Waves trapped along a breakwater

The excitation of trapped waves by the diffracted wavefield around a breakwater in varying water depth is studied. Using the parabolic approximation, the governing equation for trapped waves is first obtained. The trapped waves can be excited, when the effective concavity of the breakwater with respect to the index of refraction (local wave number) is positive. An analytical solution is then presented for the case where the breakwater is a semi-infinite straightline and is parallel to the shoreline on a uniform beach.