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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]

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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

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References

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Further reading

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Clapotis

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Clapotis is a non-breaking pattern in hydrodynamics, formed by the superposition of incoming waves with their reflections off a vertical barrier such as a , breakwater, , or shoreline, resulting in stationary oscillations where crests and troughs alternate in fixed positions. The term originates from French, referring to the "lapping" sound of against structures. This phenomenon arises when two waves of identical amplitude, frequency, and wavelength propagate in opposite directions—one as the incident wave and the other as its total reflection—leading to interference that doubles the amplitude at antinodes (points of maximum displacement) while creating nodes (points of zero displacement). Unlike traveling waves, clapotis waves do not propagate but vibrate in place, with surface elevation varying as a cosine function of position and time. In natural settings, such as coastal areas, the pattern often appears irregular due to varying wave trains and shoreline geometry, producing high peaks adjacent to calm zones that can pose hazards to vessels and kayakers. Clapotis has been studied since the , notably by French Boussinesq, who coined the term in 1877 and developed nonlinear theories for these standing waves in his work on water wave problems. In contexts, understanding clapotis is crucial for designing harbors and coastal structures to mitigate , wave run-up, and overtopping, where the clapotis height influences run-up measurements for both regular and irregular waves. Variants like clapotis gaufré (waffled standing waves) occur under strong winds, forming diamond-shaped patterns that further complicate sediment dynamics near breakwaters.

Introduction

Definition

Clapotis is a term derived from French, literally meaning "lapping of ," and was coined in by the French and Joseph Valentin Boussinesq to describe a specific type of wave motion. In hydrodynamics, it refers to a non-breaking pattern formed by the reflection of waves off a vertical barrier, such as a , breakwater, , or shoreline. This phenomenon arises from the interaction of surface waves—oscillations at the air-water interface where provides the primary restoring force—with a vertical boundary, such as a or breakwater. When these incident waves reflect off the rigid structure, they superpose with the oncoming waves, provided the waves have equal , , and but travel in opposite directions. The reflection can be partial or total, resulting in a stationary wave profile that does not propagate horizontally. Visually, the clapotis manifests as a fixed pattern along the surface, characterized by alternating nodes—points of zero vertical displacement where the remains still—and antinodes—points of maximum vertical where the surface oscillates most vigorously. This creates a effect against the boundary, distinct from progressive traveling waves, with the wave at antinodes typically twice that of the individual incident waves under ideal conditions.

Historical Background

Building on his own extensive hydraulic investigations, French mathematician and physicist Joseph Valentin Boussinesq introduced the term "le clapotis" in his seminal 1877 treatise Essai sur la théorie des eaux courantes, where he presented the first nonlinear treatment of standing gravity waves in two dimensions. Boussinesq's work described clapotis as the lapping pattern formed by interfering waves, emphasizing its relevance to hydraulic flows in channels and basins. The term originated within French hydrodynamics literature, reflecting Boussinesq's focus on practical problems such as wave reflection in confined waters. Initial theoretical developments, including Boussinesq's, were constrained to idealized mathematical models assuming perfect reflection and uniform conditions, with limited empirical validation. Comprehensive field measurements of clapotis patterns in natural settings only became feasible in the mid-20th century, enabling refinements to account for environmental variables like irregular and damping effects.

Physical Principles

Wave Reflection and Interference

Clapotis arises from the reflection of incoming progressive water waves off rigid vertical boundaries, such as seawalls or cliffs, where the boundary condition enforces zero normal horizontal at the wall. In this process, the reflected wave maintains the same as the incident wave and propagates in the opposite direction, with no phase shift in the surface elevation, ensuring that the elevation at the wall varies temporally while satisfying the velocity constraint. This reflection occurs efficiently when the boundary is impermeable and vertical, minimizing energy loss during the interaction. The interference mechanism involves the superposition of the incident and reflected waves, which travel in opposite directions and combine to form stationary wave patterns. When the of the incoming waves aligns with the dimensions of the basin or enclosure—such as lengths that are integer multiples of half the —resonant conditions enhance the interference, leading to pronounced stationary configurations without net . This superposition redistributes the wave energy spatially, creating regions of amplified and diminished motion that characterize the clapotis phenomenon. In enclosed or semi-enclosed water bodies like harbors, wave is conserved during reflection and interference under ideal conditions, with the total of the system remaining constant as it oscillates between kinetic and potential forms. The absence of significant allows the reflected to fully contribute to the interfering pattern, potentially doubling the at certain locations compared to the incident wave alone. Clapotis is often analyzed using the shallow water approximation when the water depth is much less than the (typically kh ≪ 1, with k the wave number and h the depth), which applies to long-wave dynamics in coastal settings and supports effective reflection and superposition. Additionally, non-dissipative conditions are essential, assuming an inviscid fluid with negligible or breaking, to prevent energy loss that would otherwise dampen the standing patterns. These prerequisites are commonly met in protected coastal environments during moderate wave events.

