Wind wave
In water waves are surface waves at the interface between water and air. After Walter Munk is that all water surface elevations with period durations of tens of seconds to hours (tidal wave) meant.
At wavelengths of less than 4 mm, the surface tension of the water to determine the properties of the capillary in which the toughness of the water causes a strong dissipative effect. At wavelengths greater than 7 cm, the inertia, the force of gravity and the resulting pressure and changes in motion determines the properties of the gravity wave.
- 2.1 Wave height, wave length, wave steepness
- 2.2 orbital motion
- 3.1 Gravity waves 3.1.1 approximation: the wavelengths are small relative to the water depth ( deep water waves)
- 3.1.2 approximation: the wavelengths are large relative to the water depth ( shallow water waves )
- 4.1 reflection
- 4.2 refraction
- 4.3 diffraction
- 4.4 Wave breaking
- 4.5 Examples of the behavior of waves when running on a beach
Wave emergence
Into the water thrown stones and flow obstacles create waves, propelled vessels is accompanied by a bow wave. Earthquake can cause tsunamis. On the latter, and tidal waves will no further reference is made at this point, but preferably generated by wind waves of the sea surface to be treated, depending on the water depth.
Wave formation by wind
The mechanism of wave formation by wind is the Kelvin - Helmholtz instability. In the area of origin of the swell can be distinguished as influencing variables:
- The strike length (fetch ) F = effect of distance of the wind on the water surface,
- The wind speed U and
- The wind duration as so-called Ausreifzeit the swell.
Their interaction determines the size of the waves and their shape. The greater one of these factors, the larger the waves. In shallow seas, the water depth is limiting influence. The resulting sea state is characterized by:
- The wave heights,
- Wavelengths,
- The period durations and
- The wave direction of progress (relative to the north).
In a given sea area waves occur with different bandwidths of heights and periods. For the wave forecast are defined as characteristic information:
- The significant wave height and
- The significant wave period.
Both refer to the observed over a predetermined period waves and provide statistical quantities as average values for the third of the highest waves of the collective dar.
Structure and Properties
Wave height, wave length, wave steepness
Water waves differ in shape from the regular sinusoidal shape. Their shape is both horizontally and vertically asymmetrical. The part of the shaft, which is above the still water level is called the wave crest. The position of the highest deflection of the wave crest. The part of the shaft is below the still water level, the trough. The wave height is the sum of the amounts of both neighboring Maximalauslenkungen:
The maximum positive water surface elevation exceeds in its absolute value the more negative the maximum water surface elevation, the lower the water depth. With waves in shallow water, the height of the wave crest to 3/ 4 of the total wave height H can make, while the trough H / 4 is below the static water level. As wavelength (symbol ), the sum of their disparate related to the static water level partial lengths of the comb area and the Talbereiches is known, cf picture on the right. It is
The quotient of the wave height and wavelength is an important characteristic for the assessment of the stability of the wave and is referred to as a slope S wave.
According to Stokes ( 1847) applies the theoretical limit for waves over a water depth. In fact, the wave breaking has already been made at. On the open ocean prevail wave steepness before between. For the shallow water field measurements have the formula of Miche (1944 ) confirmed, in the limiting effect of the seabed is considered.
Since the 19th century, the asymmetric shape of natural water waves beside Gerstner (1804 ) has been described mainly by Stokes ( 1847) with increasing mathematical complexity. For practical assessments which will regardless but still often used the linear wave theory by Airy -Laplace (1845 ), which starts from the regular sinusoidal shape.
Orbital motion
After the wave theories of Gerstner and Airy Laplace particles of water when passing a shaft approximately in circular paths ( orbits ) are deep water moves, the radii in the flow field below the water surface to a depth equal to about half the wavelength, according to an exponential law about decrease to zero. The circuit period is said round trip time, which corresponds to the advancement of the shaft to a full wavelength. Thus, the orbital velocity at the water surface:
And the wave celerity is
In contrast, the path lines of the water particles in accordance with the theory of after a Stokes wave period are not closed. According to this theory of the circular orbital motion superimposed on a horizontal drift velocity U in the direction of wave propagation speed C, the mass transport rate is called. The adjacent animation, the red dots represent the instantaneous positions of the massless particles that move with the flow velocity. The light blue lines are the path of these particles and the light blue dots represent the particle position after each wave period. The white dots are in the same direction fluid particles. Note that the wave period of the fluid particles near the free surface differs from that with respect to a fixed position (indicated by the light blue points). This is due to the Doppler effect. (to be completed for limited water depth)
Dispersion and group velocity
Gravity waves
While the wave celerity ( phase velocity ) is true for all types of waves, gravity waves also applies to the dispersion relation, which contains the wavelength L and the water depth d as a variable
The dependence of the phase velocity on the wavelength or the frequency shown in the two figures on the right. In addition, depending on the water depth is given d. Gravity waves come not as single monochromatic waves before, but always as a superposition of waves with close frequencies. As a result occur wave packets or wave groups with the group velocity
Move. Herein, the dispersion of the phase velocity. This is negative for gravity waves: it is normal dispersion before (as opposed to capillary waves ).
