Wave-induced surface drift of an inextensible thin film

In this study, the surface drift of an inextensible film due to a series of progressive gravity waves is investigated both analytically and experimentally. A second approximation of the conformal mapping that transforms the progressive sinusoidal surface to the horizontal axis is applied, thus allowing the analysis to formally accommodate a boundary layer thickness that is much less than the wave height. By computing the stream function to the third order that is an order higher than the past analysis, a pressure component in phase with the wave slope is revealed. The pressure force generated is comparable to the bottom shear on the thin film induced by the moving fluid and thus cannot be ignored. Based on the combined forces on the surface firm, a mean drift is estimated by assuming that the opposing force is due to the viscous drag induced by the drift motion. The experimental results show that the computed drift velocity based on the present study mostly underestimates the experimental observations, but it is in closer agreement than the classical Phillips' 7/4 estimate.