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| Titel |
Modelling of squall with the generalised kinetic equation |
| VerfasserIn |
Sergei Annenkov, Victor Shrira |
| Konferenz |
EGU General Assembly 2014
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 16 (2014) |
| Datensatznummer |
250090381
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| Publikation (Nr.) |
 EGU/EGU2014-4615.pdf |
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| Zusammenfassung |
| We study the long-term evolution of random wind waves using the new generalised kinetic
equation (GKE). The GKE derivation [1] does not assume the quasi-stationarity of a random
wave field. In contrast with the Hasselmann kinetic equation, the GKE can describe fast
spectral changes occurring when a wave field is driven out of a quasi-equilibrium state by a
fast increase or decrease of wind, or by other factors. In these cases, a random wave field
evolves on the dynamic timescale typical of coherent wave processes, rather than on the
kinetic timescale predicted by the conventional statistical theory. Besides that, the generalised
theory allows to trace the evolution of higher statistical moments of the field, notably
the kurtosis, which is important for assessing the risk of freak waves and other
applications.
A new efficient and highly parallelised algorithm for the numerical simulation of the
generalised kinetic equation is presented and discussed. Unlike in the case of the Hasselmann
equation, the algorithm takes into account all (resonant and non-resonant) nonlinear wave
interactions, but only approximately resonant interactions contribute to the spectral evolution.
However, counter-intuitively, all interactions contribute to the kurtosis. Without forcing or
dissipation, the algorithm is shown to conserve the relevant integrals. We show
that under steady wind forcing the wave field evolution predicted by the GKE is
close to the predictions of the conventional statistical theory, which is applicable in
this case. In particular, we demonstrate the known long-term asymptotics for the
evolution of the spectrum. When the wind forcing is not steady (in the simplest case, an
instant increase or decrease of wind occurs), the generalised theory is the only way
to study the spectral evolution, apart from the direct numerical simulation. The
focus of the work is a detailed analysis of the fast evolution after an instant change
of forcing, and of the subsequent transition to the new quasi-stationary state of a
wave field. It is shown that both increase and decrease of wind lead to a significant
transient increase of the dynamic kurtosis, although these changes remain small
compared to the changes of the other component of the kurtosis, which is due to bound
harmonics.
A special consideration is given to the case of the squall, i.e. an instant and large (by a
factor of 2–4) increase of wind, which lasts for O(102) characteristic wave periods. We show
that fast adjustment processes lead to the formation of a transient spectrum, which has a
considerably narrower peak than the spectra developed under a steady forcing. These
transient spectra differ qualitatively from those predicted by the Hasselmann kinetic equation
under the squall with the same parameters.
1. S.Annenkov, V.Shrira (2006) Role of non-resonant interactions in evolution of
nonlinear random water wave fields, J. Fluid Mech. 561, 181–207. |
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