On the radiation and scattering of short surface waves. Part 3

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Abstract
The radiation properties of partially immersed three-dimensional bodies, in time-periodic motion, are examined in the short-wave asymptotic limit ε → 0, where ε is a non-dimensional wavelength. The method of matched expansions is used to specify an outer approximation, away from the surface wave region, and an inner approximation where the potential, in the vicinity of the obstacle and free surface, depends only on the local geometry. Finally, the radially spreading surface wave field is estimated by ray-theory arguments. Explicit details are given for the heaving and rolling of a circular dock and for the heaving motion of a hemisphere. Some speculations are made regarding the scattering properties of such obstacles.
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