Instabilities of a power-law film over an inclined permeable plane: A two-sided model

A two-sided model is proposed to investigate the stability problem of the steady uniform flow of a power-law fluid layer down an inclined porous layer. The governing equations for the clear fluid flow are coupled with the ones for the seepage in the porous layer, for which the generalized Darcy's law is employed. A linear stability analysis of both two-dimensional and depth-integrated formulations is carried out in order to individuate the neutral stability conditions. The influence of the dimensionless governing parameters on the stability properties is deeply discussed. The nonlinear effects on the stability of the flow are finally investigated through the numerical solution of the depth-integrated model.