Characteristics of Standing Waves

In clapotis, the standing wave pattern exhibits a fixed structure of nodes and antinodes along the direction of wave propagation. Nodes are fixed points of zero vertical displacement, where water particles experience primarily horizontal motion, while antinodes are locations of maximum vertical displacement, characterized by minimal horizontal motion. These features alternate at intervals of one-quarter , resulting in nodes spaced at half-wavelength intervals. The motion of water particles in clapotis varies depending on whether the pattern is full or partial. In the ideal case of full clapotis, with complete reflection and no energy loss, particle trajectories are linear and vertical at antinodes, oscillating according to a cosine function, while horizontal oscillations dominate at nodes. In partial clapotis, where some incident wave energy dissipates—often due to or incomplete reflection—particle paths become elliptical, reflecting the superposition of unequal forward and backward wave components. Amplitude in clapotis can reach up to twice that of the incident waves at antinodes, due to the constructive interference of the reflected and incoming components, though this maximum is realized only under perfect reflection conditions. Clapotis patterns persist as long as the incident waves continue to force the system, maintaining a stationary , but their stability is highly sensitive to boundary , such as alignment or basin shape, which can disrupt the interference balance and lead to decay through frictional losses.

Mathematical Formulation

Basic Equations

The mathematical formulation of clapotis begins with linear wave theory, which assumes small-amplitude waves where the surface elevation η(x,t) satisfies the linearized under gravity. In this framework, clapotis arises as a pattern formed by the interference of oppositely propagating waves in a basin with a reflective boundary, such as a vertical wall. The governs the formation of clapotis: an incident wave η_i(x,t) = A cos(kx - ωt) travels toward the wall, where A is the , k is the (k = 2π/λ, with λ the ), and ω is the (ω = 2π/T, with T the period). Upon total reflection at the wall, it produces a reflected wave η_r(x,t) = A cos(kx + ωt) of equal but opposite direction. The total surface elevation is then η(x,t) = η_i + η_r = 2A cos(kx) cos(ωt), representing a where the spatial and temporal dependencies separate, resulting in fixed nodes and antinodes along x. This form satisfies the boundary condition at the reflective wall located at x = 0, where the normal (horizontal) must vanish to ensure no flow through the impermeable boundary. In linear theory, the horizontal u ≈ (∂φ/∂x)|_{z=0}, with φ the , and the form ensures u = 0 at x = 0; substituting the expression yields ∂η/∂x = -2A k sin(kx) cos(ωt), which equals zero at x = 0 for all t, consistent with the condition. Under shallow-water assumptions (where kh ≪ 1, with h the water depth), the phase speed simplifies to c = √(gh), independent of , where g is . The connecting ω and , derived from the linearized Euler equations and free-surface boundary conditions, is ω² = g tanh(kh); in shallow water, tanh(kh) ≈ kh, yielding ω = √(gh) and thus c = ω/ = √(gh). These relations hold for non-dispersive in shallow basins typical of clapotis scenarios.

