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]

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

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").[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.[8]

Clapotic waves on the sea surface also radiate infrasonic microbaroms into the atmosphere, and seismic signals called microseisms coupled through the ocean floor to the solid Earth.[20]

Clapotis has been called the bane and the pleasure of sea kayaking.[21]

See also


  1. ^ "clapotis". Glossary of Meteorology. American Meteorological Society. Retrieved 2007-11-27.
  2. ^ "clapotis". Glossary of Scientific Terms. University of Alberta. 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). Dictionary of Geophysics. p. 81. 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.
  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. ^ a b c Fleming, Christopher; Reeve, Dominic; Chadwick, Andrew (2004). Coastal engineering: processes, theory and design practice. London: Spon Press. p. 47. 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.
  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. 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. ^ a b "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 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. ^ a b 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.
  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. 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 978-0-521-86028-4. 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 978-981-02-3154-5. 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. Retrieved 2007-11-28. 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.
  21. ^ "Clapotis". 2010. Retrieved April 2, 2017.

Further reading

  • Boussinesq, J. (1872). "Théorie des ondes liquides périodiques". Mémoires Présentés Par Divers Savants à l'Académie des Sciences. 20: 509–616.
  • Boussinesq, J. (1877). "Essai sur la théorie des eaux courantes". Mémoires Présentés Par Divers Savants à l'Académie des Sciences. 23 (1): 1–660.
  • Hires, G. (1960). "Étude du clapotis". La Houille Blanche. 15 (2): 153–63. doi:10.1051/lhb/1960032.
  • 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.

External links

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Bahama Banks

The Bahama Banks are the submerged carbonate platforms that make up much of the Bahama Archipelago. The term is usually applied in referring to either the Great Bahama Bank around Andros Island, or the Little Bahama Bank of Grand Bahama Island and Great Abaco, which are the largest of the platforms, and the Cay Sal Bank north of Cuba. The islands of these banks are politically part of the Bahamas. Other banks are the three banks of the Turks and Caicos Islands, namely the Caicos Bank of the Caicos Islands, the bank of the Turks Islands, and wholly submerged Mouchoir Bank. Further southeast are the equally wholly submerged Silver Bank and Navidad Bank north of the Dominican Republic.

Butterfly effect

In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state.The term, closely associated with the work of Edward Lorenz, is derived from the metaphorical example of the details of a tornado (the exact time of formation, the exact path taken) being influenced by minor perturbations such as the flapping of the wings of a distant butterfly several weeks earlier. Lorenz discovered the effect when he observed that runs of his weather model with initial condition data that was rounded in a seemingly inconsequential manner would fail to reproduce the results of runs with the unrounded initial condition data. A very small change in initial conditions had created a significantly different outcome.The idea that small causes may have large effects in general and in weather specifically was earlier recognized by French mathematician and engineer Henri Poincaré and American mathematician and philosopher Norbert Wiener. Edward Lorenz's work placed the concept of instability of the Earth's atmosphere onto a quantitative base and linked the concept of instability to the properties of large classes of dynamic systems which are undergoing nonlinear dynamics and deterministic chaos.The butterfly effect can also be demonstrated by very simple systems.

Eddy J. Changkye

Eddy J. Changkye (2 February 1924 – 31 October 1994) was a Mauritian diplomat, politician, Member of the National Assembly of Mauritius, municipal councillor, mayor, jurist, writer and poet. He was a distinguished member of the Mauritius Labour Party and served as ambassador to Paris. He was an attorney-at-law by profession and he also won recognition for his literary works.

Index of wave articles

This is a list of Wave topics.

Knitty is an online knitting magazine based in Toronto and published quarterly since fall 2002.

The magazine was founded by Amy R. Singer and has been edited by her since its inception. Knitty presents free original knitting patterns, essays, and how-to articles written by professional designers and non-professional contributors. It hosts chat forums and promotes the online knitting community, and several patterns, such as Clapotis and Fetching, have experienced great popularity among knitters. It has also been influential in launching the careers of knitwear designers including Ysolda Teague, Stefanie Japel, Erica Jackofsky, Stephen West, Jillian Moreno, Cookie A, Amy Swenson, Jordana Paige, Cheryl Niamath and many others. The often-cited "Judy's Magic Cast On" and "Jeny's Surprisingly Stretchy Bind off" were first published in Knitty.

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List of social nudity places in Europe

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List of submarine volcanoes

A list of active and extinct submarine volcanoes and seamounts located under the world's oceans. There are estimated to be 40,000 to 55,000 seamounts in the global oceans. Almost all are not well-mapped and many may not have been identified at all. Most are unnamed and unexplored. This list is therefore confined to seamounts that are notable enough to have been named and/or explored.


