Global stability for penetrative convection with throughflow in a porous material

Hill, Antony A.; Rionero, S.; Straughan, B.

Abstract

This paper investigates penetrative convection in a layer of porous material saturated with water when there is throughflow present. The density is quadratic in temperature. A linearized instability analysis is derived and compared with a weighted non-linear energy stability analysis. A weighted analysis is necessary to achieve a global non-linear stability threshold. Parameter ranges are found where the linear instability boundary is close to the non-linear stability one. © The Author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

• Journal Article Type: Article
• Publication Date: Oct 1, 2007
• Journal: IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
• Print ISSN: 0272-4960
• Electronic ISSN: 1464-3634
• Publisher: Oxford University Press (OUP)
• Peer Reviewed: Peer Reviewed
• Volume: 72
• Issue: 5
• Pages: 635-643
• DOI: https://doi.org/10.1093/imamat/hxm036
• Keywords: energy method, throughflow, penetrative convection
• Public URL: https://uwe-repository.worktribe.com/output/1033014
• Publisher URL: http://dx.doi.org/10.1093/imamat/hxm036