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

Hill, Antony A.; Carr, Magda

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. © 2009 The Royal Society.

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 and Engineering Sciences, 466(2113), 127-140. https://doi.org/10.1098/rspa.2009.0322

• Journal Article Type: Article
• Publication Date: Jan 8, 2010
• Deposit Date: Oct 24, 2012
• Journal: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
• Print ISSN: 1364-5021
• Electronic ISSN: 1471-2946
• Publisher: Royal Society, The
• Peer Reviewed: Peer Reviewed
• Volume: 466
• Issue: 2113
• Pages: 127-140
• DOI: https://doi.org/10.1098/rspa.2009.0322
• Keywords: superposed porous-fluid convection, temperature-dependent viscosity, energy method
• Public URL: https://uwe-repository.worktribe.com/output/985601
• Publisher URL: http://dx.doi.org/10.1098/rspa.2009.0322