Scattering of Water Waves by a Truncated Vertical Cylinder of Arbitrary Cross Section: Asymptotic Analysis

Abstract

Scattering of water waves by a vertical truncated cylinder of arbitrary cross-section is investigated using the linear theory and asymptotic analysis. The flow domain is divided into the exterior and interior regions. The linearized boundary value problem is solved by the method of matched eigenfunctions and in an asymptotic manner that deals with the arbitrary geometry of the cross section. The cross-section shape is expanded in a Fourier series involving a small parameter that represents the deviation of the geometry from a circle. The advantage of this method is that the wave forces on the cylinder are obtained in terms of the coefficients of the Fourier series of the cylinder shape. For the case of a circular cylinder, exact analytical results are recovered. Cylinders with cross-section geometries of cosine-type radial perturbations and of a quasi-ellipse are considered for validation of the present method. Good agreement with the published results is obtained with the first and second-order asymptotic orders. New graphical analyses based on the problem parameters are presented for a vertical elliptical cylinder. Long-wave approximations of wave forces are obtained for cylinders whose cross-sections are not too different from a circle. © 2025 Elsevier Ltd