The motions of a floating slender torus

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Abstract
The motions of a floating torus oscillating in response to incident waves are analysed under the assumptions that the incident wavelength is comparable with the radius of the body section and small compared with the larger radius of the torus. This problem serves to illustrate certain features of the strip theory for ship motions, but the axisymmetric geometry and absence of body ends greatly simplify the analysis. Matched asymptotic expansions are used, with the inner solution close to the body section composed of suitable radiation and scattering problems for the two-dimensional circular cylinder. Resonant standing-wave modes in the internal basin have a singular effect upon the hydrodynamic forces acting on the body, and its response to incident waves.

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