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Local implications for self-similar turbulent plume models

Published online by Cambridge University Press:  07 March 2007

M. M. SCASE ,
C. P. CAULFIELD ,
P. F. LINDEN  and
S. B. DALZIEL
M. M. SCASE
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK
C. P. CAULFIELD
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK BP Institute, University of Cambridge, Madingley Road, Cambridge CB3 0EZ, UK
P. F. LINDEN
Affiliation:
Department of Mechanical and Aerospace Engineering, Jacobs School of Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA
S. B. DALZIEL
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK
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Abstract

The local implications of the well-known flux conservation equations of Morton et al. (Proc. R. Soc. Lond. A, vol. 234, 1956, p.1) for plumes and jets are considered. Given the vertical velocity distributions of a model plume or jet, the divergence-free radial velocity distributions are calculated. It is shown that in general the velocity of the plume boundary is not described by the local total fluid velocity in this way. A two-fluid model tracking the evolution of both ‘plume’ and ‘ambient’ fluid is proposed which resolves this apparent inconsistency and also provides a way of explicitly describing the mixing process within a model plume. The plume boundary acts as a phase boundary across which ambient fluid is entrained, and the plume boundary moves at the velocity of the plume fluid. The difference between the plume-fluid radial velocity and the total fluid velocity quantifies in a natural way the purely horizontal entrainment flux of ambient fluid into the plume across the phase boundary at the plume edge.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 575 , March 2007 , pp. 257 - 265
Copyright
Copyright © Cambridge University Press 2007

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References

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