Wave nonlinearity
The nonlinearity of surface gravity waves refers to their deviations from a sinusoidal shape.
In the fields of physical oceanography and coastal engineering, the two categories of nonlinearity are skewness and asymmetry.
[3] Wave skewness and asymmetry are often implicated in ocean engineering and coastal engineering for the modelling of random sea states, in particular regarding the distribution of wave height, wavelength and crest length.
For practical engineering purposes, it is important to know the probability of these wave characteristics in seas and oceans at a given place and time.
This knowledge is crucial for the prediction of extreme waves, which are a danger for ships and offshore structures.
Satellite altimeter Envisat RA-2 data shows geographically coherent skewness fields in the ocean and from the data has been concluded that large values of skewness occur primarily in regions of large significant wave height.
[4] At the nearshore zone, skewness and asymmetry of surface gravity waves are the main drivers for sediment transport.
Due to Non-linear effects, waves can transform from sinusoidal to a skewed and asymmetric shape.
In probability theory and statistics, skewness refers to a distortion or asymmetry that deviates from a normal distribution.
For waves having the same velocity variance, the ones with higher skewness result in a larger net sediment transport.
Skewness (Sk) and asymmetry (As) are measures of the wave nonlinearity and can be described in terms of the following parameters:[9]
The Ursell number, named after Fritz Ursell,[10] relates the skewness and asymmetry and quantifies the degree of sea surface elevation nonlinearity.
The skewness and asymmetry at a certain location nearshore can be predicted[12] from the Ursell number by:
For small Ursell numbers, the skewness and asymmetry both approach zero and the waves have a sinusoidal shape, and thus waves having small Ursell numbers do not result in net sediment transport.
For large Ursell numbers, the skewness approaches 0 and the asymmetry is maximum, resulting in an asymmetric wave shape.
Skewed waves have higher flow velocities under the crest of the waves than under the trough, resulting in a net onshore sediment transport as the high velocities under the crest are much more capable of moving large sediments.
[14] Beneath waves with high asymmetry, the change from onshore to offshore flow is more gradual than from offshore to onshore, where sediments are stirred up during peaks in offshore velocity and are transported onshore because of the sudden change in flow direction.
[15] The local sediment transport generates nearshore bar formation and provides a mechanism for the generation of three-dimensional features such as rip currents and rhythmic bars.
With the phase-averaged approach, wave skewness and asymmetry are included based on parameterizations.
Examples of these kinds of models are WAVEWATCH3 (NOAA) and SWAN (TU Delft).
WAVEWATCH3 is a global wave forecasting model with a focus on the deep ocean.
SWAN is a nearshore model and mainly has coastal applications.
Advantages of phase-averaged models are that they compute wave characteristics over a large domain, they are fast and they can be coupled to sediment transport models, which is an efficient tool to study morphodynamics.
