Solitary Wave Diffraction around Large Cylinder

Abstract

The diffraction of a solitary wave around a vertical surface-piercing circular cylinder is described to a first approximation, and the resulting forces on the cylinder are calculated. This represents a limiting case of a cnoidal wave diffraction solution given previously, and in order to treat this limit the incident wave is represented in terms of a Fourier integral rather than a Fourier series. The maximum force coefficient and the dimensionless runup depend on a single parameter which replaces the usual diffraction parameter. A criterion for diffraction to be significant for shallow water waves is established and depends upon both the diffraction parameter as well as the additional parmater used here.