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Lazy plumes

Published online by Cambridge University Press:  15 June 2005

G. R. HUNT
Affiliation:
Department of Civil and Environmental Engineering, Imperial College London, Imperial College Road, London, SW7 2AZ, UK
N. B. KAYE
Affiliation:
Department of Civil and Environmental Engineering, Imperial College London, Imperial College Road, London, SW7 2AZ, UK

Abstract

We examine the dynamics of turbulent lazy plumes rising from horizontal area sources and from vertically distributed line sources into a quiescent environment of uniform density. First, we consider plumes with internal buoyancy flux gain and, secondly, plumes from horizontal area sources that have significant momentum flux deficits. We re-cast the conservation equations of Morton et al. (1956) for a constant entrainment coefficient $(\alpha)$ in terms of three dimensionless parameters: the plume radius $\beta$; a parameter $\Gamma$ characterizing the local balance of momentum, buoyancy and volume fluxes; and a parameter $\Lambda$ that characterizes the rate of internal buoyancy flux gain with height. For a plume with a linear internal buoyancy flux gain with height the flow is shown to be a constant-velocity lazy plume. For highly lazy area sources we derive exact solutions for the key plume parameters in terms of $\Gamma$ and an approximate solution for the variation of $\Gamma$ with height. We show that near the source there is a region of zero entrainment.

Type
Papers
Copyright
© 2005 Cambridge University Press

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