Scattering of a capillary–gravity wave by a vertical cylinder

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Abstract
The scattering of a capillary–gravity wave by a surface‐piercing obstacle depends on the condition applied at the contact line between the fluid and the obstacle. A model for this condition that incorporates the effect of dynamic contact‐angle variation is used to determine the wave field close to the obstacle and at large distances from it. The solutions depend on the ratio between the wavelength of the incident wave and the radius of the obstacle, which is taken to be a circular cylinder, and on the relative size of the capillary and gravitational restoring forces. A third parameter is a constant of proportionality in the edge condition. Extreme values of this parameter relate to the special cases of orthogonal contact and of a fixed contact line. The strength of the scattered wave and the angular variation of its amplitude at large distances are calculated for a range of values of the parameters. The amplitude of the surface elevation on the boundary of the cylinder is also determined.