An analytical study of long wave propagation around two circular islands

Abstract The analytical solution of a linear long wave propagating around two circular islands is derived. Considering the mutual influence of scattered waves from each island, the multiple scattering method is used to define the local coordinate system on each island and describe the scattered waves. Then, the overall wave field at a spatial location is the superposition of the incident wave with the scattered waves from each island. Finally, Graf's addition theorem is adopted to translate the functions in different coordinate systems into the same coordinate system. The unknown parameters contained in the free surface function are obtained by coupling according to the match between the constant-depth and variable-depth boundary conditions of each island. On this basis, the influences of variations in the slopes of the two islands and the distance between them together with the incident wave period and direction on the amplitudes of the surrounding waves are analyzed.