Analytical study to long-wave transformation by a submerged circular cylinder or pit located in a general idealized bottom topography

In this paper, the problem of linear long-wave scattering by a submerged circular cylinder or a circular pit located in a general idealized bottom topography is considered. Because of the generality of the bottom topography, the problem has various physical and engineering backgrounds. By skillfully using variable transforms, a close-formed analytical solution to the long-wave equation (LWE) in terms of Fourier-cosine series is developed, which finds several existing analytical solutions to be its degenerated cases. Based on the present solution, the influence of various factors, including the convexity or concavity of the bottom topography, the submergence of the circular cylinder or circular pit, and the wavelength of incident waves on wave amplification or attenuation is investigated.