In acoustics, microbaroms, also known as the "voice of the sea", are a class of atmospheric infrasonic waves generated in marine storms

by a non-linear interaction of ocean surface waves with the atmosphere. They typically have narrow-band, nearly sinusoidal waveforms with amplitudes up to a few microbars,

and wave periods near 5 seconds (0.2 hertz). Due to low atmospheric absorption at these low frequencies, microbaroms can propagate thousands of kilometers in the atmosphere, and can be readily detected by widely separated instruments on the Earth's surface.Microbaroms are a significant noise source that can potentially interfere with the detection of infrasound from nuclear explosions that is a goal of the International Monitoring System organized under the Comprehensive Nuclear-Test-Ban Treaty (which has not entered into force). It is a particular problem for detecting low-yield tests in the one-kiloton range because the frequency spectra overlap.


In seismology, a microseism is defined as a faint earth tremor caused by natural phenomena. Sometimes referred to as a "hum", it should not be confused with the anomalous acoustic phenomenon of the same name. The term is most commonly used to refer to the dominant background seismic and electromagnetic noise signals on Earth, which are caused by water waves in the oceans and lakes. Characteristics of microseism are discussed by Bhatt. Because the ocean wave oscillations are statistically homogenous over several hours, the microseism signal is a long-continuing oscillation of the ground. The most energetic seismic waves that make up the microseismic field are Rayleigh waves, but Love waves can make up a significant fraction of the wave field, and body waves are also easily detected with arrays. Because the conversion from the ocean waves to the seismic waves is very weak, the amplitude of ground motions associated to microseisms does not generally exceed 10 micrometers.

Oceanic plateau

An oceanic or submarine plateau is a large, relatively flat elevation that is higher than the surrounding relief with one or more relatively steep sides.There are 184 oceanic plateaus covering an area of 18,486,600 km2 (7,137,700 sq mi), or about 5.11% of the oceans. The South Pacific region around Australia and New Zealand contains the greatest number of oceanic plateaus (see map).

Oceanic plateaus produced by large igneous provinces are often associated with hotspots, mantle plumes, and volcanic islands — such as Iceland, Hawaii, Cape Verde, and Kerguelen. The three largest plateaus, the Caribbean, Ontong Java, and Mid-Pacific Mountains, are located on thermal swells. Other oceanic plateaus, however, are made of rifted continental crust, for example Falkland Plateau, Lord Howe Rise, and parts of Kerguelen, Seychelles, and Arctic ridges.

Plateaus formed by large igneous provinces were formed by the equivalent of continental flood basalts such as the Deccan Traps in India and the Snake River Plain in the United States.

In contrast to continental flood basalts, most igneous oceanic plateaus erupt through young and thin (6–7 km (3.7–4.3 mi)) mafic or ultra-mafic crust and are therefore uncontaminated by felsic crust and representative for their mantle sources.

These plateaus often rise 2–3 km (1.2–1.9 mi) above the surrounding ocean floor and are more buoyant than oceanic crust. They therefore tend to withstand subduction, more-so when thick and when reaching subduction zones shortly after their formations. As a consequence, they tend to "dock" to continental margins and be preserved as accreted terranes. Such terranes are often better preserved than the exposed parts of continental flood basalts and are therefore a better record of large-scale volcanic eruptions throughout Earth's history. This "docking" also means that oceanic plateaus are important contributors to the growth of continental crust. Their formations often had a dramatic impact on global climate, such as the most recent plateaus formed, the three, large, Cretaceous oceanic plateaus in the Pacific and Indian Ocean: Ontong Java, Kerguelen, and Caribbean.

Physical oceanography

Physical oceanography is the study of physical conditions and physical processes within the ocean, especially the motions and physical properties of ocean waters.

Physical oceanography is one of several sub-domains into which oceanography is divided. Others include biological, chemical and geological oceanography.

Physical oceanography may be subdivided into descriptive and dynamical physical oceanography.Descriptive physical oceanography seeks to research the ocean through observations and complex numerical models, which describe the fluid motions as precisely as possible.

Dynamical physical oceanography focuses primarily upon the processes that govern the motion of fluids with emphasis upon theoretical research and numerical models. These are part of the large field of Geophysical Fluid Dynamics (GFD) that is shared together with meteorology. GFD is a sub field of Fluid dynamics describing flows occurring on spatial and temporal scales that are greatly influenced by the Coriolis force.

Ripple effect

A ripple effect is a situation in which, like ripples expanding across the water when an object is dropped into it, an effect from an initial state can be followed outwards incrementally.

The ripple effect is often used colloquially to mean a multiplier in macroeconomics. For example, an individual's reduction in spending reduces the incomes of others and their ability to spend.In sociology, the ripple effect can be observed in how social interactions can affect situations not directly related to the initial interaction, and in charitable activities where information can be disseminated and passed from community to community to broaden its impact.The concept has been applied in computer science within the field of software metrics as a complexity measure.


