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| Titel |
Significance of laboratory observations for modeling wind-driven seas |
| VerfasserIn |
S. I. Badulin, G. Caulliez |
| Konferenz |
EGU General Assembly 2009
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 11 (2009) |
| Datensatznummer |
250030418
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| Zusammenfassung |
| In what sense can the laboratory wind-wave observations help in investigating and modeling
wave growth in wind-driven seas? This old outstanding question is addressed by an extensive
laboratory study in the large IRPHE wind-wave tank (Caulliez, 2009). We show that for a
wide range of parameters the fetch-limited wind wave growth observed in the facility follows
fairly well the wind-wave growth law predicted by weak turbulence model (Badulin et al.,
2007). The wind speeds were ranging from 3.5 to 16 m/s and wave ages cp-U10 were smaller
than 0.15 (cp being the phase speed of spectral peak waves, and U10 the equivalent 10 m level
wind speed).
The recent model of wind wave evolution proposed by Badulin et al. (2007) assumes the
dominance of nonlinear four-wave resonant interactions over the direct wave input
from wind and wave dissipation. The model predicts that the total wave energy is
rigidly linked to the total wave energy flux (i.e. the energy growth rate dE-dt) by the
relationship:
E Ï4 ( Ï3dE -dt)1-3
--2p= α -p--2---
g g
(1)
where the wave energy E is defined in a “wind-wave study sense” as the water surface
elevation variance density -¨Î·2-©, Ïp is the wave spectral peak frequency, and α is a
self-similarity parameter. Experimental data reveal that the spectral peak wave energy
observed in the wind-wave tank at large fetches evolves in accordance with the asymptotic
weakly turbulent theory in a wide range of wind speeds. Furthermore, the found
value of the self-similarity parameter α ( α - 0.5) matches very well the estimates
from more than 20 data set collected over the last 50 years of wind-wave studies at
sea.
It is then shown that the characteristic parameters of the laboratory wave field
development follow remarkably well the 3-2 Toba’s law H ~ T3-2, H and T being the
significant wave height and period. In a definite range of fetches and wind speeds, its
dependency on friction velocity u* is also described by an expression similar to those
proposed by Toba (1972) on local energy balance and dimensional considerations,
i.e.
1-2 3-2
H = B(gu*) T
(2)
g being the gravity acceleration and B a constant. From a physical viewpoint, this heuristic
law in u* infers not only the total wave energy flux dE-dt in Eq.(1) to be constant as pointed
out by Badulin et al. (2007), but also the ratio of the form drag due to dominant waves to the
total surface drag to be constant.
Finally, the validity of the key assumption of the model, i.e. the dominance of nonlinear
transfer over the net wave energy flux, is analyzed and domain of its applicability for
laboratory observations is delimited. The weak turbulence model thus finds a new
corroboration in wind-wave tank experiments and may bring a new vision for data analysis in
the near future.
References
1. S. I. Badulin, A. V. Babanin, D. Resio, and V. Zakharov. Weakly turbulent laws of
wind-wave growth. J. Fluid Mech., 591:339–378, 2007.
2. G. Caulliez. Characteristic slopes of short wind waves and dependence on scale and wind
speed. to appear, 2009.
3. Y. Toba. Local balance in the air-sea boundary processes. I. On the growth process of
wind waves. J. Oceanogr. Soc. Japan, 28:109–121, 1972. |
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