The scattering properties of a system of structures in water waves

A fixed, rigid structure is said to be cloaked in small amplitude, time-harmonic water waves if it is possible to surround it with other fixed or moving structures or variations in the sea-bed topography in such a way that there are no scattered waves in the far field. The resulting system of structures is said to be transparent to the incident wave field. By finding inequalities which the kinetic and potential energy in the total wave field for such a system must satisfy, it is shown that transparency is impossible for a system of structures which has non-zero volume and satisfies the condition that the free surface is connected and a vertical line drawn from every point on the free surface does not intersect another structure but intersects the sea bed at a point at which the bed is horizontal.