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Unsteady turbulent line plumes

Published online by Cambridge University Press:  28 September 2018

Andrew J. Hogg Open the ORCID record for Andrew J. Hogg [Opens in a new window] ,
Edward J. Goldsmith  and
Mark J. Woodhouse
Andrew J. Hogg*
Affiliation:
School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK
Edward J. Goldsmith
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK
Mark J. Woodhouse
Affiliation:
School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK School of Earth Science, University of Bristol, Wills Memorial Building, Queens Road, Bristol BS8 1RJ, UK
*
†Email address for correspondence: [email protected]
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Abstract

The unsteady ascent of a buoyant, turbulent line plume through a quiescent, uniform environment is modelled in terms of the width-averaged vertical velocity and density deficit. It is demonstrated that for a well-posed, linearly stable model, account must be made for the horizontal variation of the velocity and the density deficit; in particular the variance of the velocity field and the covariance of the density deficit and velocity fields, represented through shape factors, must exceed threshold values, and that models based upon ‘top-hat’ distributions in which the dependent fields are piecewise constant are ill-posed. Numerical solutions of the nonlinear governing equations are computed to reveal that the transient response of the system to an instantaneous change in buoyancy flux at the source may be captured through new similarity solutions, the form of which depend upon both the ratio of the old to new buoyancy fluxes and the shape factors.

JFM classification

Convection: Plumes/thermals Turbulent Flows: Turbulent convection Turbulent Flows: Turbulent Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 856 , 10 December 2018 , pp. 103 - 134
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Copyright
© 2018 Cambridge University Press 

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