Internal shaft

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Internal waves are gravity waves at internal density levels in water. Low frequency internal waves are also known as internal tides .

Density levels can e.g. B. arise when solar radiation heats the water in the upper layers of a sea , or when fresh water flows from a river into the sea (i.e. in the so-called mixing zones ) and is only distributed on the surface. These interfaces are usually less than 100 meters deep in seas. For lakes see temperature stratification .

overview

SAR image of the Indian Ocean

Internal waves were first noticed by the phenomenon of so-called dead water zones in the oceans. There are areas near estuaries where light fresh water is layered on heavy salt water . If a ship enters the zone, it creates bow waves at the interface between salt and fresh water if the draft is sufficient . It clearly loses speed without water waves being visible on the surface of the water.

The SAR image on the right shows long-period internal waves in the Indian Ocean ( wavelength greater than 500 meters, upper arrow) that form at the interface between warm and cold water. Although the SAR practically does not penetrate the water and the waves on the water surface do not appear due to changes in the water level, the internal waves are visible in the SAR through the currents of the water surface. The short-period waves at the bottom left are surface water waves .

Generally speaking, internal waves are periodic, abrupt changes in the water column in the vertical direction, related to temperature , pressure and salinity (salinity of the water). They can occur in almost any body of water, but there must be thresholds or separation edges that have a significant influence on the current (for example in straits such as the Strait of Gibraltar , the Strait of Messina , or entrances to fjords, etc.).

Effects

Internal waves are held responsible for the fact that the continental slopes only drop very gently on average, although inclines of 15 ° are physically possible. An alternative, controversial theory blames submarine landslides alone . However, the processes are complex, so that several factors can be expected to interact with one another.

Since the internal waves arise in the upper layers (see above) of the seas, one might think that the lower layers of the continental slope are not formed by them. However, internal waves also occur at lower altitudes, because the density of the water is constantly increasing, so that there are many boundary layers. The periodic fluctuations in sea level caused by the tides also cause periodic fluctuations in the internal waves, which cause them to slosh along the continental slopes (both horizontally and vertically, reflecting off the boundary layer, creating a zigzag curve). The question of whether these waves can shape the ocean floor in the long term has been investigated since the 1960s . The Norwegian Arctic researcher and Nobel Peace Prize laureate Fridtjof Nansen found the first evidence of this thesis at the end of the 19th century . So it had to be investigated whether the internal waves are strong enough to displace material.

This thesis was confirmed by experiments in wave tanks. Furthermore, with these experiments it was possible to make predictions about the refraction behavior and the propagation speed of the internal waves (see below). The existence of internal waves has also been proven by research submarines , because in these they make themselves felt as vibrations. Recordings also show how mud is whirled up. The speed of propagation of the internal waves caused by tides is up to 40 centimeters per second.

Material is carried away from the continental slope by the internal waves if the oscillation angle of the internal waves (i.e. the angle at which the waves are reflected at the boundary layer) is the same as the slope. The angle of oscillation also really matches the slope, which supports the thesis that the ocean floor is formed by internal waves.

Speed ​​of propagation

In 1847 the British mathematician and physicist George Gabriel Stokes developed  the important relationship for the phase velocity of such waves in the presence of a single, sharp density level (characters with  'relate to the water layer above the interface, characters without  ' to the water layer below the interface) : ${\displaystyle c}$ ${\displaystyle \rho '<\rho }$

${\displaystyle c^{4}\cdot \left(\coth {\frac {2\pi h}{\lambda }}+\coth {\frac {2\pi h'}{\lambda }}+{\frac {\rho '}{\rho }}\right)-c^{2}\cdot \left(\coth {\frac {2\pi h}{\lambda }}+\coth {\frac {2\pi h'}{\lambda }}\right)\cdot {\frac {g\cdot \lambda }{2\pi }}+\left(1-{\frac {\rho '}{\rho }}\right)\cdot \left({\frac {g\cdot \lambda }{2\pi }}\right)^{2}=0}$

With

• wavelength ${\displaystyle \lambda }$
• Gravity acceleration ${\displaystyle g}$
• Liquid level ${\displaystyle h}$
• Hyperbolic cotangent ${\displaystyle \coth .}$

There are 2 special solutions to this equation:

• for short waves ${\displaystyle (h'<\lambda <h):}$

${\displaystyle c_{1}^{2}={\frac {g\cdot \lambda }{2\pi }}}$ and ${\displaystyle c_{2}^{2}=g\cdot h\cdot \left(1-{\frac {\rho '}{\rho }}\right)}$

Here, c ₁ is the phase velocity of the associated surface wave and c _{2 is} that of the internal wave.

• for long waves ${\displaystyle (h+h'<\lambda ):}$

${\displaystyle c_{1}^{2}=g\cdot (h+h')}$ and ${\displaystyle c_{2}^{2}=g\cdot h\cdot {\frac {h'}{h+h'}}\cdot \left(1-{\frac {\rho '}{\rho }}\right).}$

Mathematically, the Korteweg-de-Vries equation , the Benjamin-Ono equation and the Intermediate Long Wave (ILW) equation were also used to describe them (the ILW extrapolating between the two). You have soliton solutions .

literature

David A. Cacchione, Lincoln F. Pratson: Waves Among Waves . In: Spectrum of Science 10/05, p. 56 ff.