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| Titel |
Freak waves in nonlinear unidirectional wave trains over a sloping bottom |
| VerfasserIn |
Karsten Trulsen, Anne Raustøl, Lisa Bæverfjord Rye |
| Konferenz |
EGU General Assembly 2015
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 17 (2015) |
| Datensatznummer |
250111831
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| Publikation (Nr.) |
 EGU/EGU2015-11975.pdf |
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| Zusammenfassung |
| Water surface waves evolving on constant depth experience decreasing nonlinear modulation
with decreasing depth, and it is anticipated that the occurrence of freak waves is similarly
reduced (e.g. Mori & Janssen 2006; Janssen & Onorato 2007; Janssen 2009). Waves evolving
on non-uniform depth will additionally experience non-equilibrium effects, having to
adapt to a new depth along their path. This may cause interesting behavior with
respect to freak wave occurrence, different from that suggested above. For waves
propagating from quite shallow to even more shallow water over a slope, Sergeeva et al.
(2011) found a local maximum of extreme waves on the shallow end of the slope.
For waves propagating from quite deep to shallower water over a very long slope,
Zeng & Trulsen (2012) found no local maximum of extreme waves on the shallow
end of the slope. They found that the waves may need a considerable distance of
propagation before reaching their new equilibrium statistics. They even found some
cases of a local minimum of extreme wave occurrence at the shallow end of the
slope. Experimental evidence of a local maximum of extreme wave statistics on the
shallow end of the slope was found by Trulsen et al. (2012), and corresponding
numerical simulations were later done by Gramstad et al. (2013). The works cited
above appear to suggest two different regimes, the presence of a local maximum
of extreme waves at the shallow end of a slope, or the lack of such a maximum,
possibly depending on the depths involved, or possibly depending on the length of the
slope.
We have carried out a set of carefully controlled experiments with irregular waves
propagating over variable depth as suggested in the figure. A movable array of 16 ultrasound
probes was used to measure surface elevation, such that high resolution was achieved to catch
the location of local maxima and minima of extreme wave occurrence. We have found that
there are indeed two different regimes depending on the depth, and we have identified the
limiting depth dividing these regimes.
This research has been supported by the University of Oslo and the Research Council of
Norway through Grant No. 214556/F20.
GRAMSTAD, O., ZENG, H., TRULSEN, K. & PEDERSEN, G.ÂK. 2013 Freak waves in
weakly nonlinear unidirectional wave trains over a sloping bottom in shallow water.
Phys.ÂFluids 25, 122103.
JANSSEN, P. A. E.ÂM. 2009 On some consequences of the canonical transformation in
the Hamiltonian theory of water waves. J.ÂFluid Mech. 637, 1–44.
JANSSEN, P. A. E.ÂM. & ONORATO, M. 2007 The intermediate water depth limit of the
Zakharov equation and consequences for wave prediction. J.ÂPhys.ÂOceanogr. 37,
2389–2400.
MORI, N. & JANSSEN, P. A. E.ÂM. 2006 On kurtosis and occurrence probability of
freak waves. J.ÂPhys.ÂOceanogr. 36, 1471–1483.
SERGEEVA, A., PELINOVSKY, E. & TALIPOVA, T. 2011 Nonlinear random wave field in
shallow water: variable Korteweg–de Vries framework. Nat.ÂHazards Earth Syst.ÂSci. 11,
323–330.
TRULSEN, K., ZENG, H. & GRAMSTAD, O. 2012 Laboratory evidence of freak waves
provoked by non-uniform bathymetry. Phys.ÂFluids 24, 097101.
ZENG, H. & TRULSEN, K. 2012 Evolution of skewness and kurtosis of weakly
nonlinear unidirectional waves over a sloping bottom. Nat.ÂHazards Earth Syst.ÂSci. 12,
631–638. |
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