Nonlinear stability of the one-domain approach to modelling convection in superposed fluid and porous layers

Hill, Antony A.; Carr, Magda

Abstract

Studies of the nonlinear stability of fluid/porous systems have been developed very recently. A two-domain modelling approach has been adopted in previous works, but was restricted to specific configurations. The extension to the more general case of a Navier-Stokes modelled fluid over a porous material was not achieved for the twodomain approach owing to the difficulties associated with handling the interfacial boundary conditions. This paper addresses this issue by adopting a one-domain approach, where the governing equations for both regions are combined into a unique set of equations that are valid for the entire domain. It is shown that the nonlinear stability bound, in the one-domain approach, is very sharp and hence excludes the possibility of subcritical instabilities. Moreover, the one-domain approach is compared with an equivalent two-domain approach, and excellent agreement is found between the two. © 2010 The Royal Society.

• Presentation Conference Type: Conference Paper (published)
• Publication Date: Sep 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: 2121
• Pages: 2695-2705
• DOI: https://doi.org/10.1098/rspa.2010.0014
• Keywords: superposed porous–fluid convection, one-domain approach, energy method
• Public URL: https://uwe-repository.worktribe.com/output/985591
• Publisher URL: http://dx.doi.org/10.1098/rspa.2010.0014
• Contract Date: Apr 15, 2016