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| Titel |
Numerical investigation of breaking waves in spectral environment |
| VerfasserIn |
Dmitry Chalikov, Alexander Babanin |
| 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 |
250047107
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| Zusammenfassung |
| Mechanism of wave breaking obtains clear interpretation when number of wave modes is
small. Most typical configuration investigated numerically referred to case of single wave
with two superimposed disturbances. It seems that in such situation the main reason of
breaking is the modulational-instability type of Benjamin-Feir instability, when the main
mode is growing taking the energy from disturbances, which should carry enough energy. In
the model, development of wave breaking is usually recognized by numerical instability,
which develops when some threshold reaches a critical value. This is definitely incorrect,
since such threshold often depends on correctness of numerical scheme rather than on
physical reasons.
Much more complicated and precise method can be based on 1-D numerical models
derived in conformal coordinates. Between many advantages of this approach (for example –
very high accuracy) the main advantage is that model is able to predict the situation when part
of surface becomes vertical. After this moment, the situation never returns back to stability.
This moment can be recognized as a point of instability with good accuracy. Second
advantage of the conformal model is that its initial condition can account for a large number
of modes, thus allowing to simulate the wave fields which correspond to realistic wave
spectra.
An onset of the breaking depends on many poorly controlled factors. Even if the wave
spectrum in initial conditions is fixed, the time up to occurrence of breaking is different for
different initial set of phasesÏk. Therefore, the statistics of breaking can be investigated in the
course of large number of numerical experiments.
All calculations were done for number of modes M = 1,000and number of grid points
N = 4,000. Wavenumber at the peak of spectrum kp is equal to 10, number of modes
assigned in initial conditions is equal 100. To accelerate the approach to breaking, the initial
conditions were generated for JONSWAP spectrum at Ωp = 2 (inverse wave age). Hence, the
wind was twice the phase velocity at the peak that corresponds to the case of developing
waves. Time step Δt was equal 0.0001. As many as 5,000 runs with random set of phases
were performed up to termination due to breaking. The limiting time t = 1,000 (503 periods
of peak wave) was reached just in several runs, and these cases were excluded from
consideration.
All considered cases can be attributed to situations of strong nonlinearity: the probability
of extreme waves exceeding two significant wave height was as high as 0.01%, and
crest-to-trough wave height reached as large values as 2.5Hs. Contrary to previous
suggestions, it was found that rate of growth of wave energy is not a criterion of breaking.
Breaking waves in spectral environment do not reach the Stokes limit either. More reliable
indications of breaking are: (1) increase of horizontal asymmetry, when downwind slope
becomes much steeper than that upwind; (2) increase of negative vertical particle
acceleration; (3) growth of local skewness; and some others. However, it should be
emphasized that all these criteria have very large scatter. For example, the overall
steepness of wave (the ratio of trough-to-crest height of main mode to its wavelength
cannot be a criterion of breaking, since in the spectral environment the breaking
can develop at such low steepness as 0.1. Contrary to the modulational instability,
development of wave breaking occurs very rapidly: it goes through all phases of breaking
just over a half of dominant period in the wave field. It was found that, contrary to
breaking in idealized conditions, the breaking in a multi-mode wave field is an
essentially random phenomenon, which depends on local conditions at very short time
scales.
From practical point of view, the probability of breaking and its severity as a function of
wave spectrum is more important than understanding of the intimate mechanism of breaking
itself. This problem can be also investigated with the direct wave model. When the
model is set for simulation of long-time development of spectrum, the termination of
run due to breaking can be prevented by introducing the algorithm of breaking
parameterization, based on selective high-frequency smoothing of the interface and the
surface potential profile in a physical space. This approach allows to investigate
the spectral properties of dissipation and its dependence on the wave spectrum. |
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