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On the lognormality of the small-scale structure of turbulence

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Abstract

Higher-order moments of turbulent velocity gradients and their behavior with Reynolds number were measured in the nearly isotropic turbulent field generated by a square-mesh grid and in a turbulent boundary layer along a flat plate with zero pressure gradient. Hot-wire anemometry and instrumentation combining analog and digital methods were used to measure moments up to the fourteenth order. Measurements of such high-order moments required that particular attention be given to their validity. Involved herein was the evaluation of such effects as nonlinearity, averaging intervals, and the adequacy of the statistics for the tails of the probability density distributions. The results obtained are compared with those of other investigators for a variety of flow configurations in the laboratory as well as in the atmosphere. The concept of the intermittency of the small-scale structure and the theoretical approach involving lognormality of the probability density distribution of the dissipation rate are evaluated.

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References

  • Antonia, R. A.: 1973, ‘Some Small Scale Properties of Boundary Layer Turbulence’, Phys. Fluids 16, 1198–1206.

    Google Scholar 

  • Batchelor, G. K. and Townsend, A. A.: 1949, ‘The Nature of Turbulent Motion at Large Wave-Numbers’, Proc. Roy. Soc. A199, 238–255.

    Google Scholar 

  • Chen, W. Y.: 1971, ‘Lognormality of Small-Scale Structure of Turbulence’, Phys. Fluids 14, 1639–1647.

    Google Scholar 

  • Comte-Bellot, G.: 1965, Ecoulement turbulent entre deux parois parallèles, Publ. Sci. et Tech. du Min. de l'Air, Paris.

    Google Scholar 

  • Corrsin, S.: 1962, ‘Turbulent Dissipation Fluctuations’, Phys. Fluids 5, 1301–1302.

    Google Scholar 

  • Corrsin, S. and Kistler, A. L.: 1954, ‘The Free-Stream Boundaries of Turbulent Flows’, NACA Technical Note 3133.

  • Frenkiel, F. N.: 1952, ‘The Comparison Between the Longitudinal Correlation and the Time Correlation in a Turbulent Flow’, Phys. Rev. 88, 1380–1382.

    Google Scholar 

  • Frenkiel, F. N. and Klebanoff, P. S.: 1965, ‘Two-Dimensional Probability Distribution in a Turbulent Field’, Phys. Fluids 8, 2291–2293.

    Google Scholar 

  • Frenkiel, F. N., and Klebanoff, P. S.: 1967, ‘Higher-Order Correlations in a Turbulent Field’, Phys. Fluids 10, 507–520.

    Google Scholar 

  • Frenkiel, F. N. and Klebanoff, P. S.: 1971, ‘Statistical Properties of Velocity Derivatives in a Turbulent Field’, J. Fluid Mech. 48, 183–208.

    Google Scholar 

  • Frenkiel, F. N. and Klebanoff, P. S.: 1973, ‘Probability Distributions and Correlations in a Turbulent Boundary Layer’, Phys. Fluids 16, 725–737.

    Google Scholar 

  • Gibson, C. H. and Masiello, P. J.: 1972, ‘Observations of the Variability of Dissipation Rates of Turbulent Velocity and Temperature Fields’, in M. Rosenblatt and C. Van Atta (eds.), Statistical Models and Turbulence, pp. 427–453, Springer-Verlag.

  • Gibson, C. H., Stegen, G. R., and McConnell, S.: 1970, ‘Measurements of the Universal Constant in Kolmogoroff's Third Hypothesis for High Reynolds Number’, Phys. Fluids 13, 2448–2451.

    Google Scholar 

  • Gurvich, A. S. and Yaglom, A. M.: 1967, ‘Breakdown of Eddies and Probability Distributions for Small-Scale Turbulence’, Phys. Fluids Suppl. 10, S59-S65.

    Google Scholar 

  • Gurvich, A. S. and Zubkovskii, S. L.: 1963, Izv. Akad. Nauk SSSR, Ser. Geofiz 12, 1856.

    Google Scholar 

  • Klebanoff, P. S.: 1954, ‘Characteristics of Turbulence in a Boundary-Layer with Zero Pressure Gradient’, NACA Technical Note 3178; also 1955, NACA Report 1247.

