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Clapotis

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

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.[1][2][3][4] The resulting clapotic wave does not travel horizontally, but has a fixed pattern of nodes and antinodes.[5][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 "the lapping".[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. [14] The standing waves alternately rise and fall in a mirror image pattern, as kinetic energy is converted to potential energy, and vice versa.[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. 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]

  1. ^ "clapotis". Glossary of Meteorology. American Meteorological Society. Retrieved 2007-11-27.
  2. ^ "clapotis". Glossary of Scientific Terms. University of Alberta. Archived from the original on 2007-10-27. Retrieved 2007-11-27.
  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/l83-075. The standing wave system resulting from the reflection of a progressive wave train from a vertical wall (clapotis)…Eid, Bassem M.; Zemell, Sheldon H. (1984). "Erratum: Dynamic analysis of a suspended pump in a vertical well connected to the ocean". Canadian Journal of Civil Engineering. 11: 137. doi:10.1139/l84-025.
  4. ^ prepared by the Task Committee on Hydrology Handbook of Management Group D of the American Society of Civil Engineers. (1996). Hydrology handbook. New York: ASCE. ISBN 978-0-7844-0138-5. 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 978-0-12-161856-8. …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 (PDF). p. 81. Bibcode:2001dgaa.book.....M. ISBN 978-0-8493-2891-6. Archived from the original (PDF) on 2007-07-22. Retrieved 2007-11-28. clapotis…denotes a complete standing wave — a wave which does not travel horizontally but instead has distinct nodes and antinodes. {{cite book}}: |journal= ignored (help)
  7. ^ Beer, Tom (1997). Environmental oceanography. Boca Raton: CRC Press. p. 44. ISBN 978-0-8493-8425-7. ... 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. ^ Cite error: The named reference isbn0-415-26841-9 was invoked but never defined (see the help page).
  9. ^ Iooss, G. (2007). "J. Boussinesq and the standing water waves problem" (PDF). Comptes Rendus Mécanique. 335 (9–10): 584–589. Bibcode:2007CRMec.335..584I. doi:10.1016/j.crme.2006.11.007. Retrieved 2007-11-28. 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" (PDF). Archive for Rational Mechanics and Analysis. 177 (3): 367–478. Bibcode:2005ArRMA.177..367I. doi:10.1007/s00205-005-0381-6. S2CID 122413518. Archived from the original (PDF) on 2007-02-22. Retrieved 2007-11-29. 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. ^ "D.4.14 Glossary" (pdf). Guidelines and Specifications for Flood Hazard Mapping Partners. Federal Emergency Management Agency. November 2004. 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.; 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)" (PDF). Universität Hannover. Retrieved 2007-12-02. 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.) {{cite journal}}: Cite journal requires |journal= (help)
  13. ^ Jr, Ben H. Nunnally (2007). Construction of Marine and Offshore Structures, Third Edition. Boca Raton, Florida: CRC Press. p. 31. ISBN 978-0-8493-3052-0. 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). "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. pp. 4–33. Retrieved 2007-11-28. 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. ^ Woodroffe, C. D. (2003). Coasts: form, process, and evolution. Cambridge, UK: Cambridge University Press. p. 174. ISBN 978-0-521-01183-9. The standing wave will alternately rise and collapse as kinetic energy is converted into potential energy and back again.
  16. ^ Peabody, Cecil Hobart (1904). 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.

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