Clapotis

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Perfect reflection on a vertical wall:
the incoming wave (red) is reflected with the same sign of the amplitude (outgoing blue wave). The clapotis (black) with an antinode on the wall results from the superposition .

Streamlines of a clapotis

In the case of water waves , clapotis (from the French for 'splash') is understood to be a standing wave that is created by the reflection of a progressive monochromatic wave on a vertical wall ( pier , bank wall ).

Here, a wave train hitting the wall with the wavelength  L and the height  H (vertical distance between wave trough and wave crest) throws back a mirror image wave train. The superposition of incoming and reflected wave yields the Clapotis having a wave height 2 H . If the distance from the wall is designated with the x coordinate , antinodes with a height of 2 H are located at x  = 0 (wall), x  =  L / 2, x  = 2 L / 2 etc.

In between there are oscillation nodes at x  =  L / 4, x  = 3L / 4, x  = 5 L / 4 etc., where there is no water level deflection with a perfect clapotis . The oscillating movements of the water particles in the wave field below the water surface (second picture) are curvilinear, with a horizontal tangent at the oscillation nodes, and vertical at the wave bellies.

The perfect reflection represents an ideal case . In nature, the boundary conditions for stable waves are at best approximately given in the vicinity of the building , because losses occur on the reflection surfaces. As a result, a (broken) torn clapotis, an (imperfect) partial clapotis or a combination of both forms.

Opened clapotis

In pool formations with low reflection losses, the excitation of natural vibrations can be detected, see pool vibration . Resonance exaggeration with a supercritical wave steepness  S  =  H / L leads to the torn clapotis, in which the water shoots vertically upwards at the antinodes. On a vertical wall, the appearance of a torn clapotis is often accompanied by pressure hammer effects .

Partial clapotis on an embankment

Partial clapotis on an embankment

By frictional washing action on the building (such as on a slope , right), in particular by the process of wave breaking , a part of the wave energy is absorbed , the height of the reflected wave is smaller than that of the incoming wave , it forms a partial Clapotis. ${\displaystyle H_{\mathrm {r} }<H_{\mathrm {i} }}$

If monochromatic waves (with and ) are assumed, in contrast to the perfect clapotis, the movement of water particles in the wave field of the partial clapotis can be approximated by elliptical orbits. These are characterized in the shaft bellies by a larger vertical main axis and in the shaft nodes by a larger horizontal main axis. ${\displaystyle H_{\mathrm {i} }}$ ${\displaystyle H_{\mathrm {r} }}$

The superimposition of the incoming wave and the reflected wave results in a partially progressing wave with the same frequency , the height of which fluctuates between a maximum value and a minimum value . and result in each case at a distance of  L / 4. In the event that the envelopes of the wave peaks and the wave troughs are known, the reflection coefficient can be determined from these extreme values: ${\displaystyle H_{\mathrm {max} }=H_{\mathrm {i} }+H_{\mathrm {r} }}$ ${\displaystyle H_{\mathrm {min} }=H_{\mathrm {i} }-H_{\mathrm {r} }}$ ${\displaystyle H_{\mathrm {max} }}$ ${\displaystyle H_{\mathrm {min} }}$

${\displaystyle C_{\mathrm {r} }={\frac {H_{\mathrm {r} }}{H_{\mathrm {i} }}}={\frac {H_{\mathrm {max} }-H_{\mathrm {min} }}{H_{\mathrm {max} }+H_{\mathrm {min} }}}}$.

See also

• Kreuzsee