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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
Authors: 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.
Issue Date: 10-Jul-2017
Date of Acceptance: 18-Apr-2017
URI: http://hdl.handle.net/10044/1/46102
DOI: 10.1017/jfm.2017.259
ISSN: 0022-1120
Publisher: Cambridge University Press
Start Page: 774
End Page: 790
Journal / Book Title: Journal of Fluid Mechanics
Volume: 822
Copyright Statement: © 2017 Cambridge University Press This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Sponsor/Funder: EPSRC
Keywords: Science & Technology
Physical Sciences
Physics, Fluids & Plasmas
stratified turbulence
turbulent mixing
Fluids & Plasmas
01 Mathematical Sciences
09 Engineering
Publication Status: Published
Online Publication Date: 2017-06-08
Appears in Collections:Civil and Environmental Engineering
Faculty of Engineering