Dispersion (water waves)

For water waves ( surface waves) is understood by the wavelength or the frequency dispersion under particular the dependence of the phase velocity ( wave celerity ).

Gravity waves propagate more rapidly continues, the greater its wavelength, or the smaller its frequency. On the other hand, waves of a given wavelength over deeper water a larger phase velocity than shallower water. In contrast, capillary spread, the restoring force resulting solely from the surface tension, the more faster the shorter it is. The group velocity is the speed at which a wave group (ie the intensity maximum of several overlapping waves) moves whose wavelengths differ only slightly. The ratio of the phase velocity for the group velocity determines the type of the dispersion.

Dispersion in surface wave

Is the phase velocity for all part shafts ( component waves ) of the same group, are groups and identical phase velocity. This is not the case, there is dispersion. For all types of waves is considered according to the following relationship between Rayleigh group velocity cg and phase velocity c:

Herein, the wavelength and the phase velocity dispersion. Depending on the sign and magnitude of the differential quotient the group velocity is smaller, bigger or equal to the phase velocity. One distinguishes normal dispersion, anomalous dispersion and dispersionless wave propagation:

Dispersion in gravity waves

Notwithstanding the electromagnetic waves, the wave parameters are referred to as follows in gravity waves.

The classical dispersion relation Airy -Laplace (1840 ) is also valid for waves by the nonlinear wave theory Stokes ' second order.

It describes the different form of the dispersion as a function of depth d for this purpose is

Limited water depth

It is above the full dispersion relation.

Especially in areas where the water depth is less than half the wavelength ( d ≤ 0.5 L), significant differences may arise in nature. Possible causes are, inter alia, be considered:

• Morphological features such as reefs in the coastal zone,
• Constant currents, accelerated flows, see wave transformation
• Wind effects and
• Partially standing waves in sea areas with islands, which are upstream of the coast (even over deep water ).

In wave resonance occurs anomalous dispersion.

Deep water

With the spread of large water depth (d ≥ 0.5 L) before maximum normal dispersion and the phase velocity is independent of the water depth.

Shallow water

In shallow water ( d ≤ 0.04 L), the wave motion is practically dispersionless and depends only on the water depth.

See also: wave resonance, Doppler effect

Capillary waves

For the locomotion of capillary waves

This surface tension and liquid density mean.

The dispersion is anomalous

• Wave
• Coastal Engineering