Note on the reflexion of water waves at a wall in the presence of surface tension

Abstract

Abstract In this note we examine the influence of surface tension on surface waves incident against a fixed vertical plane wall. The motion is time harmonic and is determined by making the initial assumption that the free-surface slope at the wall is prescribed. From the unique solution obtained for the velocity potential, the parameter involved in this specification can be determined, for small laboratory-scale waves at least, using some longstanding experimental results on meniscus behaviour at a moving contact line. The effect of surface tension is to produce a motion wherein reflexion from the wall is not complete and there is a local disturbance, in contrast to the classical standing-wave motion in the absence of surface tension.