Water waves in the time domain

The initial-value problem for a structure floating on the surface of the sea is investigated under the assumptions of linear theory. Fourier transforms are used to connect the time- and frequency-domain representations of the coupled motion of the fluid and body. This allows the large-time asymptotics of the motion to be obtained from the singularity structure of the frequency-domain potential in the complex plane. Under certain initial conditions, the free motion of a body about a fixed, equilibrium position is shown not to exist for all time, and in this case the assumptions behind the linear theory are violated. For suitably moored structures, motion is found which is purely exponentially decaying in time and does not involve any oscillations.