  We report on an experimental study of the Faraday instability in a vibrated
fluid layer situated over a permeable and rough substrate, consisting either of
a flat solid plate or of woven meshes having different openings and wire
diameters, open or closed (by a sealing paint). We measure the critical
acceleration and the wavelength (on the images from top) at the onset of the
instability for vibration frequencies between 28 and 42 Hz. We observe that, in
comparison with the flat plate, a mesh leads to an increase of the critical
acceleration, whereas the wavelength is not significantly altered in none of
the explored cases. In order to rationalize the observations, we use the linear
theory written for the case of a flat bottom and a viscous fluid to define an
effective thickness of the fluid layer, which permits to define an effective
thickness at the bottom. For the closed meshes the effective thickness is
simply a linear function of the distance between wires constituting the mesh,
whereas it exhibits a more complex behavior for the open meshes. We propose a
qualitative understanding for the observed features.
