Laminar film flow down a wavy incline

Laminar how 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 nonhomogeneous 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. Copyright (C) 1996 Elsevier Science Ltd.