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# Journal of Non-Equilibrium Thermodynamics

Founded by Keller, Jürgen U.

Editor-in-Chief: Hoffmann, Karl Heinz

Managing Editor: Prehl, Janett / Schwalbe, Karsten

Ed. by Michaelides, Efstathios E. / Rubi, J. Miguel

4 Issues per year

IMPACT FACTOR 2017: 1.633
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CiteScore 2017: 1.70

SCImago Journal Rank (SJR) 2017: 0.591
Source Normalized Impact per Paper (SNIP) 2017: 1.160

Online
ISSN
1437-4358
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Volume 43, Issue 4

# Buoyancy-Driven Rayleigh–Taylor Instability in a Vertical Channel

Noufe H. Aljahdaly
Published Online: 2018-06-20 | DOI: https://doi.org/10.1515/jnet-2017-0067

## Abstract

Suppose that a vertical tube is composed of two chambers that are separated by a retractable thermally insulated thin membrane. The upper and lower chambers are filled with an incompressible fluid and maintained at temperatures ${\mathit{T}}_{\mathit{c}}$ and ${\mathit{T}}_{\mathit{h}}\mathrm{>}{\mathit{T}}_{\mathit{c}}$, respectively. Upon removal of the membrane, the two fluid masses form an unstably stratified Rayleigh–Taylor-type configuration with cold and heavy fluid overlying a warmer and lighter fluid and separated by an interface across which there is a discontinuity in the density. Due to the presence of an initial discontinuity between two homogeneous states, this problem is mathematically homologous to that of the shock tube problem with the thermal expansion playing the role of pressure. When the two fluid regions are brought directly into contact with each other and the transient interfacial fluctuations have subsided, we show the emergence of a stationary state of convection through a supercritical bifurcation provided a threshold value for the temperature difference is exceeded. We suggest a possible way for the experimental testing of the theoretical results put forth in this paper.

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Revised: 2018-05-20

Accepted: 2018-06-08

Published Online: 2018-06-20

Published in Print: 2018-10-25

Citation Information: Journal of Non-Equilibrium Thermodynamics, Volume 43, Issue 4, Pages 289–300, ISSN (Online) 1437-4358, ISSN (Print) 0340-0204,

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© 2018 Walter de Gruyter GmbH, Berlin/Boston.