Modes and Patterns

Modal analysis of clapotis in enclosed basins, such as harbors, involves solving the for the spatial distribution of the surface elevation, ∇²η + k²η = 0, where η is the elevation, k is the related to the frequency by the ω² = gk tanh(kh), g is , and h is the water depth. This equation describes the eigenmodes of the basin, with boundary conditions of zero normal along the walls. For a simple rectangular basin of L and uniform depth h, the natural frequencies of these seiche-like modes are f_n = (n c)/(2L), where c = √(gh) is the shallow-water celerity and n = 1, 2, 3, ... represents the mode number, corresponding to half-wavelength fits along the basin . In two-dimensional basins, oblique wave reflections from multiple boundaries produce complex spatial patterns known as clapotis gaufré, or "waffled clapotis," forming a grid-like interference of standing waves with diamond-shaped crests and troughs. These patterns emerge from the superposition of incident and reflected waves at non-perpendicular angles, creating localized high-amplitude regions where wave crests intersect, as governed by the same Helmholtz framework but with angular dependencies in the mode shapes. Nonlinear effects become prominent for steeper waves in clapotis, where Boussinesq's higher-order theory accounts for dispersive and nonlinear corrections beyond linear superposition. The surface elevation includes higher-order terms from perturbation expansions of the Euler equations, such as second- and third-order harmonics that capture wave steepening, energy transfer, and in steep standing waves. conditions in clapotis arise when the of driving incident waves aligns with a natural basin mode f_n, resulting in amplified oscillations due to constructive interference and minimal energy radiation. This amplification can exceed factors of 10-20 in enclosed geometries, enhancing wave heights and pressures on structures, particularly in the fundamental mode.

Types of Clapotis

Full Clapotis

Full clapotis represents the theoretical idealization of the clapotis phenomenon, occurring under conditions of perfect reflection where a monochromatic incident wave strikes a vertical, non-porous wall normally, resulting in total reflection without any energy dissipation. This setup assumes an impermeable boundary that enforces zero normal velocity at the wall, leading to constructive interference between the incident and reflected waves. Such ideal conditions are characteristic of lossless fluid dynamics models in coastal engineering, where viscosity and other dissipative effects are neglected. The profile of the surface elevation in full clapotis follows the standing wave pattern η(x,t)=2Acos⁡(kx)cos⁡(ωt)\eta(x, t) = 2A \cos(kx) \cos(\omega t), where AA is the incident wave , k=2π/λk = 2\pi / \lambda is the wave number, ω\omega is the , xx is the distance from (with x=0x=0 at ), and tt is time. Consequently, the elevation is maximum (2A2A) at antinodes located at (x=0x=0) and every half-wavelength (x=nλ/2x = n\lambda/2, n=1,2,…n=1,2,\ldots), while nodes with zero occur at quarter-wavelength intervals from (x=(2n+1)λ/4x = (2n+1)\lambda/4). This profile arises from the in-phase superposition of the incident and reflected waves at the boundary, doubling the elevation at compared to the incident wave alone. In full clapotis, the wave fronts remain planar and parallel to the reflecting boundary throughout the interference region, confining the motion to a one-dimensional along the direction perpendicular to the . This uniformity stems from the assumption of plane progressive waves incident normally on an infinitely long, straight , preventing transverse variations or oblique reflections. As with general , the pattern features fixed positions of displacement, but here it is strictly longitudinal due to the geometric constraints. The stability of full clapotis is inherent to its lossless nature; with a continuous, steady supply of incident waves of constant and frequency, the pattern persists indefinitely without or . This enduring configuration highlights the conservative energy transfer in the ideal reflection process, where all wave energy is conserved through perfect interference.

Partial Clapotis and Variations

Partial clapotis arises when incoming waves are only partially reflected, leading to a pattern with reduced amplitudes compared to the ideal full clapotis, where complete reflection produces maximum interference. This partial reflection occurs due to energy dissipation mechanisms such as along the basin boundaries, viscous effects in the , or absorption by porous structures like perforated breakwaters, which scatter and dampen the reflected wave energy. In such cases, the superposition of incident and reflected waves forms a partial characterized by a phase jump near the reflection point, typically around 180° for smooth slopes but less for structured surfaces, resulting in wave heights that are significantly lower—often 60% or less of the incident height. Additionally, the particle trajectories deviate from the linear vertical paths of ideal clapotis; instead, they follow elliptical orbits due to the residual progressive wave component and viscous damping, which introduces horizontal drift and rotational motion within the orbits. A notable variation is clapotis gaufré, or "waffled clapotis," which emerges from two-dimensional interference when waves reflect off angled or multiple walls, producing a cross-hatched of diamond-shaped crests and troughs. This forms as the reflected wave departs at the supplementary angle to the incident wave, creating intersecting wave trains that generate localized standing waves in a grid-like array, often observed in harbors with non- boundaries. The resulting motion consists of island-like crests that propagate parallel to the walls, with the complexity increasing under oblique wave attack, which is common in coastal settings and leads to transverse interference lines to the primary nodal . Dissipation further modifies partial clapotis by shortening the effective through mechanisms like and wave breaking, which convert wave energy into and , attenuating higher-frequency components more rapidly. , prominent in shallow basins, acts within a thin near the , reducing wave celerity and thus compressing the interference pattern, while breaking dissipates energy at crests, limiting amplitude growth and altering the overall . These factors collectively result in non-uniform patterns that are less stable and more irregular than ideal cases, emphasizing the role of real-world and in clapotis formation.

