Analytic study to wave scattering by a general Homma island using the explicit modified mild-slope equation

In this paper, an exact analytic solution in terms of Taylor series to the explicit modified mild-slope equation (EMMSE) for wave scattering by a general Homma island is constructed and the convergence of the series solution is analyzed. To validate the new analytic solution, comparisons are made against the existing solutions including analytic solutions to both the long-wave equation and Helmholtz equation, approximate analytic solutions to the modified mild-slope equation, numerical solutions to the mild-slope equation and experimental solutions. Because of the use of the governing equation EMMSE together with mass-conserving matching conditions along the toe of the shoal, the present model is valid for not only waves in the whole spectrum from long waves to short waves but also bathymetries with the maximal seabed slope being as high as 4.27:1. Since the general Homma island is an extension of the original Homma island, the present solution can be very conveniently used to study the effects of bottom topography on combined refraction and diffraction. It is found that the larger the shoal size is, the more significant the wave amplification against the cylinder is.