Capillary–gravity waves produced by a heaving body

Abstract

The vertical oscillation of a partially submerged body produces a surface wave that carries energy away from the body. The amplitude of this wave, when surface-tension effects are not negligible, depends on the conditions applied at the line of contact between the body and the free surface of the fluid. An edge condition that includes both dynamic variation of the contact angle and contact-angle hysteresis is used in this paper; the condition implies a dissipation of energy at the contact line. The amplitude of the wave and the amount of energy dissipated are calculated for a horizontal circular cylinder and for a simple source-and-plate model. This model is shown to be an adequate representation for the qualitative description of heaving motions and to simplify the calculations considerably. The effects of varying the relative importance of surface tension and gravity, the dynamic behaviour of the contact angle, and the amount of hysteresis, are calculated for the source-and-plate model.