Complex resonances in the water-wave problem for a floating structure
McIverPhilip
2006
This work is concerned with the linearized theory of water waves applied to the motion
of a floating structure that restricts in some way the motion of a portion of the free
surface (an example of such a structure is a floating torus). When a structure of
this type is held fixed in incident monochromatic waves, or forced to move time
harmonically with a prescribed velocity, the amplitude of the fluid motion will have
local maxima at certain frequencies of the forcing. These resonances correspond
to poles of the scattering and radiation potentials when extended to the complex
frequency domain. It is shown in this work that, in general, the positions of these
poles in the scattering and radiation potentials will not coincide with the positions of
the poles that appear in the velocity potential for the coupled problem obtained when
the structure is free to move. The poles of the potential for the coupled problem are
associated with the solution for the structural velocities of the equation of motion.
When physical quantities such as the amplitude of the fluid motion are examined as a
function of (real) frequency, there will in general be a shift in the resonant frequencies
in going from the radiation and scattering problems to the coupled problem. The
magnitude of this shift depends on the geometry of the structure and how it is moored.