Incoming wave (red) reflected at the wall produces the outgoing wave (blue), both being overlaid resulting in the clapotis (black).

In hydrodynamics, the clapotis (from French: "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. Fluid dynamics is the sub-discipline of Fluid mechanics dealing with fluid flow: Fluids ( Liquids and Gases in motion French ( français,) is a Romance language spoken around the world by 118 million people as a native language and by about 180 to 260 million people A standing wave, also known as a stationary wave, is a Wave that remains in a constant position A wave is a disturbance that propagates through Space and Time, usually with transference of Energy. Breakwaters are structures constructed on coasts as part of coastal defence or to protect an anchorage from the effects of Weather and Longshore drift. A seawall is a form of hard and strong Coastal defence constructed on the inland part of a Coast to reduce the effects of strong Waves. In Geography and Geology, a cliff is a significant vertical or near vertical rock exposure [1][2][3][4] The resulting clapotic[5] wave does not travel horizontally, but has a fixed pattern of nodes and antinodes. A node is a point along a Standing wave where the wave has minimal Amplitude. [6] These waves promote erosion at the toe of the wall,[7] and can cause severe damage to shore structures. [8] The term was coined in 1877 by French mathematician and physicist Joseph Valentin Boussinesq who called these waves ‘le clapotis’ meaning ‘standing waves’. This article is about the country For a topic outline on this subject see List of basic France topics. A mathematician is a person whose primary area of study and research is the field of Mathematics. A physicist is a Scientist who studies or practices Physics. Physicists study a wide range of physical phenomena in many branches of physics spanning Joseph Valentin Boussinesq (born March 13 1842 in Saint-André-de-Sangonis ( Hérault département) died February [9][10]

In the idealized case of "full clapotis" where a purely monotonic incoming wave is completely reflected normal to a solid vertical wall,[11][12] the standing wave height is twice the height of the incoming waves at a distance of one half wavelength from the wall. [13] 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. Ocean surface waves are Surface waves that occur on the Free surface of the Ocean. [14] The standing waves alternately rise and fall in a mirror image pattern, as kinetic energy is converted to potential energy, and vice versa. The kinetic energy of an object is the extra Energy which it possesses due to its motion Potential energy can be thought of as Energy stored within a physical system [15] 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. Cecil Hobart Peabody (1855-1934 was an American mechanical engineer, born at Burlington, Vt If attention is concentrated on a certain crest, it will be seen to grow to its greatest height, die away, and be succeeded in the same place by a hollow, and the interval of time between the successive formations of crests at a given place will be the same as the time of one of the component waves. "[16]

## Related phenomena

True clapotis is very rare, because the depth of the water or the precipitousness of the shore are unlikely to completely satisfy the idealized requirements. [15] In the more realistic case of partial clapotis, where some of the incoming wave energy is dissipated at the shore,[17] the incident wave is less than 100% reflected,[11] and only a partial standing wave is formed where the water particle motions are elliptical. [18] This may also occur at sea between two different wave trains of near equal wavelength moving in opposite directions, but with unequal amplitudes. [19] In partial clapotis the wave envelope contains some vertical motion at the nodes. [19]

When a wave train strikes a wall at an oblique angle, the reflected wave train departs at the supplementary angle causing a cross-hatched wave interference pattern known as the clapotis gaufré ("waffled clapotis"). A pair of Angles is supplementary if their measurements add up to 180 degrees If the two supplementary angles are adjacent (i Hatching ( hachure in French) and cross-hatching are artistic techniques used to create tonal or shading effects by drawing (or painting or scribing closely In physics interference is the addition ( superposition) of two or more Waves that result in a new wave pattern [8] In this situation, the individual crests formed at the intersection of the incident and reflected wave train crests move parallel to the structure. This wave motion, when combined with the resultant vortices, can erode material from the seabed and transport it along the wall, undermining the structure until it fails. V erification of the O rigins of R otation in T ornadoes Ex periment or VORTEX, is a field project that seeks to understand how a [8]

Clapotic waves on the sea surface may also radiate infrasonic microbaroms into the atmosphere, and microseismic vibrations called microseisms coupled through the ocean floor to the Earth's crust. Infrasound is Sound with a Frequency too low to be heard by the human Ear. In Acoustics, microbaroms, also known as the " voice of the sea "are a class of atmospheric Infrasonic Waves generated in Seismology (from Greek grc σεισμός seismos, "earthquake" and grc -λογία -logia) is the scientific study of Earthquakes [20]

