The effect of surface tension on the waves produced by a heaving circular cylinder

In this paper the effect of surface tension on water waves is considered. The usual assumptions of the linearized theory are made. A uniqueness theorem is derived for the waves at infinity for a general class of bounded two-dimensional obstacles in a free surface by means of an energy argument. It is shown how the wave amplitude at infinity depends on the prescribed angle at which the free surface meets the normal to the obstacle. The particular case of a heaving half-immersed circular cylinder is considered in detail, and an expression obtained for the velocity potential in terms of a convergent infinite series, the coefficients of which may be computed.