Clapotis

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

Contents

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]

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

Related Research Articles

<span class="mw-page-title-main">Wavelength</span> Distance over which a waves shape repeats

In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, troughs, or zero crossings. Wavelength is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns. The inverse of the wavelength is called the spatial frequency. Wavelength is commonly designated by the Greek letter lambda (λ). The term "wavelength" is also sometimes applied to modulated waves, and to the sinusoidal envelopes of modulated waves or waves formed by interference of several sinusoids.

<span class="mw-page-title-main">Wave</span> Repeated oscillation around equilibrium

In physics, mathematics, engineering, and related fields, a wave is a propagating dynamic disturbance of one or more quantities. Periodic waves oscillate repeatedly about an equilibrium (resting) value at some frequency. When the entire waveform moves in one direction, it is said to be a travelling wave; by contrast, a pair of superimposed periodic waves traveling in opposite directions makes a standing wave. In a standing wave, the amplitude of vibration has nulls at some positions where the wave amplitude appears smaller or even zero.

<span class="mw-page-title-main">Standing wave</span> Wave that remains in a constant position

In physics, a standing wave, also known as a stationary wave, is a wave that 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 respect to time, and the oscillations at different points throughout the wave are in phase. The locations at which the absolute value of the amplitude is minimum are called nodes, and the locations where the absolute value of the amplitude is maximum are called antinodes.

<span class="mw-page-title-main">Amphidromic point</span> Location at which there is little or no tide

An amphidromic point, also called a tidal node, is a geographical location where there is little or no difference in sea height between high tide and low tide; it has zero tidal amplitude for one harmonic constituent of the tide. The tidal range for that harmonic constituent increases with distance from this point, though not uniformly. As such, the concept of amphidromic points is crucial to understanding tidal behaviour. The term derives from the Greek words amphi ("around") and dromos ("running"), referring to the rotary tides which circulate around amphidromic points. It was first discovered by William Whewell, who extrapolated the cotidal lines from the coast of the North Sea and found that the lines must meet at some point.

<span class="mw-page-title-main">Transparency and translucency</span> Property of an object or substance to transmit light with minimal scattering

In the field of optics, transparency is the physical property of allowing light to pass through the material without appreciable scattering of light. On a macroscopic scale, the photons can be said to follow Snell's law. Translucency allows light to pass through but does not necessarily follow Snell's law; the photons can be scattered at either of the two interfaces, or internally, where there is a change in the index of refraction. In other words, a translucent material is made up of components with different indices of refraction. A transparent material is made up of components with a uniform index of refraction. Transparent materials appear clear, with the overall appearance of one color, or any combination leading up to a brilliant spectrum of every color. The opposite property of translucency is opacity. Other categories of visual appearance, related to the perception of regular or diffuse reflection and transmission of light, have been organized under the concept of cesia in an order system with three variables, including transparency, translucency and opacity among the involved aspects.

<span class="mw-page-title-main">Reflection (physics)</span> "Bouncing back" of waves at an interface

Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. The law of reflection says that for specular reflection the angle at which the wave is incident on the surface equals the angle at which it is reflected.

<span class="mw-page-title-main">Wind wave</span> Surface waves generated by wind on open water

In fluid dynamics, a wind wave, or wind-generated water wave, is a surface wave that occurs on the free surface of bodies of water as a result of the wind blowing over the water's surface. The contact distance in the direction of the wind is known as the fetch. Waves in the oceans can travel thousands of kilometers before reaching land. Wind waves on Earth range in size from small ripples to waves over 30 m (100 ft) high, being limited by wind speed, duration, fetch, and water depth.

<span class="mw-page-title-main">Wave power</span> Transport of energy by wind waves, and the capture of that energy to do useful work

Wave power is the capture of energy of wind waves to do useful work – for example, electricity generation, water desalination, or pumping water. A machine that exploits wave power is a wave energy converter (WEC).

<span class="mw-page-title-main">Internal wave</span> Type of gravity waves that oscillate within a fluid medium

Internal waves are gravity waves that oscillate within a fluid medium, rather than on its surface. To exist, the fluid must be stratified: the density must change with depth/height due to changes, for example, in temperature and/or salinity. If the density changes over a small vertical distance, the waves propagate horizontally like surface waves, but do so at slower speeds as determined by the density difference of the fluid below and above the interface. If the density changes continuously, the waves can propagate vertically as well as horizontally through the fluid.

<span class="mw-page-title-main">Node (physics)</span> Point with minimum wave amplitude

A node is a point along a standing wave where the wave has minimum amplitude. For instance, in a vibrating guitar string, the ends of the string are nodes. By changing the position of the end node through frets, the guitarist changes the effective length of the vibrating string and thereby the note played. The opposite of a node is an anti-node, a point where the amplitude of the standing wave is at maximum. These occur midway between the nodes.

