Analytical Solutions for Long Waves Scattering by a Circular Cylinder Mounted on a General Shoal

In this study, we derive an analytical solution in Taylor series for long waves scattering by a circular cylinder mounted on a general shoal. The water depth on the shoal varies in proportion to an arbitrary power of the radial distance. Separation of variables, Taylor series expansion, and Frobenius series are used to find the solutions, which are then validated by comparing them with previously developed analytical solutions. In addition, the effect of wave periods, radii of the island toe and power values to wave amplifications is also investigated.