The Forced Motion of Structures that Support Trapped or Near-Trapped Water Waves

Trapped water waves are free oscillations of an unbounded fluid with a free surface for which the fluid motion is essentially confined to the vicinity of a fixed structure. Thus the energy of the motion is finite and there is no radiation of energy to infinity. Such modes are non-trivial solutions of the linearized water-wave problem in the frequency domain, they satisfy homogeneous boundary conditions, and contain no waves in the far field (hence there is an absence of any forcing either from incident waves or from an imposed motion of the structure). In recent years trapping structures, that is structures that support trapped modes, have been constructed in both the two- and three-dimensional linear water-wave problems (see [3], and the references therein).