{{위키데이터 속성 추적}}
[[파일:Clapotis at wall.gif|섬네일|300px|right|벽에 반사되어 나오는 파동(빨강)과 벽으로 오는 파동(파랑)이 합쳐져서 만들어지는 중복파인 검정 파동.]]

[[유체동역학]]에서 '''중복파'''(Clapotis)란 [[방파제]], [[방조제]], [[절벽]]과 같이 해안선이 수직인 곳에서 진행하는 표면파와 해안선에서 반사된 반사파가 서로 만나 합쳐저서 발생하는 [[정상파]]를 의미한다.<ref name=AMS>{{웹 인용|url=http://glossary.ametsoc.org/wiki/Clapotis |website=Glossary of Meteorology | publisher = [[American Meteorological Society]]| title = clapotis |accessdate=2007-11-27 }}</ref><ref name=ualberta>{{웹 인용 |url=http://www.math.ualberta.ca/~bruce/glossary.html |title=clapotis |accessdate=2007-11-27 |website=Glossary of Scientific Terms |publisher=[[University of Alberta]] |archive-date=2007-10-27 |archive-url=https://web.archive.org/web/20071027040524/http://www.math.ualberta.ca/~bruce/glossary.html |url-status=dead }}</ref><ref name=Eid1983>{{저널 인용| last1 = Eid | first1 = B. M. | last2 = Zemell | first2 = S. H. | year = 1983 | title = Dynamic analysis of a suspended pump in a vertical well connected to the ocean | journal = Canadian Journal of Civil Engineering | volume = 10 | issue = 3 | pages = 481–491 | doi = 10.1139/l83-075 | quote = The standing wave system resulting from the reflection of a progressive wave train from a vertical wall (clapotis)…}}{{저널 인용|doi=10.1139/l84-025|title=Erratum: Dynamic analysis of a suspended pump in a vertical well connected to the ocean|year=1984|last1=Eid|first1=Bassem M.|last2=Zemell|first2=Sheldon H.|journal=Canadian Journal of Civil Engineering|volume=11|pages=137}}</ref><ref name="isbn0-7844-0138-1">{{서적 인용|author= prepared by the Task Committee on Hydrology Handbook of Management Group D of the American Society of Civil Engineers.|title=Hydrology handbook |publisher=ASCE |location=New York |year=1996 |pages= |isbn=978-0-7844-0138-5 |quote = This simplification assumes that a standing wave pattern, called clapotis, forms in front of a wall where incident and reflected waves combine. }}</ref> 이렇게 만들어진 중복파는 수평이동이 없으나 고정된 [[마디 (물리)|마디]]와 반마디가 존재한다.<ref name="isbn0-12-161856-0">{{서적 인용|author=Carter, Bill |title=Coastal environments: an introduction to the physical, ecological, and cultural systems of coastlines |publisher=Academic Press |location=Boston |year=1989 |page= 50 |isbn=978-0-12-161856-8 |quote= …if the wave travels in exactly the opposite direction then a standing, or clapotic, wave can develop.}}</ref><ref name="isbn0-8493-2891-8">{{서적 인용|author=Matzner, Richard A. |title=Dictionary of geophysics, astrophysics, and astronomy |journal=Dictionary of Geophysics |year=2001 |page=81 |isbn=978-0-8493-2891-6 |url=http://astropole.ru/astronomy/library/common/Dictionary_of_Geophysics.pdf |quote=clapotis…denotes a complete standing wave&nbsp;— a wave which does not travel horizontally but instead has distinct nodes and antinodes. |bibcode=2001dgaa.book.....M |access-date=2007-11-28 |archive-url=https://web.archive.org/web/20070722014123/http://astropole.ru/astronomy/library/common/Dictionary_of_Geophysics.pdf |archive-date=2007-07-22 |url-status=dead }}</ref> 이런 정상파는 해안선 끄트머리의 벽을 침식시키며<ref name="isbn0-8493-8425-7">{{서적 인용|author=Beer, Tom |title=Environmental oceanography |publisher=CRC Press |location=Boca Raton |year=1997 |page= 44 |isbn=978-0-8493-8425-7 | quote = ... 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.}}</ref> 해안 구조물에 심각한 손상을 줄 수 있다.<ref name="isbn0-415-26841-9"/> 중복파라는 용어는 1877년 프랑스의 [[수학자]]이자 [[물리학자]]인 [[조제프 발랑탱 부시에스크]]가 처음으로 마치 파도가 '래핑'하는 듯이 보인다고 하여 프랑스어인 'le clapotis'로 이름붙였다.<ref name=Iooss2007>{{저널 인용| author = Iooss, G. | year = 2007 | title = J. Boussinesq and the standing water waves problem | journal = Comptes Rendus Mécanique | volume = 335 | issue = 9–10 | pages = 584–589 | url = http://math.unice.fr/~iooss/publis1/Iooss-Boussinesq.pdf | accessdate = 2007-11-28 | doi=10.1016/j.crme.2006.11.007 | quote = 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’.
|bibcode = 2007CRMec.335..584I }}</ref><ref name=Iooss2005>{{저널 인용|last1       = Iooss |first1      = G. |last2       = Plotnikov |first2      = P. I. |last3       = Toland |first3      = J. F. |year        = 2005 |title       = Standing Waves on an Infinitely Deep Perfect Fluid Under Gravity |journal     = Archive for Rational Mechanics and Analysis |volume      = 177 |issue       = 3 |pages       = 367–478 |url         = http://www.maths.bath.ac.uk/~jft/Papers/working6.pdf |accessdate  = 2007-11-29 |quote       = 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. |doi         = 10.1007/s00205-005-0381-6 |bibcode     = 2005ArRMA.177..367I |url-status     = dead |archiveurl  = https://web.archive.org/web/20070222022228/http://www.maths.bath.ac.uk/~jft/Papers/working6.pdf |archivedate = 2007-02-22}}</ref>

