  We have investigated the effects of permeable walls, modeled by linear
acoustic impedance with zero reactance, on compressible channel flow via linear
stability analysis (LSA). Base flow profiles are taken from impermeable
isothermal-wall laminar and turbulent channel flow simulations at bulk Reynolds
number, $Re_b$= 6900 and Mach numbers, $M_b$ = 0.2, 0.5, 0.85. For a
sufficiently high value of permeability, Two dominant modes are made unstable:
a bulk pressure mode, causing symmetric expulsion and suction of mass from the
porous walls (Mode 0); a standing-wave-like mode, with a pressure node at the
centerline (Mode I). In the case of turbulent mean flow profiles, both modes
generate additional Reynolds shear stresses augmenting the (base) turbulent
ones, but concentrated in the viscous sublayer region; the trajectories of the
two modes in the complex phase velocity space follow each other closely for
values of wall permeability spanning two orders of magnitude, suggesting their
coexistence. The transition from subcritical to supercritical permeability does
not alter the structure of the two modes for the range of wavenumbers
investigated, suggesting that wall permeability simply accentuates pre-existing
otherwise stable modes. Results from the present investigation will inform the
design of new compressible turbulent boundary layer control strategies via
assigned wall-impedance.
