Unsteady turbulent plume models

Scase, M.M. and Hewitt, R.E. (2012) Unsteady turbulent plume models. Journal of Fluid Mechanics, 697. pp. 455-480. ISSN 1469-7645

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Four existing integral models of unsteady turbulent plumes are revisited. We demonstrate that none of these published models is ideal for general descriptions of unsteady behaviour and put forward a modified model. We show that the most recent (top-hat) plume model (Scase et al. J. Fluid Mech., vol. 563, 2006, p. 443), and the earlier (Gaussian) plume models (Delichatsios J. Fluid Mech., vol. 93, 1979, p. 241; Yu Trans. ASME, vol. 112, 1990, p.186), are all ill-posed. This ill-posedness arises from the downstream growth of short-scale waves, which have an unbounded downstream growth rate. We show that both the top-hat and the Gaussian (Yu) models can be regularized, rendering them well-posed, by the inclusion of a velocity diffusion term. The effect of including this diffusive mechanism is to include a vertical structure in the model that can be interpreted as representing the vertical extent of an eddy. The effects of this additional mechanism are small for steady applications, and cases where the plume forcing can be considered to follow a power law (both of which have been studied extensively). However, the inclusion of diffusion is shown to be crucial to the general initial-value problem for unsteady models.

Item Type: Article
Additional Information: © 2012 Cambridge University Press
Uncontrolled Keywords: Plume Jet Turbulent Pulsatile Unsteady
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 76 Fluid mechanics
MSC 2010, the AMS's Mathematics Subject Classification > 86 Geophysics
PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 40 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID MECHANICS > 47 Fluid dynamics
PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 90 GEOPHYSICS, ASTRONOMY, AND ASTROPHYSICS > 92 Hydrospheric and atmospheric geophysics
Depositing User: Dr Richard E. Hewitt
Date Deposited: 14 Nov 2013
Last Modified: 20 Oct 2017 14:13
URI: https://eprints.maths.manchester.ac.uk/id/eprint/2041

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