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| Titel |
Modulational instability and wave growth in finite water depth |
| VerfasserIn |
Leandro Fernández, Miguel Onorato, Jaak Monbaliu, Alessandro Toffoli |
| Konferenz |
EGU General Assembly 2013
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 15 (2013) |
| Datensatznummer |
250079678
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| Zusammenfassung |
| The main feature of waves dynamic is the existence of modulational instability, which is
the result of nonlinear interaction between a steep carrier wave with amplitude
a0 and wave vector k0 and two infinitesimal side-band disturbances with wave
vector k1 and k2. In finite water depth, the interaction between waves and the ocean
floor induces a mean current. This subtracts energy from wave instability and the
modulational instability ceases for relative water depth kh = 1.36. On the other
hand, in general, unstable disturbances propagate obliquely to the direction of the
carrier wave. When the depth decreases, the instability area becomes narrow and
therefore its area decreases. At present, the growth of the sidebands has been treated in
terms of the amplification of weak modulation imposed on a harmonic wave. A
higher order spectral method is used to perform simulations of the random sea
surface in arbitrary water depth. Third and fifth order of non-linearity expansion
has been used to investigate the effect of modulational instability on random wave
fields. Several configurations are considered with disturbances oblique and collinear
with the primary waves and this for different water depths. The analysis shows
that in the collinear case there is suppression of modulation instability for relative
water depth kh=1.36. However, amplifications are observed in longer simulations.
For directional cases the destabilization of a primary wave train and subsequent
growth of side band perturbations produces amplification of surface elevations. |
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