Clapotis (hydrodynamique)

L'onde incidente (en rouge) réfléchie sur la paroi produit l'onde réfléchie (en bleu). La superposition des deux produit le clapotis (en noir).

En hydrodynamique, le clapotis est une forme d'ondes stationnaires non-déferlantes provoquée entre autres par la réflexion d'un train d'ondes de surface sur un rivage presque vertical tel un brise-lames, une digue ou une falaise abrupte^[1]^,^[2]^,^[3]^,^[4]. L'onde clapotique résultante ne se déplace pas horizontalement et sa structure de nœuds et de ventres est fixe^[5]^,^[6]. Ces vagues favorisent l'érosion au pied de la paroi ^[7] et peuvent gravement endommager les structures sur le rivage^[8]. Le terme a été inventé en 1877 par le mathématicien et physicien français Joseph Valentin Boussinesq^[9]^,^[10].

Dans le cas idéal de "clapotis complet" où une onde incidente purement monotone est complètement réfléchie normalement à une paroi verticale solide^[11]^,^[12], la hauteur des ondes stationnaires est le double de la hauteur des ondes incidentes à une distance d'une demi-longueur d'onde de la paroi^[13]. Dans ce cas, les orbites circulaires des particules d'eau dans l'onde d'eau profonde sont converties en un mouvement purement linéaire, avec des vitesses verticales aux ventres et des vitesses horizontales aux nœuds^[14]. Les ondes stationnaires montent et descendent alternativement de façon symétrique, à mesure que l'énergie cinétique est convertie en énergie potentielle, et vice versa^[15].

↑ « clapotis », Glossary of Meteorology, American Meteorological Society (consulté le 27 novembre 2007)
↑ « clapotis », Glossary of Scientific Terms, University of Alberta (consulté le 27 novembre 2007)
↑ Eid et Zemell, « Dynamic analysis of a suspended pump in a vertical well connected to the ocean », Canadian Journal of Civil Engineering, vol. 10, n^o 3,‎ 1983, p. 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 et Zemell, « Erratum: Dynamic analysis of a suspended pump in a vertical well connected to the ocean », Canadian Journal of Civil Engineering, vol. 11,‎ 1984, p. 137 (DOI 10.1139/l84-025)
↑ prepared by the Task Committee on Hydrology Handbook of Management Group D of the American Society of Civil Engineers., Hydrology handbook, New York, ASCE, 1996 (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. »
↑ Carter, Bill, Coastal environments: an introduction to the physical, ecological, and cultural systems of coastlines, Boston, Academic Press, 1989 (ISBN 978-0-12-161856-8), p. 50 :
« …if the wave travels in exactly the opposite direction then a standing, or clapotic, wave can develop. »
↑ Matzner, Richard A., Dictionary of geophysics, astrophysics, and astronomy, 2001 (ISBN 978-0-8493-2891-6, Bibcode 2001dgaa.book.....M, lire en ligne), p. 81 :
« clapotis…denotes a complete standing wave — a wave which does not travel horizontally but instead has distinct nodes and antinodes. »
↑ Beer, Tom, Environmental oceanography, Boca Raton, CRC Press, 1997 (ISBN 978-0-8493-8425-7), p. 44 :
« ... 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. »
↑ Fleming, Christopher, Reeve, Dominic et Chadwick, Andrew, Coastal engineering: processes, theory and design practice, London, Spon Press, 2004, 47 p. (ISBN 978-0-415-26841-7) :
« Clapotis Gaufre When the incident wave is at an angle α to the normal from a vertical boundary, then the reflected wave will be in a direction α on the opposite side of the normal. »
↑ Iooss, G., « J. Boussinesq and the standing water waves problem », Comptes Rendus Mécanique, vol. 335, n^os 9–10,‎ 2007, p. 584–589 (DOI 10.1016/j.crme.2006.11.007, Bibcode 2007CRMec.335..584I, lire en ligne, consulté le 28 novembre 2007) :
« 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’. »
↑ Iooss, Plotnikov et Toland, « Standing Waves on an Infinitely Deep Perfect Fluid Under Gravity », Archive for Rational Mechanics and Analysis, vol. 177, n^o 3,‎ 2005, p. 367–478 (DOI 10.1007/s00205-005-0381-6, Bibcode 2005ArRMA.177..367I, lire en ligne [archive du 22 février 2007], consulté le 29 novembre 2007) :
« 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. »
↑ Guidelines and Specifications for Flood Hazard Mapping Partners, Federal Emergency Management Agency, novembre 2004, « D.4.14 Glossary » :
« 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. »
↑ Mai, S., Paesler, C. et Zimmermann, C., « 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, Universität Hannover,‎ 2004 (lire en ligne [PDF], consulté le 2 décembre 2007) :
« 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.) »
↑ Jr, Ben H. Nunnally, Construction of Marine and Offshore Structures, Third Edition, Boca Raton, Florida, CRC Press, 2007 (ISBN 978-0-8493-3052-0), p. 31 :
« 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. »
↑ van Os, Magchiel, Breaker Model for Coastal Structures : Probability of Wave Impacts on Vertical Walls, Technische Universiteit Delft, Hydraulic and Offshore Engineering division, 2002, 4–33 p., « 4.2 Pressures due to Non-Breaking Waves » :
« 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. »
↑ Woodroffe, C. D., Coasts: form, process, and evolution, Cambridge, UK, Cambridge University Press, 2003 (ISBN 978-0-521-01183-9), p. 174 :
« The standing wave will alternately rise and collapse as kinetic energy is converted into potential energy and back again. »

