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The influence of coherent structures and microfronts on scaling laws using global and local transforms

Published online by Cambridge University Press:  26 April 2006

L. Mahrt  and
J. F. Howell
L. Mahrt
Affiliation:
Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, OR 97331 USA
J. F. Howell
Affiliation:
Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, OR 97331 USA
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Abstract

This study examines the influence of coherent structures and attendant microfronts on scaling laws. Toward this goal, we analyse atmospheric observations of turbulence collected 45 m above a flat surface during the Lammefjord Experiment in Denmark. These observations represent more than 40 hours of nearly stationary strong wind conditions and include more than 1600 samples of the main coherent structures. These samples occupy about 40% of the total record and explain the majority of the Reynolds stress.

To study the dependence of the scaling laws on the choice of basis set, the time series of velocity fluctuations are decomposed into Fourier modes, the local Haar basis set and eigenvectors of the lagged covariance matrix. The three decompositions are compared by formulating joint projections. The decompositions are first applied to the samples of phased-locked coherent structures centred about eddy microfronts. The eigenvector decomposition is able to partially separate the small-scale variances due to the coherent eddy microfronts from that due to the small-scale structure with random phase. In the Fourier spectrum, both of these contributions to the variance appear together at the higher wavenumbers and their individual contributions cannot be separated. This effect is relatively minor for the scale distribution of energy but exerts an important influence on higher-moment statistics. Deviations from the −$\frac53$ scaling are observed to be slight and depend on choice of basis set.

The microfronts strongly influence the higher-order statistics such as the sixth-order structure function traditionally used to estimate the energy transfer variance. The intermittency of fine-scale structure, energy transfer variance and dissipation are not completely characterized by random phase, as often assumed, but are partly associated with microfronts characterized by systematic phase with respect to the main transporting eddies. These conclusions are supported by both the higher-order structure function and the higher-order Haar transform.

The Fourier and Haar spectra are also computed for the entire record. The peak of the Haar energy spectrum occurs at smaller scales than those of the Fourier spectrum. The Haar transform is local and emphasizes the width of the events. The Fourier spectrum peaks at the scale of the main periodicity, if it exists, which includes the spacing between the events.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 260 , 10 February 1994 , pp. 247 - 270
Copyright
© 1994 Cambridge University Press

