Stability of boundary layers over porous walls with suction

Although there is considerable interest in using wall suction to increase boundary-layer stability, stability analyses suggest that porous walls are inherently destabilizing. We explore this contradiction by performing a spatial linear stability analysis of the asymptotic suction boundary layer using a realistic model of wall suction. The porous wall is modelled as a layer of rigid, homogeneous, isotropic, porous material of small permeability, in which inertial effects maybe neglected. The porous layer is bounded above by a semi-infinite region in which a boundary layer is driven by a constant freestream velocity. The wall suction is created by applying a suction pressure to a semi-infinite region below the porous layer. Our stability analysis takes account of the full coupling between the flowfields in the boundary-layer and suction regions, governed by the Navier-Stokes equations, and the flow in the porous layer, governed by the volume-averaged Navier-Stokes equations. We find that small amounts of wall permeability destabilize the Tollmien-Schlichting wave and cause a substantial broadening of the unstable region. As a result, the stabilization of boundary layers by wall suction is substantially less effective and more expensive than what is predicted by classical boundary-layer theory.