Water wave scattering by partially reflecting breakwaters

Following the approach used by Penney and Price in 1952, analytical solutions are derived for water wave scattering by a semi-infinite breakwater or a breakwater gap of partial reflection. The water depth is constant and a regular wave train is normally incident to the breakwater. Wave scattering is studied based on the linear potential wave theory. The governing equation is transformed into ordinary differential equations by using the method of variation of parameters and coordinate transformation. Using the analytic solution, the tranquility of harbor entrance is investigated by changing the reflection coefficient at the breakwater. As expected, the wave height is reduced at the harbor entrance as the wave reflection from the breakwater decreases.