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

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.