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On the energy deficiency in self-preserving convective flows

Published online by Cambridge University Press:  29 March 2006

J. S. Turner
J. S. Turner
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
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Abstract

When similarity solutions are used to describe convective plumes or thermals, there is always found to be a discrepancy between the work done by buoyancy forces and the kinetic energy of mean motion. It is the main purpose of this paper to set down the ratio of these quantities for a wide variety of forms of buoyant elements and environmental stabilities. For consistency, the remaining fraction of the energy must appear as turbulent kinetic energy and eventually be dissipated, but these processes are not investigated in detail. The results are shown to have some relevance to the problem of convectively driven mixing across a density interface, where the largest scales of motion are dominant, and to the understanding of the transition zone between two self-preserving states of turbulent convection.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 53 , Issue 2 , 23 May 1972 , pp. 217 - 226
Copyright
© 1972 Cambridge University Press

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References

Ball, F. K. 1960 Control of inversion height by surface heating. Quart. J. Roy. Met. Soc., 86, 483–494.Google Scholar
Batchelor, G. K. 1954 Heat convection and buoyancy effects in fluids. Quart. J. Roy. Met. Soc., 80, 339–358.Google Scholar
Kraus, E. B. & Turner, J. S. 1967 A one-dimensional model of the seasonal thermocline. Tellus, 19, 88–105.Google Scholar
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Levine, J. 1959 Spherical vortex theory of bubble-like motion in cumulus clouds. J. Meteor., 16, 653–662.Google Scholar
Lamb, F. H. 1958 The hail problem. Nubila, 1, 12–96.Google Scholar
Morton, B. R. 1968 On Telford's model for clear air convection (and Telford's reply). J. Atmos. Sci. 25, 135–139.
Morton, B. R. 1971 The choice of conservation equations for plume models. Dept. of Mathematics, Monash University, G.P.D.L. Paper, no, 36.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 Transjer in the Lower Atmosphere. University of Chicago Press.
Rouse, H., YIH, C.S. & Humphreys, W. D. 1952 Gravitational convection from a boundary source. Tellus, 4, 201–210Google Scholar
Scorer, R. S. 1962 Discussion of paper by Ball. Quart. J. Roy. Met. Soc., 88, 102–105.Google Scholar
Squires, P. & Turner, J. S. 1962 An entraining jet model for cumulonimbus updraughts. Tellus, 14, 422–434Google Scholar
Telford, J. W. 1966 The convective mechanism in clear air. J. Atmos. Sci., 23, 652–666.Google Scholar
Turner, J. S. 1957 Buoyant vortex rings. Proc. Roy. Soc. A 239, 61–75.Google Scholar
Turner, J. S. 1964 The flow into an expanding spherical vortex. J. Fluid Mech., 18, 195–208Google Scholar
Turner, J. S. 1969 Buoyant plumes and thermals. Ann. Rev. Fluid Mech. 1, 29–44.Google Scholar
Warner, J. 1970 The microstructure of cumulus clouds 111. The nature of the updraft. J. Atrnos. Sci., 27, 682–688.Google Scholar
Woodward, B. 1959 The motion in and around an isolated thermal. Quart. J. Roy. Met. Soc., 85, 144–151.Google Scholar