The effect of a fixed vertical barrier on surface waves in deep water

TLDR

The motion on either side of an infinite vertical plane with prescribed normal velocity is fully determined except for simple standing waves. The study theoretically investigates two‑dimensional surface‑wave reflection from a vertical barrier in deep water. The authors prescribe normal velocity on a portion of the barrier, derive a simple integral equation from continuity across it, and analyze reflection from a fixed barrier extending from depth a to above the mean surface.

Abstract

In this paper the two-dimensional reflection of surface waves from a vertical barrier in deep water is studied theoretically. It can be shown that when the normal velocity is prescribed at each point of an infinite vertical plane extending from the surface, the motion on each side of the plane is completely determined, apart from a motion consisting of simple standing waves. In the cases considered here the normal velocity is prescribed on a part of the vertical plane and is taken to be unknown elsewhere. From the condition of continuity of the motion above and below the barrier an integral equation for the normal velocity can be derived, which is of a simple type, in the case of deep water. We begin by considering in detail the reflection from a fixed vertical barrier extending from depth a to some point above the mean surface.