<span class="mw-page-title-main">Breakwater (structure)</span> Coastal defense structure

A breakwater is a permanent structure constructed at a coastal area to protect against tides, currents, waves, and storm surges. Breakwaters have been built since antiquity to protect anchorages, helping isolate vessels from marine hazards such as wind-driven waves. A breakwater, also known in some contexts as a jetty or a mole, may be connected to land or freestanding, and may contain a walkway or road for vehicle access.

Acoustic waves are a type of energy propagation that travels through a medium, such as air, water, or solid objects, by means of adiabatic compression and expansion. Key quantities describing these waves include acoustic pressure, particle velocity, particle displacement, and acoustic intensity. The speed of acoustic waves depends on the medium's properties, such as density and elasticity, with sound traveling at approximately 343 meters per second in air, 1480 meters per second in water, and varying speeds in solids. Examples of acoustic waves include audible sound from speakers, seismic waves causing ground vibrations, and ultrasound used for medical imaging. Understanding acoustic waves is crucial in fields like acoustics, physics, engineering, and medicine, with applications in sound design, noise reduction, and diagnostic imaging.

<span class="mw-page-title-main">Breaking wave</span> Wave that becomes unstable as a consequence of excessive steepness

In fluid dynamics and nautical terminology, a breaking wave or breaker is a wave with enough energy to "break" at its peak, reaching a critical level at which linear energy transforms into wave turbulence energy with a distinct forward curve. At this point, simple physical models that describe wave dynamics often become invalid, particularly those that assume linear behaviour.

<span class="mw-page-title-main">Shallow water equations</span> Set of partial differential equations that describe the flow below a pressure surface in a fluid

The shallow-water equations (SWE) are a set of hyperbolic partial differential equations that describe the flow below a pressure surface in a fluid. The shallow-water equations in unidirectional form are also called (de) Saint-Venant equations, after Adhémar Jean Claude Barré de Saint-Venant.

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. 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.

<span class="mw-page-title-main">Boussinesq approximation (water waves)</span> Approximation valid for weakly non-linear and fairly long waves

In fluid dynamics, the Boussinesq approximation for water waves is an approximation valid for weakly non-linear and fairly long waves. The approximation is named after Joseph Boussinesq, who first derived them in response to the observation by John Scott Russell of the wave of translation. The 1872 paper of Boussinesq introduces the equations now known as the Boussinesq equations.

<span class="mw-page-title-main">Stokes wave</span> Nonlinear and periodic surface wave on an inviscid fluid layer of constant mean depth

In fluid dynamics, a Stokes wave is a nonlinear and periodic surface wave on an inviscid fluid layer of constant mean depth. This type of modelling has its origins in the mid 19th century when Sir George Stokes – using a perturbation series approach, now known as the Stokes expansion – obtained approximate solutions for nonlinear wave motion.

In fluid dynamics, Airy wave theory gives a linearised description of the propagation of gravity waves on the surface of a homogeneous fluid layer. The theory assumes that the fluid layer has a uniform mean depth, and that the fluid flow is inviscid, incompressible and irrotational. This theory was first published, in correct form, by George Biddell Airy in the 19th century.

Acoustic tweezers are a set of tools that use sound waves to manipulate the position and movement of very small objects. Strictly speaking, only a single-beam based configuration can be called acoustical tweezers. However, the broad concept of acoustical tweezers involves two configurations of beams: single beam and standing waves. The technology works by controlling the position of acoustic pressure nodes that draw objects to specific locations of a standing acoustic field. The target object must be considerably smaller than the wavelength of sound used, and the technology is typically used to manipulate microscopic particles.

Tides in marginal seas are tides affected by their location in semi-enclosed areas along the margins of continents and differ from tides in the open oceans. Tides are water level variations caused by the gravitational interaction between the Moon, the Sun and the Earth. The resulting tidal force is a secondary effect of gravity: it is the difference between the actual gravitational force and the centrifugal force. While the centrifugal force is constant across the Earth, the gravitational force is dependent on the distance between the two bodies and is therefore not constant across the Earth. The tidal force is thus the difference between these two forces on each location on the Earth.

References

  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.
  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. 1 2 3 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. 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. 1 2 "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). Vorlesungsergänzungen des Lehrstuhls für Wasserbau und Küsteningenieurwesen. 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.)
  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. 1 2 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. 1 2 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.[ page needed ]
  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. Archived from the original on 2016-03-03. 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. Archived from the original on April 3, 2017. Retrieved April 2, 2017.

Further reading

This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.