Clapotis

In hydrodynamics, a clapotis (from French for "lapping of water") is a non-breaking standing wave pattern, caused for example, by the reflection of a traveling surface wave train from a near vertical shoreline like a breakwater, seawall or steep cliff. The resulting clapotic wave does not travel horizontally, but has a fixed pattern of nodes and antinodes. These waves promote erosion at the toe of the wall, and can cause severe damage to shore structures. The term was coined in 1877 by French mathematician and physicist Joseph Valentin Boussinesq who called these waves 'le clapotis' meaning "the lapping". In the idealized case of "full clapotis" where a purely monotonic incoming wave is completely reflected normal to a solid vertical wall, the standing wave height is twice the height of the incoming waves at a distance of one half wavelength from the wall. In this case, the circular orbits of the water particles in the deep-water wave are converted to purely linear motion, with vertical velocities at the antinodes, and horizontal velocities at the nodes. The standing waves alternately rise and fall in a mirror image pattern, as kinetic energy is converted to potential energy, and vice versa. In his 1907 text, Naval Architecture, Cecil Peabody described this phenomenon: At any instant the profile of the water surface is like that of a trochoidal wave, but the profile instead of appearing to run to the right or left, will grow from a horizontal surface, attain a maximum development, and then flatten out till the surface is again horizontal; immediately another wave profile will form with its crests where the hollows formerly were, will grow and flatten out, etc. If attention is concentrated on a certain crest, it will be seen to grow to its greatest height, die away, and be succeeded...