Sharp global nonlinear stability for a fluid overlying a highly porous material
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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.
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 . DOI: 10.1098/rspa.2009.0322
Proceedings of the Royal Society A - Mathematical, Physical & Engineering Sciences
This is the author's version of this article. The published version © 2009 The Royal Society is available from http://rspa.royalsocietypublishing.org