  The effect of the variations of the permeability tensor on the
close-to-the-wall behaviour of a turbulent channel flow bounded by porous walls
is explored using a set of direct numerical simulations. It is found that the
total drag can be either reduced or increased by more than $20\%$ by adjusting
the permeability directional properties. Drag reduction is achieved for the
case of materials with permeability in the vertical direction lower than the
one in the wall-parallel planes. This configuration limits the wall normal
velocity at the interface while promoting an increase of the tangential slip
velocity leading to an almost "one-component" turbulence where the low- and
high-speed streaks coherence is strongly enhanced. On the other hand, strong
drag increase is found when a high wall-normal and low wall-parallel
permeabilities are prescribed. In this condition, the enhancement of the
wall-normal fluctuations due to the reduced wall-blocking effect triggers the
onset of structures which are strongly correlated in the spanwise direction, a
phenomenon observed by other authors in flows over isotropic porous layers or
over ribletted walls with large protrusion heights. The use of anisotropic
porous walls for drag reduction is particularly attractive since equal gains
can be achieved at different Reynolds numbers by rescaling the magnitude of the
permeability only.