  • Klebanoff, P. S. and Diehl, Z. W.: 1951, ‘Some Features of Artificially Thickened Fully Developed Turbulent Boundary Layers with Zero Pressure Gradient’, NACA Technical Note 2475; also 1952, NACA Report 1110.

  • Kline, S. J., Morkovin, M. V., Sovran, G., and Cockrell, D. J. (eds.): 1969, Proceedings of the Computation of Turbulent Boundary-Layers — 1968, AFOSR-IFP-Stanford Conference, Stanford University.

  • Kolmogoroff, A. N.: 1962, ‘A Refinement of Previous Hypothesis Concerning the Local Structure of Turbulence in a Viscous Incompressible Fluid at High Reynolds Number’, in Mécanique de la Turbulence, Centre National de la Recherche Scientifique, Paris, pp. 447–458; also 1962, J. Fluid Mech. 13, 82–85.

  • Kuo, A. Y. and Corrsin, S.: 1971, ‘Experiments on Internal Intermittency and Fine-Structure Distribution Functions in Fully Turbulent Fluid’, J. Fluid Mech. 50, 285–320.

    Google Scholar 

  • Obukhov, A. M.: 1962, ‘Some Specific Features of Atmospheric Turbulence’ J. Geophys. Res. 67, 3011–3014; also 1962, J. Fluid Mech. 13, 77–81.

    Google Scholar 

  • Orszag, S. A.: 1970, ‘Indeterminacy of the Moment Problem for Intermittent Turbulence’, Phys. Fluids 13, 2211–2212.

    Google Scholar 

  • Pond, S. and Stewart, R. W.: 1965, Izv. Atmos. Ocean. Phys. 1, 914.

    Google Scholar 

  • Sheih, C. M., Tennekes, H., and Lumley, J. L.: 1971, ‘Airborne Hot-Wire Measurements of the Small-Scale Structure of Atmospheric Turbulence’, Phys. Fluids 14, 201–215.

    Google Scholar 

  • Stewart, R. W., Wilson, J. R., and Burling, R. W.: 1970, ‘Some Statistical Properties of Small Scale Turbulence in an Atmospheric Boundary-Layer’, J. Fluid Mech. 41, 141–152.

    Google Scholar 

  • Tennekes, H.: 1968, ‘Simple Model for the Small-Scale Structure of Turbulence’, Phys. Fluids 11, 669–671.

    Google Scholar 

  • Tennekes, H. and Wyngaard, J. C.: 1972, ‘The Intermittent Small-Scale Structure of Turbulence: Data Processing Hazards’, J. Fluid Mech. 55, 93–103.

    Google Scholar 

  • Van Atta, C. W. and Chen, W. Y.: 1968, ‘Correlation Measurements in Grid Turbulence Using Digital Harmonic Analysis’, J. Fluid Mech. 34, 497–515.

    Google Scholar 

  • Wygnanski, I. and Fiedler, H. E.: 1970, ‘The Two-Dimensional Mixing Region’, J. Fluid Mech. 41, 327–361.

    Google Scholar 

  • Wyngaard, J. C.: 1968, ‘Measurements of Small-Scale Turbulence Structure with Hot Wires’, J. Sci. Instrum. (J. Phys. E) 1, 1105–1108.

    Google Scholar 

  • Wyngaard, J. C. and Tennekes, H.: 1970, ‘Measurements of the Small-Scale Structure of Turbulence at Moderate Reynolds Numbers‘, Phys. Fluids 13, 1962–1969.

    Google Scholar 

  • Yaglom, A. M.: 1966, ‘The Influence of Fluctuations in Energy Dissipation of the Shape of Turbulence Characteristics in the Inertial Interval‘, Dokl. Akad. Nauk SSSR 166, 49–52 (English translation: 1966, Sov. Phys.-Dokl. 11, 26–29).

    Google Scholar 

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Authors and Affiliations

  1. Naval Ship Research and Development Center, 20084, Bethesda, Md., USA

    François N. Frenkiel

  2. National Bureau of Standards, 20234, Wash., D.C., USA

    Philip S. Klebanoff

Authors
  1. François N. Frenkiel
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  2. Philip S. Klebanoff
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Frenkiel, F.N., Klebanoff, P.S. On the lognormality of the small-scale structure of turbulence. Boundary-Layer Meteorol 8, 173–200 (1975). https://doi.org/10.1007/BF00241336

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  • DOI: https://doi.org/10.1007/BF00241336

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