Abstract
Wavelet and quadrant analyses were applied to turbulent velocity data in order to investigate the transition from the anisotropy of energy-containing eddies to the isotropy of the inertial subrange scales. The quadrant analysis of the wavelet coefficients of longitudinal and vertical velocity components allows the evaluation of the velocity structure functions and the momentum cospectrum as a function of the separation distance and of the quadrants. In an isotropic condition the contribution both of ejections and sweeps (even quadrants), and both of reflections and deflections (odd quadrants), has to be equal. The analysis has shown that in neutrally stratified conditions the transition to isotropy occurs in a frequency range (0.2 < r/z < 3) usually referred to as internal to the inertial subrange (r is separation distance, z is height). In the transition region, as in the isotropic region, the velocity structure functions still agree with the 1941 and 1962 Kolmogorov theories; but on the other hand the structure functions of the even and odd quadrants are fitted by power laws of different slopes in the transition region. The proposed analysis allows the investigation within the transition region of the different dynamical structure in the energy transfer from the energy-containing scales to the isotropic scales.
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References
Antonia, R. A. and Raupach, M. R.: 1993, 'Spectral Scaling in a High Reynolds Number Laboratory Boundary Layer', Boundary-Layer Meteorol. 65, 289–306.
Antonov, N. V., Lanotte, A., and Mazzino, A.: 2000a, 'Persistence of Small-Scale Anisotropies and Anomalous Scaling in a Model of Magnetohydrodynamics Turbulence', Phys. Rev. E 61, 6586–6605.
Antonov, N. V., Honkonen, Y., Mazzino, A., and Muratore-Ginanneschi, P.: 2000b, 'Manifestation of Anisotropy Persistence in the Hierarchies of Magnetohydrodynamical Scaling Exponents', Phys. Rev. E 62, R5891–R5894.
Biferale, L. and Vergassola, M.: 2000, 'Isotropy vs Anisotropy in Small-Scale Turbulence', in preprint, E-print archive arXiv:nlin.CD/0010006.
Busch, N. E.: 1973, 'On the Mechanics of Atmospheric Turbulence', in D. A. Haugen (ed.), Workshop on Micrometeorology, American Meteorological Society, Boston, pp. 1–65.
Camussi, R. and Guy, G.: 1997, 'Orthonormal Wavelet Decomposition of Turbulent Flows: Intermittency and Coherent Structures', J. Fluid Mech. 348, 177–199.
Camussi, R., Ciliberto, S., Benzi, R., and Baudet, C.: 1996, 'Statistical Uncertainty of Turbulence Measurements', Phys. Rev. E 54, 100–102.
Cava, D., Giostra, U., and Tagliazucca, M.: 1999, 'Spectral Analysis of a Perturbed Stable Boundary Layer', Il Nuovo Cimento 22C(5), 693–704.
Celani, A., Lanotte, A., Mazzino, A., and Vergassola, M.: 2000, 'Universality and Saturation of Intermittency in Passive Scalar Turbulence', Phys. Rev. Lett. 84, 2385–2388.
Chambers, A. J. and Antonia, R. A.: 1984, 'Atmospheric Estimates of Power-Law Exponents µ and µ?, Boundary-Layer Meteorol. 28, 343–352.
Hayashi, T.: 1994, 'An Analysis of Wind Velocity Fluctuations in the Atmospheric Surface Layer Using an Orthonormal Wavelet Transform', Boundary-Layer Meteorol. 70, 307–326.
Hayot, F. and Jayaprakash, C.: 2000, 'Relations between Intermittency and Structure Function Exponents in Turbulence', Phys. Fluids 12, 327–334.
Henjes, K.: 1997, 'Isotropic and Anisotropic Correlations in TurbulentWind Speed Data', Boundary-Layer Meteorol. 84, 149–167.
Henjes, K.: 1999, 'On Probing the Inertial Subrange', Boundary-Layer Meteorol. 91, 367–384.
Howell, J. F. and Mahrt, L.: 1994, 'An Adaptive Decomposition: Application to Turbulence', in Wavelets in Geophysics, Academic Press, Inc., San Diego, CA, pp. 107–128.
Katul, G. G., Albertson, J. D., Chu, C. B., and Parlange, M. B.: 1994, 'Intermittency in Atmospheric Surface Layer Turbulence: The Orthonormal Wavelet Representation', in Wavelets in Geophysics, Academic Press, Inc., San Diego, CA, pp. 81–105.
Katul, G. G., Kuhn, G., Schieldge, J., and Hsieh, C.: 1997, 'The Ejection-Sweep Character of Scalar Fluxes in the Unstable Surface Layer', Boundary-Layer Meteorol. 83, 1–26.
Katul, G. G., Parlange, M. B., Albertson, J. D., and Chu, C. R.: 1995, 'Local Isotropy in the Sheared and Heated Atmospheric Surface Layer', Boundary-Layer Meteorol. 72, 123–148.
Katul, G., Vidakovic, B., and Albertson, J.: 2001, 'Estimating Global and Local Scaling Exponents in Turbulent Flows Using Discrete Wavelet Transformations', Phys. Fluids 13, 241–250.