A seiche ( SAYSH) is a standing wave in an enclosed or partially enclosed body of water. Seiches and seiche-related phenomena have been observed on lakes, reservoirs, swimming pools, bays, harbours and seas. The key requirement for formation of a seiche is that the body of water be at least partially bounded, allowing the formation of the standing wave.

The term was promoted by the Swiss hydrologist François-Alphonse Forel in 1890, who was the first to make scientific observations of the effect in Lake Geneva, Switzerland. The word originates in a Swiss French dialect word that means "to sway back and forth", which had apparently long been used in the region to describe oscillations in alpine lakes.

Seiches in harbours can be caused by long period or infragravity waves, which are due to subharmonic nonlinear wave interaction with the wind waves, having periods longer than the accompanying wind-generated waves.

Snowball effect

Metaphorically, a snowball effect is a process that starts from an initial state of small significance and builds upon itself, becoming larger (graver, more serious), and also perhaps potentially dangerous or disastrous (a vicious circle), though it might be beneficial instead (a virtuous circle). This is a cliché in cartoons and modern theatrics and it is also used in psychology.

The common analogy is with the rolling of a snowball down a snow-covered hillside. As it rolls the ball will pick up more snow, gaining more mass and surface area, and picking up even more snow and momentum as it rolls along.

In aerospace engineering, it is used to describe the multiplication effect in an original weight saving. A reduction in the weight of the fuselage will require less lift, meaning the wings can be smaller. Hence less thrust is required and therefore smaller engines, resulting in a greater weight saving than the original reduction. This iteration can be repeated several times, although the decrease in weight gives diminishing returns.

The startup process of a feedback electronic oscillator, when power to the circuit is switched on, is a technical application of the snowball effect. Electronic noise is amplified by the oscillator circuit and returned to its input filtered to contain primarily the selected (desired) frequency, gradually getting stronger in each cycle, until a steady-state oscillation is established, when the circuit parameters satisfy the Barkhausen stability criterion.

Standing wave

In physics, a standing wave, also known as a stationary wave, is a wave which oscillates in time but whose peak amplitude profile does not move in space. The peak amplitude of the wave oscillations at any point in space is constant with time, and the oscillations at different points throughout the wave are in phase. The locations at which the amplitude is minimum are called nodes, and the locations where the amplitude is maximum are called antinodes.

Standing waves were first noticed by Michael Faraday in 1831. Faraday observed standing waves on the surface of a liquid in a vibrating container. Franz Melde coined the term "standing wave" (German: stehende Welle or Stehwelle) around 1860 and demonstrated the phenomenon in his classic experiment with vibrating strings.This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling in opposite directions. The most common cause of standing waves is the phenomenon of resonance, in which standing waves occur inside a resonator due to interference between waves reflected back and forth at the resonator's resonant frequency.

For waves of equal amplitude traveling in opposing directions, there is on average no net propagation of energy.

Undersea mountain range

Undersea mountain ranges are mountain ranges that are mostly or entirely underwater, and specifically under the surface of an ocean. If originated from current tectonic forces, they are often referred to as a mid-ocean ridge. In contrast, if formed by past above-water volcanism, they are known as a seamount chain. The largest and best known undersea mountain range is a mid-ocean ridge, the Mid-Atlantic Ridge. It has been observed that, "similar to those on land, the undersea mountain ranges are the loci of frequent volcanic and earthquake activity".

Wave base

The wave base, in physical oceanography, is the maximum depth at which a water wave's passage causes significant water motion. For water depths deeper than the wave base, bottom sediments and the seafloor are no longer stirred by the wave motion above.

Wind wave

In fluid dynamics, wind waves, or wind-generated waves, are water surface waves that occur on the free surface of the oceans and other bodies (like lakes, rivers, canals, puddles or ponds). They result from the wind blowing over an area of fluid surface. Waves in the oceans can travel thousands of miles before reaching land. Wind waves on Earth range in size from small ripples, to waves over 100 ft (30 m) high.When directly generated and affected by local waters, a wind wave system is called a wind sea. After the wind ceases to blow, wind waves are called swells. More generally, a swell consists of wind-generated waves that are not significantly affected by the local wind at that time. They have been generated elsewhere or some time ago. Wind waves in the ocean are called ocean surface waves.

Wind waves have a certain amount of randomness: subsequent waves differ in height, duration, and shape with limited predictability. They can be described as a stochastic process, in combination with the physics governing their generation, growth, propagation, and decay—as well as governing the interdependence between flow quantities such as: the water surface movements, flow velocities and water pressure. The key statistics of wind waves (both seas and swells) in evolving sea states can be predicted with wind wave models.

Although waves are usually considered in the water seas of Earth, the hydrocarbon seas of Titan may also have wind-driven waves.

Ocean zones
Sea level


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