Integral identities of potential theory of radiation and diffraction of regular water waves by a body

Summary

The study presents a new general integral identity for the velocity potential of flow about a body in regular water waves. This integral identity is valid outside, inside, and exactly on the surface of the body, and is equivalent to the set of three classical identities valid strictly outside, inside, and on the body, respectively. For the usual problem of wave radiation and diffraction by a body, the integral identity yields an integral equation for determining the potential on the body surface. An interesting feature of the integral identity and related integral equation obtained in this study is that they involve an integral of the Green function over the waterplane inside the body in the case of an open sea-surface piercing body. Alternatively, these equations can be expressed in terms of a modified Green function involving the previously-noted waterplane integral of the Green function.