• J. Rogue waves, also known as freak waves, monster waves or extreme waves, are relatively large and spontaneous Ocean surface waves that are a threat Seiche is also a French term for a type of Cuttlefish (Sepiida In Mathematics and Physics, a soliton is a self-reinforcing solitary wave (a wave packet or pulse that maintains its shape while it travels at constant speed Boussinesq. Théorie des ondes liquides périodiques. Mémoires présentés par divers savants à l’Académie des Sciences. Paris 20, (1872) 509-616.
• J. Boussinesq. Essai sur la théorie des eaux courantes. Mémoires présentés par divers savants à l’Académie des Sciences. Paris 23 (1), (1877) 1-660.
• Hires, G, 1960. Étude du clapotis. La Houille Blanche 15:153-63.
• Leméhauté, B. ; Collins, J. I. (1961). Clapotis and Wave Reflection: With an Application to Vertical Breakwater Design. Civil Engineering Dept. , Queen's University at Kingston, Ontario.

## References

1. ^ clapotis. Glossary of Meteorology. American Meteorological Society. The American Meteorological Society ( AMS) promotes the development and dissemination of information and education on the atmospheric and related oceanic Retrieved on 2007-11-27. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 1095 - Pope Urban II declares the First Crusade at the Council of Clermont
2. ^ clapotis. Glossary of Scientific Terms. University of Alberta. The University of Alberta (U of A is a public research University located in Edmonton, Alberta, Canada. Retrieved on 2007-11-27. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 1095 - Pope Urban II declares the First Crusade at the Council of Clermont
3. ^ Eid, B. M. ; Zemell, S. H. (1983). "Dynamic analysis of a suspended pump in a vertical well connected to the ocean". Canadian Journal of Civil Engineering 10 (3): 481-491. doi:10.1139/cjce-10-3-481. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document. “The standing wave system resulting from the reflection of a progressive wave train from a vertical wall (clapotis)…”
4. ^ (1996) Hydrology handbook. New York: ASCE. ISBN 0-7844-0138-1.  “This simplification assumes that a standing wave pattern, called clapotis, forms in front of a wall where incident and reflected waves combine. ”
5. ^ Carter, Bill (1989). Coastal environments: an introduction to the physical, ecological, and cultural systems of coastlines. Boston: Academic Press, p. 50. ISBN 0-12-161856-0.  “…if the wave travels in exactly the opposite direction then a standing, or clapotic, wave can develop. ”
6. ^ Matzner, Richard A. (2001). Dictionary of geophysics, astrophysics, and astronomy. Boca Raton: CRC Press, p. 81. ISBN 0-8493-2891-8.  “clapotis…denotes a complete standing wave — a wave which does not travel horizontally but instead has distinct nodes and antinodes. ”
7. ^ Beer, Tom (1997). Environmental oceanography. Boca Raton: CRC Press, p. 44. ISBN 0-8493-8425-7.  “. . . the reflected wave energy interacted with the incoming waves to produce standing waves known as clapotis, which promote erosion at the toe of the wall. ”
8. ^ a b c Fleming, Christopher; Reeve, Dominic; Chadwick, Andrew (2004). Coastal engineering: processes, theory and design practice. London: Spon Press, p. 47. ISBN 0-415-26841-9.  “Clapotis Gaufre When the incident wave is at an angle a to the normal from a vertical boundary, then the reflected wave will be in a direction a on the opposite side of the normal. ”
9. ^ Iooss, G. (2007). "J. Boussinesq and the standing water waves problem". C. R. Mecanique 335 (9-10): 584-589. doi:10.1016/j.crme.2006.11.007. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document. “In this short Note we present the original Boussinesq's contribution to the nonlinear theory of the two dimensional standing gravity water wave problem, which he defined as ‘le clapotis’. ”
10. ^ Iooss, G. ; Plotnikov, P. I. ; Toland, J. F. (2005). "Standing Waves on an Infinitely Deep Perfect Fluid Under Gravity". Archive for Rational Mechanics and Analysis 177 (3): 367-478. “It was, we believe, Boussinesq in 1877 who was the first to deal with nonlinear standing waves. On pages 332-335 and 348-353 of[7]he refers to ‘le clapotis’, meaning standing waves, and his treatment, which includes the cases of finite and infinite depth, is a nonlinear theory taken to second order in the amplitude. ”
