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Breaking wave
Breaking wave
from Wikipedia

Plunging breaker
Large wave breaking

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.

The most generally familiar sort of breaking wave is the breaking of water surface waves on a coastline. Wave breaking generally occurs where the amplitude reaches the point that the crest of the wave actually overturns. Certain other effects in fluid dynamics have also been termed "breaking waves", partly by analogy with water surface waves. In meteorology, atmospheric gravity waves are said to break when the wave produces regions where the potential temperature decreases with height, leading to energy dissipation through convective instability; likewise, Rossby waves are said to break[1] when the potential vorticity gradient is overturned. Wave breaking also occurs in plasmas,[2] when the particle velocities exceed the wave's phase speed. Another application in plasma physics is plasma expansion into a vacuum, in which the process of wave breaking and the subsequent development of a fast ion peak is described by the Sack-Schamel equation.

A reef or spot of shallow water such as a shoal against which waves break may also be known as a breaker.[citation needed]

Types

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Classification of breaking wave types
Breaking wave on a slope in a laboratory wave channel (movie)
Animation showing how the slope of the seafloor along the coast affects breaking waves

Breaking of water surface waves may occur anywhere that the amplitude is sufficient, including in mid-ocean. However, it is particularly common on beaches, because wave heights are amplified in the region of shallower water because the group velocity is lower there (see also: Waves and shallow water).

There are four basic types of breaking water waves. They are spilling, plunging, collapsing, and surging.[3]

Spilling breakers

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When the ocean floor has a gradual slope, the wave will steepen until the crest becomes unstable, resulting in turbulent whitewater spilling down the face of the wave. This continues as the wave approaches the shore, and the wave's energy is slowly dissipated in the whitewater. Because of this, spilling waves break for a longer time than other waves, and create a relatively gentle wave. Onshore wind conditions make spillers more likely.

Plunging breakers

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A plunging wave occurs when the ocean floor is steep or has sudden depth changes, such as from a reef or sandbar. The crest of the wave becomes much steeper than a spilling wave, becomes vertical, then curls over and drops onto the trough of the wave, releasing most of its energy at once in a relatively violent impact. A plunging wave breaks with more energy than a significantly larger spilling wave. The wave can trap and compress the air under the lip, which creates the "crashing" sound associated with waves. With large waves, this crash can be felt by beachgoers on land. Offshore wind conditions can make plungers more likely.

If a plunging wave is not parallel to the beach (or the ocean floor), the section of the wave which reaches shallow water will break first, and the breaking section (or curl) will move laterally across the face of the wave as the wave continues. This is the "tube" that is so highly sought after by surfers (also called a "barrel", a "pit", and "the greenroom", among other terms). The surfer tries to stay near or under the crashing lip, often trying to stay as "deep" in the tube as possible while still being able to shoot forward and exit the barrel before it closes. A plunging wave that is parallel to the beach can break along its whole length at once, rendering it unrideable and dangerous. Surfers refer to these waves as "closed out".

Collapsing

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Collapsing waves are a cross between plunging and surging, in which the crest never fully breaks, yet the bottom face of the wave gets steeper and collapses, resulting in foam.

Surging

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Surging breakers originate from long period, low steepness waves and/or steep beach profiles. The outcome is the rapid movement of the base of the wave up the swash slope and the disappearance of the wave crest. The front face and crest of the wave remain relatively smooth with little foam or bubbles, resulting in a very narrow surf zone, or no breaking waves at all. The short, sharp burst of wave energy means that the swash/backwash cycle completes before the arrival of the next wave, leading to a low value of Kemp's phase difference (< 0.5). Surging waves are typical of reflective beach states. On steeper beaches, the energy of the wave can be reflected by the bottom back into the ocean, causing standing waves.

Physics

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Spilling breaker
Spilling breaker
Plunging breaker
Plunging breaker
Collapsing breaker
Collapsing breaker
Surging breaker
Surging breaker
Different breaking-wave types, drawn after photos from a lab experiment, can be associated with the value of the Iribarren number.

As ocean surface waves enter shallow water, the water particle velocities begin to move faster relative to the speed of the waveform. As a result, the waveform becomes unstable and the crest of the wave overturns, which is known as the wave breaking process.[4] During breaking, a deformation (usually a bulge) forms at the wave crest, either leading side of which is known as the "toe".[clarification needed] Parasitic capillary waves are formed, with short wavelengths. Those above the "toe" tend to have much longer wavelengths. This theory is anything but perfect,[clarification needed] however, as it is linear. There have been a couple non-linear theories of motion (regarding waves). One put forth uses a perturbation method to expand the description all the way to the third order, and better solutions have been found since then. As for wave deformation, methods much like the boundary integral method and the Boussinesq model have been created.

