The onset of convection in porous layers with multiple horizontal partitions

Neutral stability curves are found to organise themselves into natural groups of N members when there are N sublayers. When the disturbance wavenumber, k, is large, each member of any group lies within an O(k−1) distance of all other members, but within an O(1) distance of other groups. When the number of sublayers is large, the system tends towards one with a critical Darcy-Rayleigh number of 12 and a critical wavenumber of zero; this is the well-known property of a single porous layer with constant heat flux boundary conditions. An asymptotic analysis is performed in order explore these two apparently disparate configurations. Finally, another asymptotic analysis is used to determine the critical Rayleigh number and its associated wavenumber when the number of sublayers is large.