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

Antony A. Hill; Magda Carr

doi:10.1098/rspa.2009.0322

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

Antony A. Hill, Magda Carr

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	127-140
Number of pages	14
Journal	Proceedings of the Royal Society A - Mathematical, Physical & Engineering Sciences
Volume	466
Issue number	2113
Early online date	30 Sept 2009
DOIs	https://doi.org/10.1098/rspa.2009.0322
Publication status	Published - 8 Jan 2010

Keywords

Superposed porous-fluid convection
Temperature-dependent viscosity
Energy method
Heat-transfer
Convection
Layer
Flow
Interface
Liquid

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10.1098/rspa.2009.0322

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

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