MCIVER, M. and MCIVER, P., 2011. Water waves in the time domain. Journal of Engineering Mathematics, 70 (1-3), pp.111-128.
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.