It has been found that high-frequency detail present in a breaking wave plays a part in crest deformation and destabilization. The same theory expands on this, stating that the valleys of the capillary waves create a source for vorticity. It is said that surface tension (and viscosity) are significant for waves up to about 7 cm (3 in) in wavelength.[5]

These models are flawed, however, as they can't take into account what happens to the water after the wave breaks. Post-break eddy forms and the turbulence created via the breaking is mostly un-researched. Understandably, it might be difficult to glean predictable results from the ocean.[citation needed]

After the tip of the wave overturns and the jet collapses, it creates a very coherent and defined horizontal vortex. The plunging breakers create secondary eddies down the face of the wave. Small horizontal random eddies that form on the sides of the wave suggest that, perhaps, prior to breaking, the water's velocity is more or less two dimensional. This becomes three dimensional upon breaking.[citation needed]

The main vortex along the front of the wave diffuses rapidly into the interior of the wave after breaking, as the eddies on the surface become more viscous. Advection and molecular diffusion play a part in stretching the vortex and redistributing the vorticity, as well as the formation turbulence cascades. The energy of the large vortices are, by this method, transferred to much smaller isotropic vortices.

Experiments have been conducted to deduce the evolution of turbulence after break, both in deep water and on a beach.

A theoretical limit on the steepness of non-breaking waves in finite depth is given by the Miche criterion, derived by French engineer Robert Miche in 1944.[6][7][8]

See also

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References

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Revisions and contributorsEdit on WikipediaRead on Wikipedia
from Grokipedia
A breaking wave, also known as a breaker, is an ocean wave whose crest becomes and collapses forward, transforming organized wave into turbulent motion and dissipation, typically when the horizontal velocity of particles at the crest exceeds the wave's phase speed or celerity. This arises primarily in shallow near shorelines, where shoaling causes to increase and to shorten due to interaction with the , leading to a steepness limit where the ratio of (H) to (L) exceeds approximately 1/7. In deeper , breaking can also occur through when the deep-water steepness (H₀/L₀) surpasses about 0.05, driven by wind forcing. Breaking waves are classified into several types based on the beach slope and incident wave characteristics, such as the Iribarren parameter, which relates bottom steepness to wave steepness. Spilling breakers form on gentle slopes, where the crest gradually spills foam forward over several wavelengths, dissipating energy with minimal reflection. Plunging breakers occur on moderate slopes, featuring a curling crest that plunges downward, creating high turbulence and often forming surfable tubes, with partial energy reflection and transmission. Surging breakers develop on steep shores with long-period, low-amplitude waves, sliding up the beach with little foam and over 50% reflection, while collapsing breakers represent a transitional form between plunging and surging. These phenomena play a pivotal role in coastal dynamics and ocean-atmosphere interactions, serving as the primary mechanism for dissipating wind-generated wave energy and limiting wave growth. Breaking induces in the surface layer, which mixes heat, momentum, and nutrients vertically, while also enhancing air-sea for gases like and oxygen. Additionally, breakers shape coastlines through , , and deposition, influencing morphology and nearshore ecosystems.

Overview

Definition

A breaking wave occurs in surface waves, which are oscillations at the air-water interface where serves as the primary restoring force. These waves become breakers when their height exceeds a critical threshold relative to the , causing the crest to become unstable and overturn or collapse under the combined effects of and . This typically develops as the wave front steepens to a vertical or overhanging profile, marking the onset of breaking. Key characteristics of a breaking wave include the rapid onset of at the wave front, often resulting in the formation of a bore or whitecap as the crest spills or plunges forward. This process transitions the wave from coherent, progressive motion—where propagates with the wave—to dissipative , where is converted into and mixing. The systematic study of breaking waves began with George Gabriel Stokes in 1880, who analyzed the limiting configuration of waves and highlighted the critical role of steepness in deep water conditions. Stokes determined that breaking initiates when the ratio of wave height HH to LL surpasses approximately 1/71/7 (or H/L>0.142H/L > 0.142), beyond which the wave profile cannot maintain stability without fracturing.