Real-World Examples

In Harbors and Coastal Structures

In man-made harbors, clapotis forms when incoming waves reflect off vertical walls or breakwaters, creating patterns that amplify wave heights within confined basins. A prominent example occurs in , , where reflections in the Ocean Terminals basins generate longitudinal and transverse clapotis during periods of moderate swell from the Atlantic. These patterns are particularly evident when wave periods of 4–8 seconds enter the harbor, leading to that disrupts normal operations. Engineering observations from the highlight the amplification effects of clapotis in such environments. In , measurements recorded during wave events showed vertical bow movements of moored vessels reaching 5–9 feet (approximately 1.5–2.75 meters) due to resonance, effectively doubling the of incident waves in depths around 10 meters. These height increases, observed under near-resonant conditions with natural basin periods of 10–136 seconds longitudinally, underscore the potential for clapotis to transform modest incoming swells into hazardous oscillations within enclosed port areas. Post-1950s case studies illustrate the risks to vessels from clapotis in confined ports. On October 18, 1967, in , incoming waves with a predominant 6-second period excited multiple resonant modes, causing severe pitching and heaving of ships during loading and unloading. This resulted in operational delays and structural stresses on moorings, with container vessels experiencing amplified motions that threatened stability and cargo integrity, though no total losses were reported. Similar amplification has been noted in other ports, where partial clapotis contributes to erratic vessel behavior during storms. Historical observations of clapotis in operational harbors like Halifax relied on wave and tide gauges to record oscillatory patterns in water levels and basin responses during events, helping identify resonant periods and variations.

Natural Occurrences

Clapotis can form in the open sea through the interference of opposing wave trains, particularly when shifts generate waves traveling in contrary directions, leading to patterns across expansive natural water bodies such as the North Atlantic. These occurrences are detectable via microseismic vibrations in the , , and adjacent land, as well as atmospheric microbaroms measured by sensors, highlighting their prevalence in regions with variable regimes. In fetch-limited natural environments like semi-enclosed bays and fjords, clapotis arises from wave reflection off steep natural boundaries such as cliffs, creating partially or fully standing waves depending on the —full standing waves near vertical cliffs and partial ones along sloped beaches. Narrow fjords, including those along the Norwegian , exhibit pronounced basin resonances during tidal surges or storm-driven swells, where the confined amplifies wave energy and promotes interference patterns akin to clapotis. Such resonances tie the wave periods to the basin's dimensions, often resulting in oscillations that disrupt local water levels. These natural clapotis patterns are most prominent for swells with periods of 10 to 20 seconds (frequencies 0.05–0.1 Hz) and infra-gravity waves below 0.05 Hz, as higher-frequency (>0.1 Hz) experience minimal reflection in open or semi-enclosed settings. In steady swell conditions within fetch-limited areas, such as coastal bays, these standing waves become common, contributing to resonant seiches with amplitudes up to 1 meter that can lead to temporary flooding. This interference from reflections underscores the dynamic nature of unmodified water bodies, distinct from confined artificial environments.

