Analytical solutions of waves

Long Waves Propagating over Circular Island

An analytic solution of long waves scattering by a cylindrical island mounted on a permeable circular shoal was obtained by solving the linear long wave equation LWE. The solution is in terms of the Bessel function expressed by complex variables. The present solution is suitable for arbitrary bottom configurations described by a power function with two independent parameters.(Kuo et al., 2012)

Numerical Results

Wave over Axi-symmetric Topography (San, 2014)

The newly derived solution is further employed to investigate the key patterns of wave transformation over a circular island mounted on different axi-symmetric shoals and different submerged truncated axi-symmetric shoals subjecting to varying conditions of incident wave period and values of the arbitrary power of radial distance.

Numerical Results


Y. S. Kuo, T. W. Hsu, Chia-Cheng Tsai* and Y. H. Huang (2012, Oct). An extended analytic solution of combined refraction and diffraction of long waves propagating over circular island. Journal of Applied Mathematics, Article Number:742705.

Sieu-Cuong San, (2014) Master thesis.