[AMS-1] « clapotis », Glossary of Meteorology, American Meteorological Society (consulté le 27 novembre 2007)

[ualberta-2] « clapotis », Glossary of Scientific Terms, University of Alberta (consulté le 27 novembre 2007)

[Eid1983-3] Eid et Zemell, « Dynamic analysis of a suspended pump in a vertical well connected to the ocean », Canadian Journal of Civil Engineering, vol. 10, n^o 3,‎ 1983, p. 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 et Zemell, « Erratum: Dynamic analysis of a suspended pump in a vertical well connected to the ocean », Canadian Journal of Civil Engineering, vol. 11,‎ 1984, p. 137 (DOI 10.1139/l84-025)

[isbn0-7844-0138-1-4] repared by the Task Committee on Hydrology Handbook of Management Group D of the American Society of Civil Engineers., Hydrology handbook, New York, ASCE, 1996 (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. »

[isbn0-12-161856-0-5] Carter, Bill, Coastal environments: an introduction to the physical, ecological, and cultural systems of coastlines, Boston, Academic Press, 1989 (ISBN 978-0-12-161856-8), p. 50 :
« …if the wave travels in exactly the opposite direction then a standing, or clapotic, wave can develop. »

[isbn0-8493-2891-8-6] Matzner, Richard A., Dictionary of geophysics, astrophysics, and astronomy, 2001 (ISBN 978-0-8493-2891-6, Bibcode 2001dgaa.book.....M, lire en ligne), p. 81 :
« clapotis…denotes a complete standing wave — a wave which does not travel horizontally but instead has distinct nodes and antinodes. »

[isbn0-8493-8425-7-7] Beer, Tom, Environmental oceanography, Boca Raton, CRC Press, 1997 (ISBN 978-0-8493-8425-7), p. 44 :
« ... 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. »

[isbn0-415-26841-9-8] Fleming, Christopher, Reeve, Dominic et Chadwick, Andrew, Coastal engineering: processes, theory and design practice, London, Spon Press, 2004, 47 p. (ISBN 978-0-415-26841-7) :
« Clapotis Gaufre When the incident wave is at an angle α to the normal from a vertical boundary, then the reflected wave will be in a direction α on the opposite side of the normal. »

[Iooss2007-9] Iooss, G., « J. Boussinesq and the standing water waves problem », Comptes Rendus Mécanique, vol. 335, n^os 9–10,‎ 2007, p. 584–589 (DOI 10.1016/j.crme.2006.11.007, Bibcode 2007CRMec.335..584I, lire en ligne, consulté le 28 novembre 2007) :
« 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’. »

[Iooss2005-10] Iooss, Plotnikov et Toland, « Standing Waves on an Infinitely Deep Perfect Fluid Under Gravity », Archive for Rational Mechanics and Analysis, vol. 177, n^o 3,‎ 2005, p. 367–478 (DOI 10.1007/s00205-005-0381-6, Bibcode 2005ArRMA.177..367I, lire en ligne [archive du 22 février 2007], consulté le 29 novembre 2007) :
« 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. »

[FEMA-11] Guidelines and Specifications for Flood Hazard Mapping Partners, Federal Emergency Management Agency, novembre 2004, « D.4.14 Glossary » :
« 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. »

[Nach-12] Mai, S., Paesler, C. et Zimmermann, C., « 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, Universität Hannover,‎ 2004 (lire en ligne [PDF], consulté le 2 décembre 2007) :
« 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.) »

[isbn0-8493-3052-1-13] Jr, Ben H. Nunnally, Construction of Marine and Offshore Structures, Third Edition, Boca Raton, Florida, CRC Press, 2007 (ISBN 978-0-8493-3052-0), p. 31 :
« 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. »

[van_Os-14] van Os, Magchiel, Breaker Model for Coastal Structures : Probability of Wave Impacts on Vertical Walls, Technische Universiteit Delft, Hydraulic and Offshore Engineering division, 2002, 4–33 p., « 4.2 Pressures due to Non-Breaking Waves » :
« 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. »

[isbn0-521-01183-3-15] Woodroffe, C. D., Coasts: form, process, and evolution, Cambridge, UK, Cambridge University Press, 2003 (ISBN 978-0-521-01183-9), p. 174 :
« The standing wave will alternately rise and collapse as kinetic energy is converted into potential energy and back again. »

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