The Obukhov-Bolgiano Inertial Range in a Shell Model of Turbulent Convection

  • S. A. Lozhkin
  • P. G. Frick
Part of the Fluid Mechanics and Its Applications book series (FMIA, volume 46)


The very earliest studies of the peculiarities of developed turbulence in a medium with an inhomogeneous density, attributed to the essential influence of buoyancy forces on the inertial range dynamics, have been carried out by Obukhov [1] and Bolgiano [2]. Obukhov established the existence of a boundary scale lB, above which the input of kinetic energy by buoyancy forces is essential in comparison with the Kolmogorov spectral flux. Bolgiano studied turbulence in a medium with a stable stratification, when the kinetic energy was transformed into the potential, and derived, by performing the dimensional analysis, the spectral laws for kinetic energy and energy of fluctuations of temperature, (Eυ (k) ~ k-11/5 and Et(k) ~ k-7/5).


  1. 1.
    Obukhov A.M. (1959), Dokl. Akad. Nauk SSSR, 125:6, pp. 1246–1248.Google Scholar
  2. 2.
    Bolgiano R. (1959), J. Geophys. Res, 64:12, pp. 2226–2229.ADSCrossRefGoogle Scholar
  3. 3.
    Lozhkin S.A., Frick P.G. Izv. RAN. Mekhanika Zhidkosti i Gaza, in press.Google Scholar
  4. 4.
    Lozhkin S.A., Frick P.G. (1996) Mat. Mod. Sist. i Proces., N 4. pp. 53–60.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • S. A. Lozhkin
    • 1
  • P. G. Frick
    • 1
  1. 1.Institute of Continuous Media MechanicsPermRussia

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