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Breakage models: lognormality and intermittency

Published online by Cambridge University Press:  26 April 2006

Hidekatsu Yamazaki
Hidekatsu Yamazaki
Affiliation:
The Johns Hopkins University, Chesapeake Bay Institute. The Rotunda. 315, 711 West 40th Street, Baltimore, MA 21211. USA
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Abstract

A breakage model for the statistical distribution of the dissipation rate is proposed: this model, B-model, is a modification of the Gurvich & Yaglom model (1967) taking the criticism of Mandelbrot (1974) into account. The B-model uses the beta distribution for the breakage coefficient α. The universal power spectrum of velocity for the B-model has a slightly flatter slope (positive correction) than the ‘−5/3’ in contrast to all other previously proposed models, and this positive correction agrees with a theoretical argument made in Yakhot et al. (1989). The B-model predicts the structure functions of velocity observed by Anselmet et al. (1984) remarkably well without an empirical fit to the data.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 219 , October 1990 , pp. 181 - 193
Copyright
© 1990 Cambridge University Press

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References

Anselmet, F., Gagne, Y., Hopfinger, E. J. & Antonia, R. A., 1984 High-order velocity structure functions in turbulent shear flows. J. Fluid Mech. 140, 63–89.Google Scholar
Antonia, R. A., Phan-Thien, N. & Satyaprakash, B. R. 1981 Autocorrelation and spectrum of dissipation fluctuations in a turbulent jet. Phys. Fluids 24, 554–555.Google Scholar
Belyaev, V. S., Lubimtzev, M. M. & Ozmidov, R. V., 1975 The rate of dissipation of turbulence energy in the upper layer of the ocean. J. Phys. Oceanogr. 5, 499–505.Google Scholar
Benzi, R., Paladin, G., Parisi, G. & Vulpiani, A., 1984 On the multifractal nature of fully developed turbulence and chaotic system. J. Phys. A: Math. Gen. 17, 3521–3531.Google Scholar
Benzi, R. & Vulpiani, A., 1980 Small-scale intermittency of turbulent flows. J. Phys. A: Math. Gen. 13, 3319–3324.Google Scholar
Foias, C., Manley, O. P. & Teman, R., 1987 Self-similar invariant families of turbulent flows. Phys. Fluids 30, 2007–2020.Google Scholar
Frisch, U., Sulem, P. & Nelkin, M., 1978 A simple dynamical model of intermittent fully developed turbulence. J. Fluid Mech. 87, 719–736.Google Scholar
Fujisaka, H. & Mori, H., 1979 A maximum principle for determining the intermittency exponent μ of fully developed steady turbulence. Prog. Theor. Phys. 62, 54–60.Google Scholar
Gradshteyn, I. S. & Ryzhik, I. M., 1980 Table of integrals, series and products. Academic. 1160 pp.
Gurvich, A. S. & Yaglom, A. M., 1967 Breakdown of eddies and probability distributions for small scale turbulence. Phys. Fluids 10, 59–65.Google Scholar
Hentschel, H. G. E. & Procaccia, I. 1983 Fractal nature of turbulence as manifested in turbulent diffusion. Phys. Rev. A 27, 1266–1269.Google Scholar
Hosokawa, I.: 1989 An advanced model of dissipation cascade in locally isotropic turbulence. Phys. Fluids A 1, 186–189.Google Scholar
Kolmogorov, A. N.: 1941a Local turbulent structure in incompressible fluids at very high Reynolds number. Dokl. Akad. Nauk SSSR 30, 299–303.Google Scholar
Kolmogorov, A. N.: 1941b On the logarithmical normal particle size distribution caused by particle crushing. Dokl. Akad. Nauk SSSR 31, 99–102.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
Levich, E.: 1987 Certain problems in the theory of developed hydrodynamical turbulence. Phys. Rep. 151, 129–238.Google Scholar
Mandelbrot, B. B.: 1974 Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier. J. Fluid Mech. 62, 331–358.Google Scholar
Mandelbrot, B. B.: 1976 Intermittent turbulence and fractal dimension: kurtosis and the spectral exponent 5/3β. In Turbulence and Navier–Stokes Equations (ed. R. Teman). Lecture Notes in Mathematics, vol. 565, pp. 121–145. Springer.
Mandelbrot, B. B.: 1982 The Fractal Geometry of Nature. Freeman.
Monin, A. S. & Ozmidov, R. V., 1985 Turbulence in the Ocean. Dordrecht: D. Reidel. 247 pp.
Mood, A. M., Graybill, F. A. & Boes, D. C., 1974 Introduction to the Theory of Statistics, 3rd edn. McGraw-Hill. 564 pp.
Nelkin, M.: 1981 Do the dissipation fluctuations in high Reynolds number turbulence define a universal exponent? Phys. Fluids 24, 556–557.Google Scholar
Paladin, G. & Vulpiani, A., 1987 Anomalous scaling laws in multifractal objects. Phys. Rep. 154, 147–225.Google Scholar
Pond, S. & Stewart, R. W., 1965 Measurement of statistical characteristics of small-scale turbulence. Izv. Akad. Nauk SSSR Fiz Atmosfi Okeana 1, 914–919.Google Scholar
Procaccia, I.: 1984 Fractal structures in turbulence. J. Stat. Phys. 36, 649–663.Google Scholar
Shimizu, K. & Crow, E. L., 1988 History, genesis and properties. In Lognormal Distributions: Theory and Applications (ed. E. L. Crow & K. Shimizu). Marcel Dekker.
Sreenivasan, K. R. & Meneveau, C., 1986 The fractal facets of turbulence. J. Fluid Mech. 173, 357–386.Google Scholar
Stewart, R. W., Wilson, J. R. & Burling, R. W., 1970 Some statistical properties of small scale turbulence in an atmospheric boundary layer. J. Fluid Mech. 41, 141–152.Google Scholar
Turcotte, D. L.: 1988 Fractals in Fluid Mechanics. Ann. Rev. Fluid Mech. 20, 5–16.Google Scholar
Van Atta, C. W. & Antonia, R. A. 1980 Reynolds number dependence of skewness and flatness factors of turbulent velocity derivatives. Phys. Fluids 23, 252–257.Google Scholar
Van Atta, C. W. & Chen, W. Y. 1970 Structure function of turbulence in the atmospheric boundary layer over the ocean. J. Fluid Mech. 44, 145–159.Google Scholar
Van Atta, C. W. & Yeh, T. T. 1975 Evidence for scale similarity of internal intermittency in turbulent flows at large Reynolds numbers. J. Fluid Mech. 71, 417–440.Google Scholar
Wong, V. C.: 1989 On the similarity of the small-scale structure of turbulence. Seventh Symposium on Turbulent Shear Flows, Stanford University, August 21–23, 1989, pp. 30.4.1–30.4.6.Google Scholar
Yakhot, V., She, Z. S. & Orszag, S. A., 1989 Deviations from the classical Kolmogorov theory of the inertial range of homogenous turbulence. Phys. Fluids A 1, 289–293.Google Scholar