Linear stability of fluid flow down a porous inclined plane

We investigate the linear stability of a fluid flowing down an inclined per meable plane by studying the evolution in time of infinitesimal disturbance s of long wavelength. We assume that the how through the porous medium is g overned by Darcy's law, and determine the critical conditions for the onset of instability in the case when the characteristic length scale of the por e space is much smaller than the depth of the fluid layer above. The result s reveal that increasing the permeability of the inclined plane destabilize s the how of the fluid layer flowing above.