Stability of the Newtonian Film Flow Down an Oscillating Inclined Plane. I. Orr-Sommerfeld Problem in a Long-Wave Asymptote

Stability of the film flow an oscillating inclined plane is analyzed. Following the previous analysis by Bauer and von Kerczek (1991), the 2D linearized equations of fluctuating motion around the primary (superposed oscillatory) flow field a for a Newtonian Fluid are analyzed. The long-wave (small wave number ?)asymptotic expansion in solved up to the order O(?)