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Matched asymptotic solutions for turbulent plumes

Published online by Cambridge University Press:  12 April 2012

Fabien Candelier  and
Olivier Vauquelin
Fabien Candelier*
Affiliation:
Aix-Marseille Univ. – Laboratoire IUSTI, UMR 6595, 5 rue Enrico Fermi, 13453 Marseille CEDEX 13, France
Olivier Vauquelin
Affiliation:
Aix-Marseille Univ. – Laboratoire IUSTI, UMR 6595, 5 rue Enrico Fermi, 13453 Marseille CEDEX 13, France
*
†Email address for correspondence: fabien.candelier@univ-amu.fr
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Abstract

Recent analytical investigations have shown that the vertical evolution of turbulent plumes variables can be derived straightforwardly from the knowledge of a single function (called the plume function) which is the solution of a nonlinear differential equation. This article presents matched asymptotic solutions of this equation in the cases corresponding to highly lazy or highly forced plumes. First, it is shown that, far from the source, the asymptotic expression of the plume function can be derived by means of a perturbation method based on a Padé-like approximation. The resulting outer solution is invariant under translation (with respect to the vertical coordinate) so that we are led to the classical problem concerning the location of the plume (asymptotic) virtual origin. In order to determine this virtual origin location as a function of the conditions at the source, the far-field asymptotic solution is matched to an inner expansion of the solution which is valid near the source. Comparisons between these asymptotic solutions and numerical results are finally made in order to test their validity.

JFM classification

Convection: Plumes/thermals
Type
Papers
Information
Journal of Fluid Mechanics , Volume 699 , 25 May 2012 , pp. 489 - 499
Copyright
Copyright © Cambridge University Press 2012

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