Diffraction by a circular island of long waves produced by a riparian source: PMM vol. 35, n≗6, pp. 1015–1022, 1971

Abstract

The diffraction of long cylindrical waves by a circular island situated in a rotating tank is considered. It is shown that, when the wavelength is small in comparison with the island radius, a resonanace capture of waves by the island takes place. Unlike in the author's paper [1] which analyzed the diffraction of monochromatic plane waves by a circular island in a rotating tank of constant depth, here the diffraction of cylindrical waves produced by a source at the island boundary is considered. As in [1], the wavelength is assumed to be considerable in comparison with the depth of the tank, but small relative to the island radius. A solution in the form of a conventional slowly convergent Fourier series is first derived, and then transformed by Watson's method into a fast convergent series, which makes it possible to determine the pattern of wave diffraction, at least along the island periphery. Many details of the derivation of solution have been omitted here. One of these details can be found in [1, 2], while others may be obtained by small alterations in the calculations presented in those papers.