들어오는 순수 [[단조함수|단조]] 파동이 단단한 수직벽에 완전히 정상으로 반사되어 나가는 이상적인 중복파에서는<ref name=FEMA>{{서적 인용| title = Guidelines and Specifications for Flood Hazard Mapping Partners | chapter = D.4.14 Glossary | publisher = [[Federal Emergency Management Agency]] | date = November 2004 | chapter-url = http://www.fema.gov/library/file?type=publishedFile&file=frm_cfd414.pdf&fileid=4de56330-91f7-11db-b057-000bdba87d5b | chapter-format = pdf | accessdate = | quote =  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.}}</ref><ref name=Nach>{{저널 인용|author1=Mai, S. |author2=Paesler, C. |author3=Zimmermann, C. | year = 2004 | title = 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) | url = http://www.dr-smai.de/Literatur/Geb-4/80_fi_heft_90a_mai_cpa_zi.pdf#page=51 | accessdate = 2007-12-02 | publisher = [[Leibniz University Hannover|Universität Hannover]] | format = PDF | quote = 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.)}}</ref> 정상파의 [[파고]]는 벽에서 반파장 거리에서 들어오는 파동의 파고의 2배이다.<ref name="isbn0-8493-3052-1">{{서적 인용|author=Jr, Ben H. Nunnally |title=Construction of Marine and Offshore Structures, Third Edition |publisher=CRC Press |location=Boca Raton, Florida |year= 2007|page= 31|isbn=978-0-8493-3052-0 |quote = 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.}}</ref> 이 경우 [[파도|심해파]]의 물 입자의 원운동이 반마디에서 수직속도만, 마디에서 수평속도만 남으며 직선형으로 바뀌게 된다.<ref name="van Os">{{서적 인용 | author = van Os, Magchiel | year = 2002 | title = Breaker Model for Coastal Structures : Probability of Wave Impacts on Vertical Walls | chapter-url = http://citeseer.ist.psu.edu/489083.html | chapter = 4.2 Pressures due to Non-Breaking Waves | pages = 4–33 | accessdate = 2007-11-28 | publisher = [[Technische Universiteit Delft]], Hydraulic and Offshore Engineering division | quote = 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. | archive-date = 2007-12-05 | archive-url = https://web.archive.org/web/20071205134055/http://citeseer.ist.psu.edu/489083.html | url-status =  }}</ref> 정상파의 경우 [[운동 에너지]]가 [[위치 에너지]]로, 다시 위치 에너지가 운동 에너지로 바뀌며 서로 번갈아가며 거울처럼 위로 올라갔다 내려간다.<ref name="isbn0-521-01183-3">{{서적 인용|author=Woodroffe, C. D. |title=Coasts: form, process, and evolution |publisher=Cambridge University Press |location=Cambridge, UK |year=2003 |page= 174|isbn=978-0-521-01183-9 |quote = The standing wave will alternately rise and collapse as kinetic energy is converted into potential energy and back again.}}</ref>

