The turbulent Prandtl number in a pure plume is 3/5

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Title: The turbulent Prandtl number in a pure plume is 3/5
Author(s): Craske, J
Salizzoni, P
Van Reeuwijk, M
Item Type: Journal Article
Abstract: We derive a new expression for the entrainment coefficient in a turbulent plume using an equation for the squared mean buoyancy. Consistency of the resulting expression with previous relations for the entrainment coefficient implies that the turbulent Prandtl number in a pure plume is equal to 3 / 5 when the mean profiles of velocity and buoyancy have a Gaussian form of equal width. Entrainment can be understood in terms of the volume flux, the production of turbulence kinetic energy or the production of scalar variance for either active or passive variables. The equivalence of these points of view indicates how the entrainment coefficient and the turbulent Prandtl and Schmidt numbers depend on the Richardson number of the flow, the ambient stratification and the relative widths of the velocity and scalar profiles. The general framework is valid for self-similar plumes, which are characterised by a power-law scaling. For jets and pure plumes it is shown that the derived relations are in reasonably good agreement with results from direct numerical simulations and experiments.
Date of Acceptance: 27-Mar-2017
ISSN: 1469-7645
Publisher: Cambridge University Press (CUP)
Journal / Book Title: Journal of Fluid Mechanics
Copyright Statement: This paper is embargoed until publication. Once published will be available fully open access.
Sponsor/Funder: EPSRC
Keywords: Fluids & Plasmas
01 Mathematical Sciences
09 Engineering
Publication Status: Accepted
Embargo Date: publication subject to indefinite embargo
Appears in Collections:Faculty of Engineering
Civil and Environmental Engineering

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