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| Titel |
Evolution of random wind wave fields under rapidly changing wind |
| VerfasserIn |
Victor Shrira, Sergei Annenkov |
| Konferenz |
EGU General Assembly 2011
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 13 (2011) |
| Datensatznummer |
250049605
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| Zusammenfassung |
| Modelling of evolution of nonlinear random wave fields in nature (and, in particular, their
most common example – wind waves in the ocean) is based on the kinetic equation paradigm
that assumes a proximity to stationarity and homogeneity. In the case of wind waves these
assumptions are often violated due the variability of wind, which is present at all timescales.
In a recent study, we have found that a single strong instant change of wind leads to a rapid
adjustment of a wave field, which occurs on a dynamic O(É-2) timescale, É being the
measure of nonlinearity, which is much faster than the O(É-4) timescale predicted by the
Hasselmann equation. However, even when wind is nearly constant on average, it is
often characterised by a considerable level of gustiness, which formally violates the
applicability of the existing statistical theory at every instant of time. At present, this
problem is commonly ignored, and the existing wave forecasting models based on the
kinetic equation are used beyond the limits of their applicability, due to the lack of
alternatives. In this study we consider, by direct numerical simulation (DNS), a random
wave field generated by a non-stationary wind with constant mean and constant
direction. Three different models of changing wind are considered: (i) wind instantly
alternating between two fixed values, at regular intervals, (ii) sinusoidal wind, (iii)
realistic gusty wind. The results are compared with constant forcing experiments. We
use a DNS algorithm based on the Zakharov integrodifferential equation for water
waves.
It is now well-known that the evolution of a random wave field generated by constant
forcing is self-similar at large durations or fetches. We show that this self-similarity survives
under changing forcing, with averaged statistical characteristics of the wave field
corresponding to a field generated by a certain ‘effective’ wind, which in our examples is
slightly above the average of the changing forcing. In particular, the total wave energy is
shown to oscillate around its ‘effective wind value’, that is following on average the
powerlike dependence on time predicted by self-similarity, while the dispersion of these
oscillations is slowly decreasing. To summarise: The simulations show that the nonlinear
adjustment of a random wave field to changing forcing occurs on fast dynamic timescale and
does not break the averaged self-similarity properties, which justifies the use of wave
forecasting models based on slowly varying forcing for realistic winds. However,
the link between the ‘true’ gusty wind and smoothed ‘effective’ one needs further
investigation. |
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