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Nonlinear Stability of Convection in a Porous Layer with Solid Partitions

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Abstract

We show that for many classes of convection problem involving a porous layer, or layers, interleaved with finite but non-deformable solid layers, the global nonlinear stability threshold is exactly the same as the linear instability one. The layer(s) of porous material may be of Darcy type, Brinkman type, possess an anisotropic permeability, or even be such that they are of local thermal non-equilibrium type where the fluid and solid matrix constituting the porous material may have different temperatures. The key to the global stability result lies in proving the linear operator attached to the convection problem is a symmetric operator while the nonlinear terms must satisfy appropriate conditions.

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Authors and Affiliations

  1. Department of Mathematics, University of Durham, Durham, DH1 3LE, UK

    B. Straughan

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  1. B. Straughan
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Correspondence to B. Straughan.

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Communicated by G.P. Galdi

Research supported by a “Tipping Points, Mathematics, Metaphors and Meanings” grant of the Leverhulme Trust. I am indebted to an anonymous referee for helpful criticism.

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Straughan, B. Nonlinear Stability of Convection in a Porous Layer with Solid Partitions. J. Math. Fluid Mech. 16, 727–736 (2014). https://doi.org/10.1007/s00021-014-0183-4

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  • DOI: https://doi.org/10.1007/s00021-014-0183-4

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