Significance

Breaking waves play a crucial role in oceanographic processes by driving turbulent mixing in the upper layers, which facilitates the vertical transport of , , and dissolved substances. This mixing enhances nutrient upwelling from deeper waters to the sunlit surface, supporting primary productivity in marine ecosystems and influencing global biogeochemical cycles. Additionally, the turbulence generated by breaking waves promotes air-sea , particularly for sparingly soluble gases like CO₂ and O₂, by increasing the air-water interface area through bubble entrainment and surface renewal. These interactions contribute to regulation by modulating the 's capacity to absorb atmospheric CO₂ and distribute , thereby affecting global patterns and circulation. In environmental contexts, breaking waves are the primary mechanism behind during storms, where intense wave action fractures the sea surface and ejects sea spray into the atmosphere. This process generates marine aerosols that influence cloud formation, , and , with shoreline breaking particularly enhancing aerosol emissions near coastal zones. The resulting sea spray aerosols can travel far inland, impacting regional air quality and weather patterns. From a perspective, breaking waves are essential to coastal dynamics, where they drive through undertows and longshore currents, shaping morphology and influencing or accretion patterns over seasonal and storm timescales. They also form the foundation of , providing the predictable, energy-rich curls that define the sport and support coastal economies. Furthermore, the released during breaking is harnessed in wave energy converters, such as shoreline devices that capture hydraulic pressure from crashing waves to generate , offering a with potential to power thousands of households. Quantitatively, breaking waves dissipate a substantial portion of the energy transferred from to the surface, with global estimates indicating that they account for over 50% of the approximately 57 TW of annual wind energy input to waves, primarily through deep-water breaking processes totaling around 33 TW.

Formation

Wave Evolution Leading to Breaking

As waves propagate from deep water toward the shore, they undergo shoaling, a process where decreasing water depth causes the waves to slow down, their to shorten, and their height to increase in order to conserve . This transformation begins when the water depth dd becomes less than half the LL (i.e., d<L/2d < L/2), marking the transition from deep-water to intermediate-water conditions where the seabed begins to influence wave motion. In typical coastal settings, this leads to a progressive buildup of wave amplitude over distances of several kilometers, with the wave period remaining relatively constant. Once in shallower water, nonlinear effects dominate the wave evolution, causing the wave profile to steepen as the higher-velocity crests advance faster than the troughs due to nonlinear effects, where the phase speed depends on wave amplitude. This asymmetry arises because particle velocities under the crest exceed those under the trough, resulting in a forward-leaning wave front that becomes increasingly unstable. Studies of nonlinear shallow-water waves confirm that this steepening is exacerbated in regions where the Ursell number (a measure of nonlinearity) exceeds unity, promoting higher harmonics and further distortion of the wave shape. External factors such as wind forcing, ocean currents, and bathymetric variations significantly modulate this evolution by amplifying wave instability. Offshore winds can enhance wave growth through momentum transfer, accelerating the onset of steepening, while opposing currents may increase effective wave height by altering relative propagation speeds. Bathymetry, including reefs or sandbars, induces rapid depth changes that intensify shoaling and nonlinear interactions, often leading to localized wave focusing and heightened breaking potential. The overall timeline of wave evolution spans from generation in deep water, where fetch-limited growth under wind action establishes initial wave fields, to nearshore transformation. In deep water (d > L/2), waves propagate linearly with minimal distortion over hundreds of kilometers; upon entering the coastal zone (typically within 5-10 km of shore), shoaling and nonlinearity drive rapid changes over 1-5 km, culminating in conditions ripe for breaking. This progression is observed in field measurements across various coastal environments, highlighting the interplay of these processes in setting the stage for wave collapse.

Breaking Criteria

Breaking waves initiate when specific quantitative thresholds in wave parameters relative to water depth are exceeded, marking the transition from stable propagation to instability. A primary steepness criterion, derived from Stokes , predicts breaking when the ratio of HH to LL surpasses 0.14 in deep conditions, where the water depth is much greater than half the . In shallower , Miche's criterion extends this limit as H/L=0.142tanh(kh)H/L = 0.142 \tanh(kh), where k=2π/Lk = 2\pi/L is the wave number and hh is the depth; this approximates to H/h0.89H/h \approx 0.89 in very shallow conditions, indicating depth-induced breaking when the wave height approaches 89% of the local depth. This threshold arises from the condition where orbital velocities at the wave crest equal the phase speed, leading to instability. Depth-limited breaking further constrains the maximum sustainable wave height, with empirical observations confirming Hb0.78dH_b \approx 0.78 d at the breakpoint, where HbH_b is the breaker height and dd is the local water depth. This limit, originally proposed by McCowan for solitary waves, has been widely adopted for periodic waves in shallow water, providing a practical bound for predictions; slight variations exist, such as 0.75dd in some early formulations, but 0.78dd aligns with theoretical solitary wave stability analyses. Updated models incorporate nonlinearity via the Ursell number Ur=HL2/d3Ur = H L^2 / d^3, where Ur>25Ur > 25 indicates the regime, characterized by strong nonlinearity that enhances wave steepening and increases the potential for breaking in intermediate to shallow depths, transitioning from linear to nonlinear regimes. The slope also modulates breaking thresholds, influencing the dominant breaker type without altering the core steepness or depth limits. On gentler slopes (ratios of 1:50 to 1:100), spilling breakers predominate as waves gradually destabilize, while steeper slopes (>1:10) promote plunging breakers through rapid height growth. This dependence is captured by the surf similarity parameter ξ=tanβ/H0/L0\xi = \tan \beta / \sqrt{H_0 / L_0}
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