Onset of Convection in a Porous Layer with Continuous Periodic Horizontal Stratification. Part I. Two-Dimensional Convection

Reference:

Rees, D. A. S. and Tyvand, P. A., 2009. Onset of Convection in a Porous Layer with Continuous Periodic Horizontal Stratification. Part I. Two-Dimensional Convection. Transport in Porous Media, 77 (2), pp. 187-205.

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Official URL:

http://dx.doi.org/10.1007/s11242-008-9324-7

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.

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