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

Antony A. Hill, Magda Carr

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)
3 Downloads (Pure)


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 languageEnglish
Pages (from-to)127-140
Number of pages14
JournalProceedings of the Royal Society A - Mathematical, Physical & Engineering Sciences
Issue number2113
Early online date30 Sept 2009
Publication statusPublished - 8 Jan 2010


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


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