The two-dimensional wave spectrum describes the distribution of the wave energy as a function of frequency and propagation direction. In numerical implementation, the spectrum is discretized using 36 frequencies and 36 directions. The frequency spectrum is obtained by integrating over all directions. The wave components in the spectrum are divided into wind sea (wind waves) and swell.
full wave spectrum: wind waves + total swell
wind sea:wind sea is defined as those wave components that are still growing or being sustained by the wind. In contrast to swell, these waves propagate mainly in the direction of the wind.
swell: the remaining part of the spectrum is termed swell. Swell consists of a series of mechanical waves that propagate along the interface between water and air (surface gravity waves)
total swell: if the full remaining part of the spectrum is considered as one entity (full spectrum excluding wind waves).
first/second/third swell: when the remaining part of the spectrum is split into the 3 most energetic systems (descending in the respective wave heights).
moments for periods:
first: reciprocal of mean frequency
second: reciprocal of the variance of the frequency spectrum
significant height: the average height of the highest third of the waves
peak period: defined for the full wave spectrum, reciprocal of the peak frequency (period of the most energetic frequency)
wave direction: according to meteorological convention - 0° means from northern direction
stokes drift: stokes drift caused by full wave spectrum
Interaction With Ocean Currents
Ocean current models do not consider the stokes drift in the calculation of current speeds and directions. The stokes drift can overshoot the surface ocean current in stormy conditions, but rapidly decreases with depth. In order to get a complete picture of the surface drift however, the ocean current and the stokes drift can be overlaid.
Significant Wave Height
The significant wave height is traditionally defined as the mean wave height (trough to crest) of the highest third of the waves. Nowadays, it is usually defined as four times the standard deviation of the surface elevation or equivalently as four times the square root of the zeroth-order moment (area) of the full wave spectrum. 1
The peak wave period is defined as the wave period associated with the most energetic waves in the total wave spectrum at a specific point. Wave regimes that are dominated by wind waves tend to have smaller peak wave periods, and regimes that are dominated by swell tend to have larger peak wave periods. 2
Spectral mean direction in degrees over all frequencies and directions of the total swell spectrum. The total swell spectrum is obtained by only considering the components of the two-dimensional wave spectrum that are not under the influence of the local wind. Please note that we are using the meteorological convention to define directions (Read more here).
Spectral mean direction in degrees over all frequencies and directions of the two-dimensional wave spectrum. Please note that we are using the meteorological convention to define directions (Read more here).
From a theory of wave height distribution that includes non-linear effects, the estimation value of the largest single wave height in a record of 20 minutes is derived.
Spectral mean direction over all frequencies and direction of the wind waves spectrum. The wind waves spectrum is obtained by only considering the components of the two-dimensional wave spectrum that are still under the influence of the local wind. Please note that we are using the meteorological convention to define directions (Read more here).
Spectral mean wave period obtained using the reciprocal frequency moment of the total swell spectrum. The total swell spectrum is obtained by only considering the components of the two-dimensional wave spectrum that are not under the influence of the local wind.
Spectral mean wave period obtained using the reciprocal integral moment of the wind waves spectrum. The wind waves spectrum is obtained by only considering the components of the two-dimensional wave spectrum that are under the influence of the local wind. The integration is performed to infinitely high frequencies.
Spectral mean wave direction computed using the first-most energetic partition of the swell spectrum The swell spectrum is obtained by only considering the components of the two-dimensional wave spectrum that are not under the influence of the local wind. Please note that we are using the meteorological convention to define directions (Read more here).
Spectral mean wave direction computed using the second-most energetic partition of the swell spectrum The swell spectrum is obtained by only considering the components of the two-dimensional wave spectrum that are not under the influence of the local wind. Please note that we are using the meteorological convention to define directions (Read more here).
Spectral mean wave direction computed using the third-most energetic partition of the swell spectrum. The swell spectrum is obtained by only considering the components of the two-dimensional wave spectrum that are not under the influence of the local wind. Please note that we are using the meteorological convention to define directions (Read more here).
Spectral mean wave period obtained using the reciprocal frequency moment of the full wave spectrum. The integration is performed over all theoretical frequencies up to infinity. Again, the frequency wave spectrum is obtained by integrating the two-dimensional wave spectrum over all directions.
Spectral mean wave period obtained using the first frequency moment of the total swell spectrum. The integration is performed over all theoretical frequencies up to infinity. The frequency wave spectrum is obtained by integrating the two-dimensional wave spectrum over all directions.
Spectral mean wave period obtained using the first integral moment of the total swell frequency spectrum. The integration is performed over all theoretical frequencies up to infinity. The total swell frequency spectrum is obtained by integrating the two-dimensional wave spectrum over all directions for all wave components that are no longer under the influence of the local wind (full spectrum without wind sea).
Spectral mean wave period obtained using the second integral moment of the frequency wave spectrum. The integration is performed over all theoretical frequencies up to infinity. The frequency wave spectrum is obtained by integrating the two-dimensional wave spectrum over all directions.
Spectral mean wave period obtained using the second integral moment of the total swell frequency spectrum. The integration is performed over all theoretical frequencies up to infinity. The total swell frequency spectrum is obtained by integrating the two-dimensional wave spectrum over all directions for all wave components that are not under the influence of the local wind (full spectrum without wind sea).
Mean wave period computed using the reciprocal frequency moment of the third most energetic partition of the swell spectrum. The swell spectrum is obtained by only considering the components of the two-dimensional wave spectrum that are not under the influence of the local wind (full spectrum without wind sea).
4 times the square root of the integral over all directions and all frequencies of the total swell spectrum. The total swell spectrum is obtained by only considering the components of the two-dimensional wave spectrum that are not under the influence of the local wind.
4 times the square root of the integral over all directions and all frequencies of the windsea wave spectrum. The wind waves spectrum is obtained by only considering the components of the two-dimensional wave spectrum that are under the influence of the local wind (wind sea).
Significant wave height for the first most energetic partition of the swell spectrum, where the significant wave height is defined as 4 times the square root of the integral over all directions and all frequencies of the first partition of the swell spectrum. The swell spectrum is obtained by only considering the components of the two-dimensional wave spectrum that are not under the influence of the local wind.
Significant wave height for the second most energetic partition of the swell spectrum, where the significant wave height is defined as 4 times the square root of the integral over all directions and all frequencies of the second partition of the swell spectrum. The swell spectrum is obtained by only considering the components of the two-dimensional wave spectrum that are not under the influence of the local wind.
Significant wave height for the third most energetic partition of the swell spectrum, where the significant wave height is defined as 4 times the square root of the integral over all directions and all frequencies of the third partition of the swell spectrum. The swell spectrum is obtained by only considering the components of the two-dimensional wave spectrum that are not under the influence of the local wind.
For a pure wave motion in fluid dynamics, the Stokes drift velocity is the average velocity of a specific fluid parcel as it travels with the fluid flow. For instance, a particle floating at the free surface of water waves experiences a net Stokes drift velocity in the direction of wave propagation. Along with effects such as Ekman drift and geostrophic currents, the Stokes drift is one of the most relevant processes in the transport of marine debris. Please note that we are using the meteorological convention to define directions (Read more here).
These parameters describe the velocity of the ocean currents. Please note that we are using the meteorological convention to define directions (Read more here).
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