, A. M. 1966 Sov. Phys. Dokl. 11, 26.