Linear stability of fluid flow down a porous inclined plane

We investigate the linear stability of a fluid flowing down an inclined permeable plane by studying the evolution in time of infinitesimal disturbances of long wavelength. We assume that the flow through the porous medium is governed by Darcy's law, and determine the critical conditions for the onset of instability in the case when the characteristic length scale of the pore space is much smaller than the depth of the fluid layer above. The results reveal that increasing the permeability of the inclined plane destabilizes the flow of the fluid layer flowing above.