A linear stability analysis of the destabilizing effects of wall permeability in channel flows /

We perform a three-dimensional linear stability analysis of a laminar flow in a channel delimited by rigid, homogeneous, isotropic, porous blocks. We consider porous materials in which the permeability is small and the inertial effects can be neglected. We solve the coupled linear stability problem, arising from the adjacent channel and porous flows, using a spectral collocation technique. We consider symmetric flows in channels with two identical porous walls and skewed flows in channels with only one porous wall. In both cases, permeability significantly affects the Orr-Sommerfeld spectrum; however, the homogeneous Squire modes remain damped. In channels with two porous walls, permeability destabilizes up to two Orr-Sommerfeld wall modes and introduces two new damped wall modes on the left branch of the spectrum. In channels with only one porous wall, permeability destabilizes up to one wall mode and introduces one new damped wall mode on the left branch of the spectrum. In both channels, permeability also introduces a new class of damped modes associated with the porous regions. We find that very small amounts of wall permeability can dramatically decrease the stability of the channel flow. The neutral curve becomes significantly larger and the critical Reynolds number can decrease to only 10% its Poiseuille value