Laminar flow of a liquid, down an inclined wall with sinusoidal corrugations, is considered. A linear analysis, valid for small-amplitude disturbances but arbitrary wavelength and Re number, leads to an Orr-Sommerfeld type equation with nonhomogeneus boundary conditions. The free-surface amplitude and phase relative to the wall are examined. In a range of Re numbers, a resonance phenomenon is calculated, leading to amplification of the wall corrugations. This behavior has not been encountered in previous analyses of thin film flow, based on the Stokes approximation.
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