The destabilizing effects of wall permeability in channel flows: A linear stability analysis

We perform a three-dimensional linear stability analysis of a laminar flow in a channel delimited by rigid, homogeneous, isotropic, porous blocks sealed by impermeable walls. We consider porous materials with small permeability and neglect inertial effects in the porous flow. We solve the coupled linear stability problem, arising from the adjacent channel and porous flows, using a spectral collocation technique. We find that very small amounts of wall permeability can dramatically decrease the stability of the channel flow with respect to Poiseuille flow. We also observe two new wall modes and a new class of modes in the porous regions.