Faraday waves over a permeable rough substrate

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. 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.