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References

Anselmet, F., Gagne, Y. & Hopfinger, E. J. 1984 High-order velocity structure functions in turbulent shear flows. J. Fluid Mech. 140, 63–89.Google Scholar
Antonia, R. A., Satyaprakash, B. R. & Hussain, A. K. M. F. 1982 Statistics of fine-scale velocity in turbulent plane and circular jets. J. Fluid Mech. 119, 55–89.Google Scholar
Antonia, R. A. & Atta, Van C. W. 1978 Structure functions of temperature fluctuations in turbulent shear flows. J. Fluid. Mech. 84, 561–580.Google Scholar
Blaisdell, G. A., Reynolds, W. C. & Mansour, N. N. 1991 Compressibility effects on the growth and structure of homogeneous turbulent shear flow. In Eighth Symp. on Turbulent Shear Flows, Vol. 1, pp. 111–116. Tech. Univ. of Munich.
Borgas, M.S. 1992 A comparison of intermittency models in turbulence. Phys. Fluids A 4, 2055–2061.Google Scholar
Chen, C. H. P. & Blackwelder, R. F. 1978 Large-scale motion in turbulent boundary layer: A study using temperature contamination. J. Fluid Mech. 89, 1–31.Google Scholar
Chorin, A. J. 1982 The evolution of a turbulent vortex. Commun. Math. Phys. 83, 517–535.Google Scholar
Courant, R. & Hilbert, D. 1953 Methods of Mathematical Physics, Vol. 1. Interscience.
Farge, M. & Rabrrau, G. 1988 Transformée en ondelettes pour détecter et analyser les structures cohérentes dans les écoulements turbulents bidimensionnels. C.R. Acad. Sci. Paris 307, (IIREFPPF), 1479–1486.Google Scholar
Frisch, U. & Morf, R. 1981 Intermittency in nonlinear dynamics and singularities at complex times. Phys. Rev. A 23, 2673–2705.Google Scholar
Frisch, U., Sulem, P. L. & Nelkin, M. 1978 A simple dynamical model of intermittent fully developed turbulence. J. Fluid Mech. 87, 719–736.Google Scholar
Gamage, N. K. K. 1990 Modeling and analysis of geophysical turbulence: Use of optimal transforms and basis sets PhD Thesis, Oregon State University.
Gerz, T., Howell, J. & Mahrt, L. 1994 Vortex structures and microfronts. Phys. Fluids A (submitted).Google Scholar
Gilbert, A. D. 1988 Spiral structures and spectra in two-dimensional turbulence. J. Fluid. Mech. 193, 475–497.Google Scholar
Grossmann, A., Kronland-Martinet, R. & Morlet, J. 1989 Reading and understanding continuous wavelet transforms. In Wavelets: Time-Frequency Methods and Phase Space (ed. J. M. Combes et al.), pp. 1–20. Springer.
Grossmann, A. & Morlet, J. 1984 Decomposition of Hardy functions into square integrable wavelets of constant shape. SIAM J. Math. Anal. 15, 723–736.Google Scholar
Hunt, J. C. R. & Carruthers, D. J. 1990 Rapid distortion theory and the ‘problems’ of turbulence. J. Fluid Mech. 212, 497–532.Google Scholar
Hunt, J. C. R. & Vassilicos, J. C. 1991 Kolmogorov's contributions to the physical and geometrical understanding of small-scale turbulence and recent developments. Proc. R. Soc. Lond. A 434, 183–210.Google Scholar
Kharkevich, A. A. 1960 Spectra and Analyses. Consultants Bureau.
Knight, B. & Sirovich, L. 1990 Kolmogorov inertial range for inhomogeneous turbulence flows. Phys. Rev. Lett. 65, 1356–1359.Google Scholar
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.Google Scholar
Kraichnan, R. 1974 On Kolmogorov's inertial-range theories. J. Fluid Mech. 62, 305–330.Google Scholar
Kristensen, L., Lenschow, D. H., Kirkegaard, P. & Courtney, M. 1989 The spectral velocity tensor for homogeneous boundary-layer turbulence. Boundary-Layer Met. 47, 149–193.Google Scholar
Kuznetsov, V. R., Praskovsky, A. A. & Sabelnikov, V. A. 1992 Fine-scale turbulence structure of intermittent shear flows. J. Fluid Mech. 243, 595–622.Google Scholar
Lesieur, M. 1987 Turbulence in Fluids. Kluwer.
Liandrat, J. & Moret-Bailly, F. 1990 The wavelet transform: some applications to fluid dynamics and turbulence. Eur. J. Mech. B/Fluids 9, 1–19.Google Scholar
Lumley, J. L. 1970 Stochastic Tools in Turbulence. Academic.
Mahrt, L. 1991a Eddy asymmetry in the sheared heated boundary layer. J. Atmos. Sci. 48, 472–492.Google Scholar
Mahrt, L. 1991b Eigen-structure of eddies; continuous weighting versus conditional sampling. In Non-linear Variability in Geophysics (ed. D. Schertzer & S. Lovejoy), pp. 145–156. Kluwer.
Mahrt, L. & Frank, H. 1988 Eigen structure of eddy microfronts. Tellus 40A, 107–119.Google Scholar
Majda, A. J. 1991 Vorticity, turbulence and acoustics in fluid flow. SIAM Rev. 33, 349–388.Google Scholar
Mallat, S. G. 1989 Multifrequency channel decompositions of images and wavelet models. Trans. Acoustics, Speech Signal Proc. 37, 2091–2109.Google Scholar
Mandelbrot, B. B. 1976 Intermittent turbulence and fractal dimension: kurtosis and the spectral exponent 5/3 + β. In Turbulence and Navier—Stokes Equations (ed. R. Teman). Lecture Notes in Mathematics, vol. 565, pp. 121–145. Springer.
Meneveau, C. 1991 Analysis of turbulence in the orthonormal wavelet representation. J. Fluid. Mech. 232, 469–520.Google Scholar
Moffatt, H. K. 1984 Simple topological aspects of turbulent vorticity dynamics. In Turbulence and Chaotic Phenomena in Fluids, (ed. T. Tatsumi), pp. 223–230. Elsevier.
Morrison, J. F. & Bradshaw, P. 1991 Bursts and sources of pressure fluctuations in turbulent boundary layers. In Eighth Symp. on Turbulent Shear Flows, Vol. 1, pp. 211–216. Tech. Univ. of Munich.
Morrison, J. F., Subramanian, C. S. & Bradshaw, P. 1992 Bursts and the law of the wall in turbulent boundary layers. J. Fluid Mech. 241, 75–108.Google Scholar
Nelkin, M. & Bell, T. L. 1978 One-exponent scaling for very high-Reynolds-number turbulence. Phys. Rev. A 17, 363–369.Google Scholar
Novikov, E. A. & Stewart, R. W. 1964 Intermittency and dissipation fluctuation spectrum. Izv. Akad. Nauk SSSR 32, 22–24.Google Scholar
Oboukhov, A. M. 1962 Some specific features of atmospheric turbulence. J. Fluid Mech. 13, 77–81.Google Scholar
Pierrehumbert, R. T. & Widnall, S. E. 1982 The two- and three-dimensional instabilities of a spatially periodic shear layer. J. Fluid Mech. 114, 59–82.Google Scholar
Saffman, P. G. 1971 On the spectrum and decay of random two-dimensional vorticity distributions at large Reynolds number. Stud. Appl. Maths 50, 377.Google Scholar
Sirovich, L. 1987 Turbulence and the dynamics of coherent structures. Part I: Coherent structures. Q. Appl. Maths 45, 561–571.Google Scholar
Tennekes, H. 1976 Fourier-transform ambiguity in turbulence dynamics. J. Atmos. Sci. 33, 1660–1663.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.
Yaglom, A. M. 1966 Dependence of inertial subrange characteristics on dissipation fluctuations. Dokl. Akad. Nauk SSSR 166, 49–52.Google Scholar
Yakhot, V., She, Z.-S. & Orszag, S. A. 1989 Deviations from the classical Kolmogorov theory of the inertial range of homogeneous turbulence. Phys. Fluids A 1, 289–293.Google Scholar
Yamada, M. & Ohkitani, K. 1990 Orthonormal wavelet expansion and its application to turbulence. Prog. Theor. Phys. 83, 819–823.Google Scholar
Yamazaki, H. 1990 Breakage models: lognormality and intermittency. J. Fluid Mech. 219, 181–193.Google Scholar
Yeung, P. K. & Brasseur, J. G. 1991 The response of isotropic turbulence to isotropic and anisotropic forcing at the large scales. Phys. Fluids A 3, 884–897.Google Scholar