Approximation: the wavelengths are small relative to the water depth ( deep water waves)
For waters with a depth of at least one-half wavelength () approaches the value in (1) 1 Then is the velocity of propagation:
Or c = L / T:
Refers to the period of the frequency, follows with from (3):
The dispersion is maximum, the phase velocity is independent of the water depth:
From ( 2), the group velocity results to
Waves with large wavelengths propagate faster and have a greater period than those with small wavelengths. At a wavelength of 1 km, the propagation speed is about 140 km / h and the period of 25 seconds, at a wavelength of 100 m about 50 km / h and 8 s a result of the above Dispersion relation have to wave packets that leave the field of their production, change in the way that the longest wave components arriving at a predetermined location first. In addition, since the short-period waves are attenuated more, take storm waves in remote areas as a true long-period swell.
Approximation: the wavelengths are large relative to the water depth ( shallow water waves )
At wavelengths which are greater than the depth of water (), the propagation velocity depends only on the depth, no longer wavelength. For small and thus we obtain from (1)
Does not show the propagation velocity dispersion, i.e. it is independent of the wavelength. Therefore, the phase velocity is equal to the group velocity:
Capillary waves
At wavelengths shorter than a few centimeters, the surface tension determines the propagation speed. For capillary waves applies:
Therein represents the surface tension and the density of the liquid. Dispersion of the capillary is less than zero, and therefore abnormal
Wave effects
Reflection
Wave reflection means for progressive water waves, throwing a portion of their energy ( wave energy ) on a structure ( breakwater, seawall embankment ) or in places where the configuration changes of the natural seabed (strong). According to the law of reflection optics, another part of the wave energy is propagated at the same time and the remainder through the processes of wave breaking, the liquid and ground friction dissipated or absorbed, etc., cf wave transformation, wave absorption.
Refraction
Under refraction is defined as a dependent on the water depth change in the direction of wave travel. In gently sloping beaches, its effect causes wave fronts increasingly einbeugen parallel to the shore line and the observer on the beach (not necessarily breaking ) sees waves come up. As in the refraction of light and here the Snell's law is applicable, on the basis of Huygens' principle.
Diffraction
In diffraction, the diffraction of the wave fronts is understood at the ends of islands or on the edges of buildings. As the diffraction of light at edges Huygens' principle can also be applied here. For protective structures ( breakwaters and jetties ), the diffraction of the wave fronts, the result is that some of the energy of the incoming waves behind the protective structure or in the passes through moles against wave effects to be protected a harbor entrance.
Wave breaking
Denotes wave breaking the critical level of wavelet transform in which the surface tension is overcome in the wave crest, the orbital motion will lose its characteristic shape and falls into the water emerging from the front slope of the wave contour. With respect to their geometry about four crusher forms can be distinguished.
Examples of the behavior of waves when running on a beach
Example 1: wave breaking
A wave approaches a slowly rising shore, decreases with decreasing water depth, the velocity of propagation of the wavefront. The subsequent waves rolling over the wavefront until they too are slowed down. The wavelength decreases as a result of energy conservation increases the wave height to the wave breaking occurs.
Example 2: Refraction
A wave front approaches a slowly rising shore at an oblique angle, the waves slow down in shallow area. The outlying further maintain their speed. Similar to the refraction of light at the glass, thereby rotating the wavefront until it runs parallel to the beach line.
Interfacial waves
In the considerations above, only the parameters of a medium a go. This assumption is justified for surface waves of water in the air, since the influence due to the small density of air is negligible.
The expanded version of equation (3) takes into account the density of the two phases, and designated
And in capillary applies:
See also Internal waves
Special shafts
Breakers ( Breaking waves near the beach ). About the maximum possible wave height H ( vertical distance between trough and crest ) in surf zones ( = breaker height ) decide the criteria of wave breaking. Field measurements have shown that breaker heights may very well be greater than the local water depth.
Tsunamis are caused by undersea earthquake. They are characterized by a very large wavelength and on the high seas by small amplitudes of less than one meter. The propagation velocity of tsunamis follows the relation ( 5), because the wavelength of a plurality of 100 km is considerably greater than the depth of the sea. Tsunami spreads ( with an average water depth of 5 km) at a speed of 800 km / h. Near the coast, the speed decreases, while the amount increases. Devastating the damage they cause when running on flat coasts.
Tide waves are waves that are caused by the tide.
On the layering of light freshwater to heavy saltwater observed interfacial waves are, their effects are referred to as dead-water ships. Retracts a ship in the zone, it can generate bow waves on the surface of the salt water layer at a sufficient depth. It loses considerable momentum, without at the water surface water waves would be detected.
As Grundsee a short, steep and breaking water wave is called, the wave trough reaches to the ground.
In the design of ships you have previously assumed that waves with a height of more than 15 m would occur very rarely. Satellite observations showed, however, that so-called rogue waves actually exist ( in sailor language called " Kaventsmänner " ) with heights of more than 30 m. Recent attempts to explain the monster waves apply quantum mechanics to the physics of water waves.