Kolmogorov, A. N.: 1941, 'The Local Structure of Turbulence in Incompressible Viscous Fluid for Very Large Reynolds Number', Dokl. Akad. Nauk. SSSR 30, 9–13.
Kolmogorov, A. N.: 1962, 'A Refinement of Previous Hypotheses Concerning the Local Structure of Turbulence in a Viscous Incompressible Fluid at High Reynolds Number', J. Fluid Mech. 13, 82–85.
Kraichnan, R. H.: 1974, 'On Kolmogorov's Inertial-Range Theories', J. Fluid. Mech. 62, 305–330.
Kumar, P. and Foufoula-Georgiou, E.: 1994, 'Wavelet Analysis in Geophysics: An Introduction', in Wavelets in Geophysics, Academic Press, Inc., San Diego, CA, pp. 1–43.
Lumley, J. L.: 1967, 'Similarity and the Turbulent Energy Spectrum', Phys. Fluids 10, 855–858.
Lykossov, V. N. and Wamser, C.: 1995, 'Turbulence Intermittency in the Atmospheric Surface Layer over Snow-Covered Sites', Boundary-Layer Meteorol. 72, 393–409.
McMillen, R. T.: 1988, 'An Eddy Correlation Technique with Extended Applicability to Non-Simple Terrain', Boundary-Layer Meteorol. 43, 231–245.
Mestayer, P.: 1982, 'Local Isotropy in a High-Reynolds-Number Turbulent Boundary Layer', J. Fluid Mech. 125, 475–503.
Mestayer, P. G., Gibson, C. H., Coantic, M. F., and Patel, S.: 1976, 'Local Anisotropy in Heated and Cooled Turbulent Boundary Layer', Phys. Fluids 19, 1279–1287.
Monin, A. S. and Yaglom, A. M.: 1975, Statistical Fluid Mechanics, Vol. 2, MIT Press, Cambridge, 453 pp.
Mydlarski, L. and Warhaft, Z.: 1998, 'Passive Scalar Statistics in High-Peclet-Number Grid Turbulence', J. Fluid Mech. 358, 135–175.
Nelkin, M.: 1999, 'Resource Letter TF-1: Turbulence in Fluids', in preprint, E-print archive chaodyn/9906023.
Obukhov, A. M.: 1962, 'Some Specific Features of Atmospheric Turbulence', J. Fluid Mech. 13, 77–81.
Pond S., Stewart, R. W., and Burling, R. W.: 1963, 'Turbulence Spectra in the Wind over Waves', J. Atmos. Sci. 20, 319–324.
Pumir, A. and Shraiman, B. I.: 1995, 'Persistent Small-Scale Anisotropy in Homogeneous Shear Flow', Phys. Rev. Lett. 75, 3114–3117.
She, Z. S. and Leveque, E.: 1994, 'Universal Scaling Laws in Fully Developed Turbulence', Phys. Rev. Lett. 72, 336–339.
Shraiman, B. I. and Siggia, E. D.: 2000, 'Scalar Turbulence', Nature 405, 639–646.
Sreenivasan, K. R.: 1991, 'On Local Isotropy of Passive Scalars in Turbulent Shear Flows', Proc. Roy. Soc. (London) A434, 165–182.
Sreenivasan, K. R. and Antonia, R. A.: 1997, 'The Phenomenology of Small-Scale Turbulence', Annu. Rev. Fluid. Mech. 29, 435–472.
Sreenivasan, K. R., Antonia, R. A., and Britz, D.: 1979, 'Local Isotropy and Large Structures in a Heated Turbulent Jet', J. Fluid Mech. 94, 745–775.
Stolovitzky, G. and Sreenivasan, K. R.: 1993, 'Scaling of Structure Functions', Phys. Rev. E 48, 33–36.
Tennekes, H.: 1973, 'Intermittency of the Small-Scale Structure of Atmospheric Turbulence', Boundary-Layer Meteorol. 4, 241–250.
Van Atta, C.: 1991, 'Local Isotropy on the Smallest Scales of Turbulent Scalar and Velocity Fields', in J. C. R. Hunt, O. M. Phillips, and D. Williams (eds.), Turbulence and Stochastic Processes: Kolmogorov's Ideas 50 Years On, Royal Society, 240 pp.
Wang, L. P., Chen, S., Brasseur, J. G., and Wyngaard, J. C.: 1996, 'Examination of Hypothesis in the Kolmogorov Refined Turbulence Theory through High-Resolution Simulations. Part 1. Velocity field', J. Fluid Mech. 309, 113–156.
Wyngaard, J. C. and Coté, O. R.: 1972, 'Cospectral Similarity in the Atmospheric Surface Layer', Quart. J. Roy. Meteorol. Soc. 98, 590–603.
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Giostra, U., Cava, D. & Schipa, S. Structure Functions In A Wall-Turbulent Shear Flow. Boundary-Layer Meteorology 103, 337–359 (2002). https://doi.org/10.1023/A:1014917120110
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DOI: https://doi.org/10.1023/A:1014917120110