Implications and Applications

Engineering Considerations

In coastal and harbor , clapotis poses significant challenges by amplifying wave heights through reflection, necessitating designs that minimize wave reflection to protect infrastructure and operations. Absorptive breakwaters, such as rubble mound or types, are commonly employed to dissipate wave energy. Angled or sloping walls further mitigate clapotis by promoting wave breaking and energy absorption rather than full reflection, with studies showing reductions in Kr by 25-35% when combined with structural modifications like submerged horizontal plates. These approaches are prioritized in harbor layouts to prevent excessive agitation, as seen in various designs where reflection control directly correlates with reduced clapotis amplitudes. Risk assessment for clapotis in port layouts relies on advanced modeling tools to predict wave amplification and inform site-specific planning. The SWAN (Simulating WAves Nearshore) software, a third-generation spectral wave model, is widely used to simulate wave propagation, reflection, and patterns within enclosed basins, enabling engineers to forecast clapotis-induced height increases of up to 1.5-2 times incident waves under certain geometries. By incorporating , breakwater configurations, and incident wave spectra, SWAN facilitates optimization of harbor geometries to avoid resonant conditions that exacerbate clapotis. Post-2000 guidelines from the Permanent International Association of Navigation Congresses (PIANC) emphasize integrating clapotis considerations into harbor planning to ensure operational reliability. The PIANC Working Group 40 report (2003) on berm breakwaters provides recommendations for structures in wave-agitated environments through permeable armor layers and dynamic reshaping capabilities. Similarly, PIANC Report No. 121 (2014) on harbour approach channels addresses wave resonance risks, including standing waves, by outlining criteria for basin dimensions and breakwater placements to minimize downtime from clapotis. These standards promote a holistic approach, combining hydrodynamic modeling with empirical data for resilient . Despite these advancements, gaps persist in addressing clapotis under scenarios, particularly with rising s altering wave-structure interactions. Current linear models often underestimate amplification in nonlinear regimes through intensified tidal-surge-wave couplings. There is a critical need for updated nonlinear models that incorporate projected sea level increases (e.g., 0.28–0.55 m under low emissions or 0.63–1.01 m under high emissions by 2100, as per IPCC AR6) to better predict evolving resonant patterns and inform adaptive designs.

Environmental and Recreational Impacts

Clapotis waves in enclosed bays and coastal areas can lead to resuspension, increasing and altering light penetration for aquatic organisms. This process occurs as the oscillatory motion of standing waves disturbs bottom , particularly in shallow zones where wave energy interacts with the , potentially reducing primary productivity in affected ecosystems. In coastal ecosystems, clapotis contributes to enhanced vertical mixing, which may distribute nutrients but also exacerbate levels, influencing benthic habitats and filter-feeding . Such mixing effects are observed in microtidal systems where standing waves like clapotis amplify sediment , supporting dynamic but stressed ecological conditions. From a recreational perspective, clapotis poses significant hazards to sea kayakers due to sudden high peaks formed by intersecting reflected and incident waves, often causing capsizes in rocky or cliff-lined areas. A study of sea kayaking incidents documented environmental factors, including clapotis, as contributing to approximately 15% of cases, with 51% of the 45 analyzed incidents involving capsizes, many linked to confused water conditions regardless of moderate wind speeds. Natural clapotis zones attract adventure enthusiasts for kayaking and small-craft surfing, where the standing waves provide thrilling but unpredictable rides. These sites draw recreational users for their unique wave patterns, though they require advanced skills to navigate safely. Safety concerns extend to swimmers along reflective coastlines. Over time, persistent clapotis contributes to coastal erosion patterns by promoting scour at shorelines through reflected wave energy, accelerating sediment loss in vulnerable areas.

