Passive trapped modes in the water-wave problem for a floating structure

Trapped modes in the linearized water-wave problem are free oscillations of an unbounded fluid with a free surface that have finite energy. It is known that such modes may be supported by particular fixed structures, and also by certain freely floating structures in which case there is, in general, a coupled motion of the fluid and structure; these two types of mode are referred to respectively as sloshing and motion trapped modes, and the corresponding structures are known as sloshing and motion trapping structures. Here a trapped mode is described that shares characteristics with both sloshing and motion modes. These 'passive trapped modes' are such that the net force on the structure exerted by the fluid oscillation is zero and so, in the absence of any forcing, the structure does not move even when it is allowed to float freely. In the paper, methods are given for the construction of passive trapping structures, a mechanism for exciting the modes is outlined using frequency-domain analysis, and the existence of the passive trapped modes is confirmed by numerical time-domain simulations of the excitation process.