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On the two-dimensional mixing region

  • F. H. Champagne (a1), Y. H. Pao (a2) and I. J. Wygnanski (a3)


An experimental investigation of the two-dimensional incompressible mixing layer was carried out. The measurements provide new information on the development of the mean and turbulent fields towards a self-preserving state and on the higher-order statistical characteristics of the turbulent field. The relevance of initial conditions to the development of the flow is discussed in the light of both present and previous data. Measurements of spectra, probability densities and moments to eighth order of all three velocity-component fluctuations at various transverse positions across the flow were carried out using an on-line digital data acquisition system. The probability density distributions of the derivative and the squared derivative of the longitudinal and lateral velocity fluctuations were also determined. Direct measurements of moments to eighth order of the velocity derivatives were attempted and are discussed in the light of the simultaneously measured histograms. The problems in obtaining higher-order statistical data are considered in some detail. Estimates of the integral time scale of many of the higher-order statistics are presented. The high wave-number structure was found to be locally anisotropic according to both spectral and turbulent velocity-gradient moment requirements. Higher-order spectra to fourth order of the longitudinal velocity fluctuations were measured and are discussed. Finally the lognormality of the squared longitudinal and lateral velocity-derivative fluctuations was investigated and the universal lognormal constant μ was evaluated.



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Batt, R. G. 1974 TRW TR Rep. no. 18117-6023. (See also SAMSO TR no. 74810.)
Batt, R. G., Kubota, T. & Laufer, J. 1970 A.I.A.A. Reacting Turbulent Flows Conf., San Diego.
Blackman, R. B. & Tukey, J. W. 1958 The Measurement of Power Spectra. Dover.
Bradshaw, P. 1966 J. Fluid Mech. 26, 225.
Bradshaw, P. 1967 Nat. Phys. Lab. Aero Rep. no. 1220.
Brown, G. & Roshko, A. 1971 AGARD Fluid Dyn. Panel Specialists Meeting on Turb. Shear Flows, London.
Castro, I. P. 1973 Ph.D. thesis, Department of Aeronautics, Imperial College, London.
Champagne, F. H., Harris, V. G. & Corrsin, S. 1970 J. Fluid Mech. 41, 81.
Champagne, F. H., Sleicher, C. A. & Wehrmann, O. 1967 J. Fluid Mech. 28, 153.
Comte-Bellot, G. & Corrsin, S. 1971 J. Fluid Mech. 48, 273.
Cooley, J. W., Lewis, P. A. W. & Welch, P. D. 1967 IBM Watson Res. Center, York-town Heights, New York, Paper, RC-1743.
Corrsin, S. 1950 J. Aero Sci. 17, 396.
Corrsin, S. 1957 Proc. 1st Naval Hydro-Symp., Nat. Acad. Sci./Nat. Res. Counc. publ. 515, p. 373.
Corrsin, S. 1958 N.A.C.A. Res. Memo. RM 58B11.
Crow, S. & Champagne, F. H. 1971 J. Fluid Mech. 48, 547.
Frenkiel, F. N. & Klebanoff, P. S. 1971 J. Fluid Mech. 48, 183.
Friehe, C. A., VAN ATTA, C. W. & Gibson, C. H. 1971 AGARD Conf. Proc. no. 93, paper 18810.
Gibson, C. H. & Masiello, P. 1972 Proc. Symp. on Stratified Models and Turbulence, Lecture Notes in Physics, vol. 12, p. 426. Springer.
Gibson, C. H., Stegen, G. R. & Williams, R. B. 1970 J. Fluid Mech. 41, 153.
Gurvich, A. S. & Yaglom, A. M. 1967 Phys. Fluids Suppl. 10, S59.
Hinze, J. O. 1959 Turbulence. McGraw-Hill.
Kolmogorov, A. N. 1941 Dokl. Akad. Nauk. SSR 30, 301.
Kolmogorov, A. N. 1962 J. Fluid Mech. 13, 82.
Kuo, A. 1970 Ph.D. thesis, Department of Mechanics, Johns Hopkins University.
Kuo, A. & Corrsin, S. 1972 J. Fluid Mech. 56, 447.
Liepman, H. W. & Laufer, J. 1947 N.A.C.A. Tech. Note, no. 1257.
Lumley, J. L. 1965 Phys. Fluids, 8, 1056.
Lumley, J. L. 1970 Stochastic Tools in Turbulence. Academic.
Lumley, J. L. & Panofsky, H. 1964 Structure of Atmospheric Turbulence. Interscience.
Oboukhov, A. M. 1962 J. Fluid Mech. 13, 77.
Pao, Y. H., Hansen, S. & Macgregor, G. 1969 Boeing Sci. Res. Lab. Doc. D1-82-0863.
Patel, R. P. 1973 A.I.A.A. J. 11, 67.
Spencer, B. W. 1970 Ph.D. thesis, Department of Nuclear Engineering, University of Illinois.
Spencer, B. W. & Jones, B. G. 1971 A.I.A.A. Paper, no. 71810.
Stewart, R. W., Wilson, J. R. & Burling, R. W. 1970 J. Fluid Mech. 41, 141.
Sunyach, M. 1971 Ph.D. thesis, L'Universite’ Claude Bernard de Lyon.
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.
Van Atta, C. W. & Chen, W. Y. 1970 J. Fluid Mech. 44, 145.
Weiler, H. S. & Burling, R. W. 1967 J. Atmos. Sci. 24, 653.
Winant, C. 1972 Ph.D. thesis, Department of Aerospace Engineering, University of Southern California.
Wygnanski, I. J. & Fiedler, H. 1970 J. Fluid Mech. 41, 327.
Wygnanski, I. J. & Gartshore, I. S. 1963 McGill University, Mech. Engng Tech. Note, no. 63810.
Wyngaard, J. C. 1968 J. Sci. Instrum. 1 (2), 1105.
Wyngaard, J. C. 1969 J. Sci. Instrum. 2 (2), 983.
Wyngaard, J. C. & Pao, Y. H. 1972 In Proc. of Symp. on Statistical Models and Turbulence, Lecture Notes in Physics, vol. 12, p. 384, Springer.
Wyngaard, J. C. & Tennekes, H. 1970 Phys. Fluids, 13, 1962.
Yaglom, A. M. 1966 Dokl. Akad. Nauk. SSR, 116, 49.
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