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Abstract

The singular and highly oscillatory properties of unsteady ship waves are studied by considering potential flows generated by a point source pulsating and advancing at a uniform forward speed located close to or at the free surface. The wave component of the free-surface potential defined by Noblesse and Chen by a single integral along the dispersion curves defined by the dispersion relation is analysed by developing asymptotic expansions of the open dispersion curves at large wave numbers. The asymptotic analysis of the wave component contributed by the leading asymptotic term of a parabolic form shows that unsteady ship waves are highly oscillatory with infinitely increasing amplitude and infinitely decreasing wavelength, when a field point approaches the track of the source point at the free surface. The highly oscillatory property and complex singular behaviour of unsteady ship waves are further expressed in an original and analytically closed form.

Keywords

unsteady ship waves ship-motion Green function highly oscillatory terms short waves singularity along the track of source point asymptotic analysis

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Highly oscillatory properties of unsteady ship waves

Abstract

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