Breaking waves

Surfer at a surge breaker

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A breaking wave on a rising ground in a laboratory wave channel

Waves breaking on the coast of Chile

In water waves , wave breaking describes the critical degree of wave transformation at which the surface tension at the crest of the wave is overcome, the orbital movement loses its characteristic shape and water emerging from the wave contour falls into the fore slope. Such unstable waves are called breakers . Other names are Sturzwoge , plunging breakers or heavy sea .

Breakwater (in this case tetrapods )

The energy required to generate the sea waves ( gravity waves ) is transmitted over hundreds of kilometers by the wind to the surface of the water and, if necessary, propagates as a wave over thousands of kilometers. The conversion of this energy into heat takes place through the process of the breakwater, mostly in zones of shallower water, often only a few meters in the surf zone . Particularly with such boundary conditions, devastating forces of destruction can occur on the coasts. The breaking process of the wave itself is characterized by the orbital movement of the wave, which is continuously deforming up to the breaking point.

Breaking criteria

Both the ratio of the instantaneous orbital velocity w to the phase velocity c of the wave (wave progression velocity) and the ratio of the orbital acceleration a to the gravitational acceleration g are important. According to George Gabriel Stokes , periodic waves become unstable if the tangent angle at the crest of the wave increases with increasing wave height . For deep-water waves has John Michell the associated limiting steepness to H / L = 0.142 is determined ( H = wave height , L = wavelength ) and Rankine (1860) the consistency of the orbital speed w at the wave crest to the wave propagation velocity c . ${\displaystyle \gamma \leq 120^{\circ }}$

For the breaking of waves in surf zones, the same above statements apply for the critical ridge angle and for the critical orbital velocity w . However, the maximum possible limit steepness H / L in shallow water is also dependent on the water depth d , which, according to the theory of individual waves, is also expressed in the ratio of the crusher height to the water depth . The criteria for breaking waves in shallow water zones are : ${\displaystyle H_{b}}$ ${\displaystyle d_{b}}$

${\displaystyle {\frac {\text{Orbitalgeschwindigkeit}}{\text{Wellenfortschrittsgeschwindigkeit}}}={\frac {w}{c}}\geq 1}$

${\displaystyle {\text{Brecherkammwinkel:}}\quad \gamma \leq 120^{\circ }}$

${\displaystyle {\frac {\text{Orbitalbeschleunigung}}{\text{Schwerebeschleunigung}}}={\frac {a}{g}}\geq 1}$

${\displaystyle {\text{Grenzsteilheit:}}\quad \max {\frac {H}{L}}=0{,}142\tanh {\frac {2\pi d}{L}}}$

Relative wave height:

${\displaystyle 0{,}82\leq {\frac {H_{b}}{d_{b}}}\leq 1{,}93}$.

Crusher forms

The fascination of water waves is based on the fact that they often appear to the observer as waves with an imperfect shape, the more the more they deviate from a regular sine shape. This is particularly the case with breaking waves in which a two-phase mixture ( foam ) consisting of water and air occurs in the crest area . In marine structures and ships, it is of particular importance that the force effects emanating from breaking waves reach their maximum in the crest area. Extreme force effects - such as pressure hammer in buildings and sea hammer (slamming) in ships - depend on the current crusher shape .

In contrast to the wave breaking forms (white capping) created by strong winds on the open sea, different breaker forms can be defined near the shore , depending on the

• Lake bottom slope (or artificial embankment slope ) ${\displaystyle 1:n=\tan \alpha }$

and the

• Wave steepness . ${\displaystyle S=H/L\,}$

Here, as a result of refraction and decreasing water depth towards the coast ( shoaling ), the wave height H increases and the wave length L decreases until the waves break at the maximum wave steepness max ( S ). Using the crusher index from Irribarren and Nogales (1949)

${\displaystyle \xi ={\frac {\tan \alpha }{\sqrt {\frac {H}{L_{o}}}}}={\frac {1}{\sqrt {\frac {H}{L_{o}}}}}\cdot {\frac {1}{n}}}$

${\displaystyle {\text{wird mit }}L_{o}={\frac {g}{2\pi }}\cdot T^{2}}$

${\displaystyle (L_{o}=\,}$ ${\displaystyle \mathrm {Wellenl{\ddot {a}}nge} {\text{ im Tiefwasser}};T={\text{Wellenperiode}})\,}$

${\displaystyle \xi =\xi (H,T,n)={\sqrt {\frac {g}{2\pi }}}\cdot {\frac {1}{\sqrt {H}}}\cdot T\cdot {\frac {1}{n}}}$

3 main forms can be distinguished from each other as follows:

${\displaystyle \xi <0{,}5\,\ \ \qquad \qquad {\text{Schwallbrecher (spilling breaker) }}}$

${\displaystyle 0{,}5\leq \xi \leq 3{,}3\,\qquad {\text{Sturzbrecher (plunging breaker)}}}$

${\displaystyle \xi >3{,}3\,\ \ \qquad \qquad {\text{Reflexionsbrecher (surging breaker)}}}$

These are particularly striking shapes. In contrast, a steady transition from one shape to the other can often be observed in nature.

In the case of surge breakers , the surface tension at the relatively symmetrical crest of the wave is overcome first; bubbles form which, together with the water emerging from the wave, move down the front of the wave. The wave energy is converted into turbulence and finally into heat over a distance that corresponds to several times the wavelength. After fall breakers , this is the preferred form of breaker for surfers .

Surge crusher

Fall breaker

Partial fall breaker

Reflection breaker

The fall crusher is characterized by the fact that, with increasing steepness, increasing asymmetry occurs until the slope of the wave towards the coast is vertical. Only then does water emerge from the ridge and move - following the parabola - over the slope into the trough of the waves in front of it. On the one hand, the impacting water reaches the ground together with the blown air; on the other hand, it is transported back to the crest of the wave in a roller according to the direction of the orbital velocity there. Both mechanisms cause the air to mix intensely, so that the energy is converted over a distance that corresponds to a fraction of the wavelength. If the fall breaker hits a surface that is roughly free of water, pressure shock occurs.

The surfing under the parabolic breaker tongue is a tube-surfing referred.

With the reflection breaker , the water leakage and the formation of bubbles are minimal and a proper breaking process can hardly be followed. This is a movement process that can be compared more with a standing wave ( clapotis ).

This is to be distinguished from a transitional form on the border with the fall breaker , which is referred to as a partial fall breaker . With this only the lower part of the coastal slope is vertical. The point at which water first emerges from the wave is towards the coast and a lot deeper than the crest of the wave.

Related mechanism

The breaking of the unsteady waves in surf zones is comparable to the process of the alternating jump known from the steady channel flow : In both processes, energy conversion rates occur that are orders of magnitude higher than friction at the bottom or internal friction between the liquid particles. It is noteworthy that in both natural processes the aforementioned considerable energy conversion can take place over a relatively short distance.

Individual evidence

1. ↑ Duden online: Brecher , see section "Synonyms"

Web links

Commons : Breaking waves  - collection of images, videos and audio files

• Fritz Büsching : Breaking the waves (PDF; 667 kB)