Onset of convection in a porous layer with continuous periodic horizontal stratification, Part II: Three-dimensional convection

The onset of convection in a porous layer which is heated from below is considered. In particular we seek to determine the effect of spatially periodic variations in the permeability field on the identity of the onset mode as a function of both the period PP of this variation and its amplitude AA. A Floquet theory is assumed in order to ensure that the analysis is as general as possible. It is found that convection is always three-dimensional and that the critical Rayleigh number always decreases as either the period or the amplitude of the permeability variation increases. Furthermore, the corresponding Floquet exponent νν is either 0 or 1, and the range of values of PP over which ν=1ν=1 corresponds to the favoured mode has been obtained as a function of AA.