== 관련 현상 ==
실제 세계에선 물의 깊이나 해안의 침전물 때문에 이상적인 상황과는 달라 순수한 중복파는 거의 보기 힘들다.<ref name="isbn0-521-01183-3"/> 보다 현실적으로 들어오는 에너지 일부가 해안선에서 흡수되거나 흩어져<ref name=Hirayama2001>{{저널 인용| author = Hirayama, K. | year = 2001 | title = Numerical Simulation of Nonlinear Partial Standing Waves using the Boussinesq Model with New Reflection Boundary | journal = Report Ff the Port and Airport Research Institute | volume = 40 | issue = 4 | pages = 3–48 | quote = The waves in front of actual seawalls and harbor breakwaters, however, are rather partial standing waves such that some incident wave energy is dissipated…}}</ref> 입사파의 100%가 온전히 반사되지 못하는<ref name=FEMA/> 부분적인 중복파의 경우 물입자가 타원형을 그리며 움직이는 유사 정상파가 형성된다.<ref name="isbn0-521-86028-8">{{서적 인용|author=Leo H. Holthuijsen |title=Waves in Oceanic and Coastal Waters |publisher=Cambridge University Press |location=Cambridge, UK |year= 2007|page= 224|isbn=978-0-521-86028-4 | quote = 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.}}</ref> 또한 바다에서 서로 반대 방향으로 움직이는 거의 같은 파장을 가진 파동이 서로 만나면서 유사중복파가 만들어질 수 있으나 진폭이 일정하지 않다.<ref name="isbn981-02-3154-7">{{서적 인용|author=Silvester, Richard |title=Coastal Stabilization |publisher=World Scientific Publishing Company |year= 1997 |pages= |isbn=978-981-02-3154-5 |quote = 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.}}</ref> 유사중복파의 경우 마디 자체가 약간 수직운동을 하는 경우도 있다.<ref name="isbn981-02-3154-7"/>

입사파가 벽에 수직으로 오지 않고 비스듬한 각도로 부딪힐 경우, 반사파는 입사파의 [[보각]]으로 반사되며 이 경우 격자형 중복파(clapotis gaufré)라는 [[해칭|십자 해칭]] 모양 [[간섭 (파동 전파)|간섭]] 패턴이 만들어진다.<ref name="isbn0-415-26841-9">{{서적 인용|author1=Fleming, Christopher |author2=Reeve, Dominic |author3=Chadwick, Andrew |title=Coastal engineering: processes, theory and design practice |publisher=Spon Press |location=London |year=2004 |pages= 47 |isbn=978-0-415-26841-7 | quote = 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.}}</ref> 이 경우 파동의 각각의 최고점은 입사파와 반사파의 교차점에서 만들어지며 구조물과 평행하게 움직인다.<ref name="isbn0-415-26841-9"/>

== 같이 보기 ==
* [[거대파]] (Rouge wave)
* [[세이시]]

== 각주 ==
{{각주}}

== 참고 문헌 ==
* {{저널 인용|last=Boussinesq |first=J. |year=1872 |title=Théorie des ondes liquides périodiques |journal=Mémoires Présentés Par Divers Savants à l'Académie des Sciences |volume=20 |pages=509–616}}
* {{저널 인용|last=Boussinesq |first=J. |year=1877 |title=Essai sur la théorie des eaux courantes |journal=Mémoires Présentés Par Divers Savants à l'Académie des Sciences |volume=23 | issue=1 |pages=1–660}}
* {{저널 인용|last=Hires |first= G. |year=1960|title=Étude du clapotis|journal= La Houille Blanche |volume=15 |issue= 2 |pages=153–63|doi= 10.1051/lhb/1960032 }}
* {{서적 인용|last1=Leméhauté |first1=B. |last2=Collins |first2=J. I. |year=1961 |title=Clapotis and Wave Reflection: With an Application to Vertical Breakwater Design |publisher=Civil Engineering Dept., Queen's University at Kingston, Ontario |isbn=}}

== 외부 링크 ==
* {{웹 인용|author=Willi Water |url=https://www.youtube.com/watch?v=E3vzAB1vY_Q |title=Clapotis Wave Action |type=Video |via=[[YouTube]] |date=March 11, 2010}}

[[분류:파동역학]]
[[분류:해안공학]]
[[분류:해파]]