Skip to main content
SpringerLink
Log in

Power laws of high Rayleigh number convection

  • Published:
Boundary-Layer Meteorology Aims and scope Submit manuscript

Abstract

Previous theoretical and observational investigations have shown that vertical plumes are formed in the high Rayleigh number convection field over heated horizontal surfaces and that these plumes become unsteady and turbulent when the Rayleigh number is higher than about 20 times its critical value R c. Based on these results, we conclude that the dissipation of kinetic energy takes place mainly in the surface boundary layer in high Rayleigh number laminar convection and mainly in the vertical plumes in turbulent convection, while the conversion of eddy potential energy into kinetic energy is accomplished mainly in the well-mixed main body of the fluid. On making use of these rather general conclusions concerning the kinetic energy generation and dissipation processes in the energy integrals, we are able to derive the well known 5/4 and 4/3 power laws of upward heat transfer by laminar and turbulent convections theoretically.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Gaynor, J. E. and Mandic, P. A.: 1978, ‘Analysis of the Tropical Marine Boundary Layer During GATE Using Acoustic Sounder Data’, Mon. Wea. Rev. 106, 223–232.

    Google Scholar 

  • Herring, J. R.: 1963, ‘Investigation of Problems of Thermal Convection’, J. Atmos. Sci. 20, 325–338.

    Google Scholar 

  • Jacob, M.: 1949, Heat Transfer, John Wiley and Sons, New York, Vol. 1, 785pp.

    Google Scholar 

  • Kuo, H. L.: 1961, ‘Solutions of the Nonlinear Equations of Cellular Convection and Heat Transport’, J. Fluid Mech. 10, 611–634.

    Google Scholar 

  • Kuo, H. L. and Sun, W. Y.: 1976, ‘Convection in the Lower Atmosphere and its Effects’, J. Atmos. Sci. 33, 21–40.

    Google Scholar 

  • Priestley, C. H. B.: 1954, ‘Convection from a Large Horizontal Surface’, Australian J. Phys. 7, 176–201.

    Google Scholar 

  • Rossby, H. T.: 1969, ‘A Study of Benard Convection With and Without Rotation’, J. Fluid Mech. 36, 309–335.

    Google Scholar 

  • Saltzman, B.: 1962, ‘Finite Amplitude Free Convection as an Initial Value Problem’, J. Atmos. Sci. 19, 329–341.

    Google Scholar 

  • Silveston, P. L.: 1958, ‘Warmedurchgang in waagerechten Flussigkeitsschichten’, Forsch. Ing. 24, 29–32; 59–69.

    Google Scholar 

  • Sutton, O. A.: 1953, Micrometeorology, McGraw-Hill Co., New York, 331 pp.

    Google Scholar 

  • Thomas, D. B. and Townsend, A. A.: 1957, ‘Turbulent Convection Over a Heated Horizontal Surface’, J. Fluid Mech. 2, 473–492.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Geophysical Sciences, The University of Chicago, 60637, Chicago, Ill., USA

    H. L. Kuo

Authors
  1. H. L. Kuo
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kuo, H.L. Power laws of high Rayleigh number convection. Boundary-Layer Meteorol 17, 29–39 (1979). https://doi.org/10.1007/BF00121935

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00121935

Keywords

Search

Navigation