  Although the stability properties of the wake past impervious bluff bodies
have been widely examined in the literature, similar analyses regarding the
flow around and through porous ones are still lacking. In this work, the effect
of the porosity and permeability on the wake patterns of porous rectangular
cylinders is numerically investigated at low to moderate Reynolds numbers in
the framework of direct numerical simulation combined with local and global
stability analyses. A modified Darcy-Brinkman formulation is employed here so
as to describe the flow behavior inside the porous media, where also the
convective terms are retained to correctly account for the inertial effects at
high values of permeability. Different aspect ratios of the cylinder are
considered, varying the thickness-to-height ratios, t/d, from 0.01 (flat plate)
to 1.0 (square cylinder). The results show that the permeability of the bodies
has a strong effect in modifying the characteristics of the wakes and of the
associated flow instabilities, while the porosity weakly affects the resulting
flow patterns. In particular, the fluid flows through the porous bodies and,
thus, as the permeability is progressively increased, the recirculation
regions, initially attached to the rear part of the bodies, at first detach
from the body and, eventually, disappear even in the near wakes. Global
stability analyses lead to the identification of critical values of the
permeability above which any linear instability is prevented. Moreover, a
different scaling of the non-dimensional permeability allows to identify a
general threshold for all the configurations here studied that ensures the
suppression of vortex shedding, at least in the considered parameter space.
