Onset of Convection in a Porous Layer with Continuous Periodic Horizontal Stratification. Part I. Two-Dimensional Convection |
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Authors: | D Andrew S Rees Peder A Tyvand |
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Institution: | 1.Department of Mechanical Engineering,University of Bath,Bath,UK;2.Department of Mathematical Sciences and Technology,Norwegian University of Life Sciences,?s,Norway |
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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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