Seiches and Other Oscillations

Seiches represent free oscillations in closed or semi-enclosed basins, such as lakes, harbors, or bays, typically initiated by sudden disturbances like wind gusts, changes, or seismic activity, and they differ from clapotis primarily in the absence of continuous external forcing. Once triggered, seiches persist as standing waves that gradually decay due to frictional damping, with the largest water level fluctuations occurring at the basin's ends and minimal motion at the central node. In contrast, clapotis arises from the sustained interference of incident waves with their reflections off basin boundaries, maintaining its pattern only as long as the incoming waves continue, without the free-decay characteristic of seiches. Both phenomena exhibit patterns, where antinodes of maximum displacement alternate with nodes of minimal motion, but seiches generally feature longer periods ranging from minutes to hours, reflecting the larger-scale resonant modes of the basin, whereas clapotis periods align closely with those of the driving incident waves, often on the order of seconds to minutes. This temporal distinction underscores their hydrodynamic differences: seiches embody the natural, unforced resonant frequencies of the water body, akin to the sloshing in a after initial agitation, while clapotis is a forced response directly tied to external wave energy input. Harbor oscillations, a of seiches in port environments, often manifest as when the harbor has a narrow entrance connecting a broader inner basin, creating a three-dimensional pumping mode where water surges in and out like air in an acoustic resonator. This configuration amplifies low-frequency waves through the constricted mouth, analogous to clapotis in producing amplified standing patterns but extending into vertical and along-entrance dynamics beyond the primarily horizontal, surface-focused interference of clapotis. In open coastal settings, edge waves along provide another point of comparison, as these are progressive waves trapped nearshore by over increasing depth, traveling parallel to the without the fixed nodal structure of standing waves like clapotis. Unlike the reflective, basin-confined nature of clapotis, edge waves propagate indefinitely along the shoreline, often contributing to rhythmic morphology such as cusps, but lacking the interference-driven amplification within enclosed spaces.

Acoustic and Seismic Effects

Clapotis, as a standing wave pattern formed by the interference of incident and reflected surface waves in coastal or confined waters, generates low-frequency infrasonic waves known as microbaroms through nonlinear pressure fluctuations at the air-sea interface. These microbaroms typically occur in the 0.1–0.5 Hz range, with a prominent peak around 0.2 Hz, arising from the second-order interactions of opposing wave trains that produce coherent atmospheric pressure oscillations. Nonlinear wave interactions in coastal settings can contribute to this process, with infrasound detectable over global distances due to atmospheric propagation. Seismic microseisms, faint ground vibrations induced by clapotis, result from the transmission of dynamic pressure variations from the ocean floor to the solid Earth, primarily through nonlinear mechanisms in shallow coastal waters. Seminal theoretical work established that these signals peak at twice the frequency of the generating ocean waves (typically 0.07–0.5 Hz for secondary microseisms), as the standing wave pattern produces unattenuated second-order pressure fluctuations that couple efficiently to the seabed. Studies since the 2000s have confirmed coastal clapotis as a key contributor, with reflections of gravity waves generating energetic Scholte waves (interface waves between water and sediment) that dominate local seismic noise in coastal regions. Measurement of these effects relies on global networks such as the International Monitoring System (IMS), which uses arrays to localize microbarom sources by correlating signal back azimuths with swell models, revealing patterns tied to coastal wave reflections. Similarly, seismic arrays within the IMS detect microseism correlations with clapotis by analyzing beamformed noise spectra, enabling source discrimination between pelagic and coastal origins through frequency-wavenumber analysis. Current models for clapotis contributions remain incomplete, particularly in accounting for nonlinear enhancements under climate-driven changes like intensified storms and rising sea levels, which amplify wave heights and thus microseism amplitudes. While pelagic sources are well-modeled, coastal nonlinear interactions like clapotis in varying and conditions introduce uncertainties, limiting precise forecasts of climate-era seismic noise trends.

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  39. https://www.drna.pr.gov/wp-content/uploads/2024/11/CEH-Part-II-Nature-based-solutions-for-tropical-coastal-systems.pdf
  40. https://oceanservice.noaa.gov/facts/seiche.html
  41. https://www.coastalwiki.org/wiki/Seiche
  42. https://www.nps.gov/articles/coastal-geohazards-seiches.htm
  43. https://www.usgs.gov/programs/earthquake-hazards/seismic-seiches
  44. https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/helmholtz-resonance-of-harbours/5541AB48019D04F2EB5D48756B75E42B
  45. https://deepcreekscience.com/levels/documents/seiches/Handbook_Chapter9.pdf
  46. https://www.coastalwiki.org/wiki/Edge_wave
  47. https://www.sciencedirect.com/topics/earth-and-planetary-sciences/edge-wave
  48. https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2005jd006690
  49. https://www.poi.dvo.ru/sites/default/files/Documents/Articles/Research_of_the_Area_of_Generation_of_High-Frequency_Infrasound_Oscillations_in_the_Sea_of_Japan_Caused_by_Typhoons.pdf
  50. https://www.nature.com/articles/s41467-023-42673-w
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