Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-13T00:57:32.021Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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