THE SCATTERING OF LONG WATER-WAVES BY A GROUP OF SUBMERGED, HORIZONTAL CYLINDERS

The method of matched asymptotic expansions is used to analyse the scattering of water waves by a line of identical, horizontal circular cylinders all submerged to the same depth. The main assumptions are that the wavelength and cylinder spacing are both much larger than the cylinder radius. Two different asymptotic solutions are presented. The first is derived under the further assumption that the wavelength and spacing are of the same order of magnitude and may be thought of as simply a small-body approximation. The second takes the wavelength to be much larger than the spacing and may be used to investigate the long-wave limit relative to all geometrical parameters. The reflection and transmission properties and the implications for wave forces of these solutions are discussed. © 1990 Oxford University Press.