Step transition for plane waves at a free surface

Refraction and reflection are phenomena known to occur as light travels across different media, with its speed being modulated by the refractive index. We explain how plane waves propagating at a free surface of an inviscid incompressible liquid behave in a similar manner and use a regularised wave equation, which serves as an approximation to the full water-wave equation, to show different scenarios involving constructive and destructive interference of water waves past an interface or step transition. In our case, wavespeeds are modulated by the wave frequency and the local fluid depth.