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Sharp global nonlinear stability for a fluid overlying a highly porous material

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HillCarr.pdf (177.6Kb)
Date
08/01/2010
Author
Hill, Antony A.
Carr, Magda
Keywords
Superposed porous-fluid convection
Temperature-dependent viscosity
Energy method
Heat-transfer
Convection
Layer
Flow
Interface
Liquid
QA Mathematics
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Abstract
The stability of convection in a two-layer system in which a layer of fluid with a temperature-dependent viscosity overlies and saturates a highly porous material is studied. Owing to the difficulties associated with incorporating the nonlinear advection term in the Navier-Stokes equations into a stability analysis, previous literature on fluid/porous thermal convection has modelled the fluid using the linear Stokes equations. This paper derives global stability for the full nonlinear system, by utilizing a model proposed by Ladyzhenskaya. The nonlinear stability boundaries are shown to be sharp when compared with the linear instability thresholds.
Citation
Hill , A A & Carr , M 2010 , ' Sharp global nonlinear stability for a fluid overlying a highly porous material ' , Proceedings of the Royal Society A - Mathematical, Physical & Engineering Sciences , vol. 466 , no. 2113 , pp. 127-140 . https://doi.org/10.1098/rspa.2009.0322
Publication
Proceedings of the Royal Society A - Mathematical, Physical & Engineering Sciences
Status
Peer reviewed
DOI
https://doi.org/10.1098/rspa.2009.0322
ISSN
1364-5021
Type
Journal article
Rights
This is the author's version of this article. The published version © 2009 The Royal Society is available from http://rspa.royalsocietypublishing.org
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  • University of St Andrews Research
URL
http://www.scopus.com/inward/record.url?scp=73949116432&partnerID=8YFLogxK
URI
http://hdl.handle.net/10023/3399

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