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  • Journal of Fluid Mechanics, Volume 644
  • February 2010, pp. 165-192

Universal solutions for Boussinesq and non-Boussinesq plumes

  • T. S. VAN DEN BREMER (a1) and G. R. HUNT (a1)
  • DOI: http://dx.doi.org/10.1017/S0022112009992199
  • Published online: 11 February 2010
Abstract

Closed-form solutions describing the behaviour of buoyant axisymmetric turbulent rising plumes and fountains, emitted vertically from area sources in unconfined quiescent environments of uniform density, are proposed in a form that is universally applicable to Boussinesq and non-Boussinesq plumes. This paper, thereby, generalizes the results obtained separately for steady Boussinesq and non-Boussinesq plumes, including asymptotic virtual source corrections. The flux balance parameter Γ = Γ(z), a local Richardson number, is instrumental in describing the behaviour of steady plumes and the initial rise behaviour of fountains with height z. Non-dimensional graphs (cf. the ‘scale diagrams’ of Morton & Middleton, J. Fluid Mech., vol. 58, 1973, pp. 165–176) are plotted, showing certain characteristic heights for different source conditions, characterized by one single source flux balance parameter, giving a unique representation of the behaviour of Boussinesq fountains and both Boussinesq and non-Boussinesq plumes. Finally, a length scale has been identified that characterizes the height over which non-Boussinesq effects are important for lazy plumes rising from area sources.

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Email address for correspondence: gary.hunt@imperial.ac.uk
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B. R. Morton , G. Taylor & J. S. Turner 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A 234, 123.

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H. Wang & A. W-K. Law 2002 Second-order integral model for a round turbulent buoyant jet. J. Fluid Mech. 459, 397428.

A. W. Woods 1997 A note on non-Boussinesq plumes in an incompressible stratified environment. J. Fluid Mech. 345, 347356.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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