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Universal solutions for Boussinesq and non-Boussinesq plumes

  • T. S. VAN DEN BREMER (a1) and G. R. HUNT (a1)

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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B. M. Cetegen , E. E. Zukoski & T. Kubota 1984 Entrainment in the near field and far field of fire plumes. Combust. Sci. Technol. 39, 305331.

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P. F. Linden 1999 The fluid mechanics of natural ventilation. Annu. Rev. Fluid Mech. 31, 201238.

B. R. Morton , G. Taylor & J. S. Turner 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A 234, 123.

C. H. B. Priestley & F. K. Ball 1955 Continuous convection from an isolated source of heat. Quart. J. R. Meteorol. Soc. 81, 144157.

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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