Falling film of power-law fluid on a high-frequency oscillating inclined plane

We consider a 2D thin film flow of a power-law fluid on an inclined plane due to gravity. The plane oscillates harmonically keeping the inclination angle constant. The longitudinal oscillations produce additional shear. We calculate the effect of these oscillations on the mean flow rate for fixed film thickness assuming that free surface is flat. Using the integral boundary layer approach, we investigate the stability of the waveless flow due to low-frequency disturbances. We show that the oscillations of the plane stabilize the flow.