Abstract
The unsteady ascent of a buoyant, turbulent line plume through a quiescent, uniform environment is modelled in terms of the widthaveraged vertical velocity and density deficit. It is demonstrated that for a wellposed, 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 ‘tophat’ distributions in which the dependent fields are piecewise constant are illposed. 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.
Original language  English 

Pages (fromto)  103134 
Number of pages  32 
Journal  Journal of Fluid Mechanics 
Volume  856 
Early online date  28 Sep 2018 
DOIs  
Publication status  Published  10 Dec 2018 
Keywords
 plumes/thermals
 turbulent convection
 turbulent ﬂows
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Dive into the research topics of 'Unsteady turbulent line plumes'. Together they form a unique fingerprint.Profiles

Professor Andrew J Hogg
 School of Mathematics  Professor of Fluid Mechanics
 Cabot Institute for the Environment
 Fluids and materials
 Applied Mathematics
Person: Academic , Member

Dr M J Woodhouse
 School of Earth Sciences  NERC Knowledge Exchange Fellow
 Cabot Institute for the Environment
 Applied Mathematics
Person: Academic , Member