11. ^ a b (2004-11) "D. 4. 14 Glossary", Guidelines and Specifications for Flood Hazard Mapping Partners (pdf), Federal Emergency Management Agency. The purpose of FEMA is to coordinate the response to a Disaster which has occurred in the United States and which overwhelms the resources of local and state authorities  “CLAPOTIS The French equivalent for a type of STANDING WAVE. In American usage it is usually associated with the standing wave phenomenon caused by the reflection of a nonbreaking wave train from a structure with a face that is vertical or nearly vertical. Full clapotis is one with 100 percent reflection of the incident wave; partial clapotis is one with less than 100 percent reflection. ”
12. ^ Mai, S. ; Paesler, C. and Zimmermann, C. (2004). "Wellen und Seegang an Küsten und Küstenbauwerken mit Seegangsatlas der Deutschen Nordseeküste : 2. Seegangstransformation (Waves and Sea State on Coasts and Coastal Structures with Sea State Atlas of the German North Sea Coast : 2. Sea State Transformation)". Universität Hannover. The University of Hanover, officially the Gottfried Wilhelm Leibniz Universität Hannover or LUH, is a University located in Hanover, “Ein typischer extremer Fall von Reflektion tritt an einer starren senkrechten Wand auf. (A typical case of extreme reflection occurs on a rigid vertical wall. )”
13. ^ Jr, Ben H. Nunnally. Construction of Marine and Offshore Structures, Third Edition. Boca Raton, FL: CRC Press, p. 31. ISBN 0-8493-3052-1.  “Waves impacting against the vertical wall of a caisson or against the side of a barge are fully reflected, forming a standing wave or clapotis, almost twice the significant wave height, at a distance from the wall of one-half wavelength. ”
14. ^ van Os, Magchiel (2002-01). "4. 2 Pressures due to Non-Breaking Waves", Breaker Model for Coastal Structures : Probability of Wave Impacts on Vertical Walls. Technische Universiteit Delft, Hydraulic and Offshore Engineering division, p. The Delft University of Technology ( Technische Universiteit Delft in Dutch) in Delft, the Netherlands, is the nation's largest technical 4-33. Retrieved on 2007-11-28. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. For the town in Argentina, see 28 de Noviembre. Events  “This phenomenon is also called "Clapotis" and the circular orbits of the particle movements have degenerated into straight lines. This results in only vertical velocities at the antinodes and horizontal velocities at the nodes. ”
15. ^ a b Woodroffe, C. D. (2003). Coasts: form, process, and evolution. Cambridge, UK: Cambridge University Press, p. 174. ISBN 0-521-01183-3.  “The standing wave will alternately rise and collapse as kinetic energy is converted into potential energy and back again. ”
16. ^ Peabody, Cecil Hobart (1904). Cecil Hobart Peabody (1855-1934 was an American mechanical engineer, born at Burlington, Vt " Naval architecture. New York: J. Wiley & Sons, p. 287.  “This action is most clearly seen where a wave is reflected from a vertical sea-wall, and is known as the clapotis. ”
17. ^ Hirayama, K. (2001). "Numerical Simulation of Nonlinear Partial Standing Waves using the Boussinesq Model with New Reflection Boundary. ". Report ff the Port and Airport Research Institute 40 (4): 3-48. ISSN 1346-7832. An International Standard Serial Number ( ISSN) is a unique eight-digit number used to identify a print or electronic Periodical publication. “The waves in front of actual seawalls and harbor breakwaters, however, are rather partial standing waves such that some incident wave energy is dissipated…”
18. ^ Leo H. Holthuijsen (2007). Waves in Oceanic and Coastal Waters. Cambridge, UK: Cambridge University Press, p. 224. ISBN 0-521-86028-8.  “A partially standing wave due to the (partial) reflection of an incident wave against an obstacle. The ellipses are the trajectories of the water particles as they undergo their motion in one wave period. ”
19. ^ a b Silvester, Richard (1997). Coastal Stabilization. World Scientific Publishing Company. ISBN 981-02-3154-7.  “Should one of the opposing progressive waves be smaller in height than the other, as in partial reflection from a wall, the resulting nodes and antinodes will be located in the same position but the water-particle orbits will not be rectilinear in character. ”
20. ^ Tabulevich, V. N. ; Ponomarev, E. A. ; Sorokin, A. G. ; Drennova, N. N. (2001). "Standing Sea Waves, Microseisms, and Infrasound". Izv. Akad. Nauk, Fiz. Atmos. Okeana 37: 235-244. “In this process, the interference of differently directed waves occurs, which forms standing water waves, or the so-called clapotis. …To examine and locate these waves, it is proposed to use their inherent properties to exert (“pump”) a varying pressure on the ocean bottom, which generates microseismic vibrations, and to radiate infrasound into the atmosphere. ”

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