Journal of Fluid Mechanics

Papers

Universal solutions for Boussinesq and non-Boussinesq plumes

T. S. VAN DEN BREMERa1 and G. R. HUNTa1 c1

a1 Department of Civil and Environmental Engineering, Imperial College London, Imperial College Road, London SW7 2AZ, UK

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.

(Received March 04 2009)

(Revised September 10 2009)

(Accepted September 11 2009)

Correspondence:

c1 Email address for correspondence: gary.hunt@imperial.ac.uk

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