Linear water waves: the horizontal motion of a structure in the time domain

The framework of the linearised theory of water waves in the time domain is used to examine the horizontal motion of an unrestrained floating structure. One of the principle assumptions of the theory is that an infinitesimal disturbance of the rest state will lead to an infinitesimal motion of the fluid and structure. It has been known for some time that for some initial conditions the theory predicts an unbounded horizontal motion of the structure that violates this assumption, but the possibility does not appear to have been examined in detail. Here some circumstances that lead to predictions of large motions are identified and, in addition, it is shown that not all non-trivial initial conditions lead to violations of the assumptions. In particular, it is shown that the horizontal motion of a floating structure remains bounded when it is initiated by the start up of a separate wave maker. The general discussion is supported by specific calculations for a vertical circular cylinder.