Hostname: page-component-84b7d79bbc-l82ql Total loading time: 0 Render date: 2024-07-26T10:33:03.743Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulent buoyant convection from a source in a confined region

Published online by Cambridge University Press:  29 March 2006

W. D. Baines  and
J. S. Turner
W. D. Baines
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
J. S. Turner
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper considers the effect of continuous convection from small sources of buoyancy on the properties of the environment when the region of interest is bounded. The main assumptions are that the entrainment into the turbulent buoyant region is at a rate proportional to the local mean upward velocity, and that the buoyant elements spread out at the top of the region and become part of the non-turbulent environment at that level. Asymptotic solutions, valid at large times, are obtained for the cases of plumes from point and line sources and also periodically released thermals. These all have the properties that the environment is stably stratified, with the density profile fixed in shape, changing at a uniform rate in time at all levels, and everywhere descending (with ascending buoyant elements).

The analysis is carried out in detail for the point source in an environment of constant cross-section. Laboratory experiments have been conducted for this case, and these verify the major predictions of the theory. It is then shown how the method can be extended to include more realistic starting conditions for the convection, and a general shape of bounded environment. Finally, the model is applied quantitatively to a variety of problems in engineering, the atmosphere and the ocean, and the limitations on its use are discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 37 , Issue 1 , 5 June 1969 , pp. 51 - 80
Copyright
© 1969 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

Elder, J. W. 1965 Laminar free convection in a vertical slot J. Fluid. Mech. 23, 77–98.Google Scholar
Ellison, T. H. & TURNER, J. S. 1959 Turbulent entrainment in stratified flows. J. Fluid Mech. 6, 423–48.Google Scholar
Gill, A. E. 1966 The boundary-layer régime for convection in a rectangular cavity. J. Fluid Mech. 26, 515–36.Google Scholar
Gille, J. 1967 Interferometric measurement of temperature gradient reversal in a layer of convecting air. J. Fluid Mech. 30, 371–84.Google Scholar
Herring, J. R. 1964 Investigation of problems in thermal convection. J. Atmos. Sci. 21, 277–90.Google Scholar
Morton, B. R. 1959 Forced plumes. J. Fluid Mech. 5, 151–63.Google Scholar
Morton, B. R., TAYLOR, G. I. & TURNER, J. S. 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. Roy. Soc. A 234, 1–23.Google Scholar
Priestley, C. H. B. 1959 Turbulent Transfer in the Lower Atmosphere. University of Chicago Press.
Pugh, D. T. 1969 Temperature measurements in the bottom layers of the Red Sea basins. Chapter in: Hot brines and Recent Heavy Metal Deposits in the Red Sea. Ed. E. T. Degers, D. A. Ross. New York: Springer-Verlag.
Rouse, H., YIH, C. S. & HUMPHREYS, H. W. 1952 Gravitational convection from a boundary source. Tellus 4, 201–10.Google Scholar
Schwind, R. G. & VLIET, G. C. 1964 Observations and interpretations of natural convection and stratification in vessels. Proc. Heat Transf. and Fluid Mech. Inst. 51–68.Google Scholar
Turner, J. S. 1963 The motion of buoyant elements in turbulent surroundings. J. Fluid Mech. 16, 1–16.Google Scholar
Warner, J. & TELFORD, J. W. 1967 Convection below cloud base. J. Atmos. Sci 24, 374–82.Google Scholar