Onset of convection in a porous layer with continuous periodic horizontal stratification. Part I. Two-dimensional convection

D. Andrew S. Rees, Peder A. Tyvand

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10 Citations (Scopus)

Abstract

The onset of convection in a horizontal porous layer is investigated theoretically. The permeability of the porous medium is a continuous periodic function of the horizontal x coordinate. Floquet theory has been employed to determine the favoured two-dimensional mode of convection. For a wide range of periods of the permeability variation, a matrix eigenvalue technique with eighth order accuracy has been employed to find the critical Darcy- Rayleigh number. This is supplemented by a multiple-scales analysis of the large-period limit, and a brief consideration of the anisotropic limit for very short periods.
Original languageEnglish
Pages (from-to)187-205
Number of pages19
JournalTransport in Porous Media
Volume77
Issue number2
DOIs
Publication statusPublished - Mar 2009

Keywords

  • Nonuniform permeability
  • Floquet theory
  • Linear stability theory
  • Free convection
  • Multiple scales

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