Editorial Type:
Article
Article Type:
Research Article

Second-Order Theory and Setup in Surface Gravity Waves: A Comparison with Experimental Data

A. Toffoli Katholieke Universiteit Leuven, Leuven, Belgium

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J. Monbaliu Katholieke Universiteit Leuven, Leuven, Belgium

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M. Onorato Universitá di Torino, Turin, Italy

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A. R. Osborne Universitá di Torino, Turin, Italy

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A. V. Babanin Swinburne University of Technology, Hawthorn, Australia

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E. Bitner-Gregersen Det Norske Veritas, Høvik, Norway

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Print Publication:
01 Nov 2007
DOI:
https://doi.org/10.1175/2007JPO3634.1
Page(s):
2726–2739
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Abstract

The second-order, three-dimensional, finite-depth wave theory is here used to investigate the statistical properties of the surface elevation and wave crests of field data from Lake George, Australia. A direct comparison of experimental and numerical data shows that, as long as the nonlinearity is small, the second-order model describes the statistical properties of field data very accurately. By low-pass filtering the Lake George time series, there is evidence that some energetic wave groups are accompanied by a setup instead of a setdown. A numerical study of the coupling coefficient of the second-order model reveals that such an experimental result is consistent with the second-order theory, provided directional spreading is included in the wave spectrum. In particular, the coupling coefficient of the second-order difference contribution predicts a setup as a result of the interaction of two waves with the same frequency but with different directions. This result is also confirmed by numerical simulations. Bispectral analysis, furthermore, indicates that this setup is a statistically significant feature of the observed wave records.

& Current affiliation: Det Norske Veritas, Høvik, Norway

Corresponding author address: Alessandro Toffoli, Det Norske Veritas, Veritasveien 1, 1322 Høvik, Norway. Email: alessandro.toffoli@dnv.com

Abstract

The second-order, three-dimensional, finite-depth wave theory is here used to investigate the statistical properties of the surface elevation and wave crests of field data from Lake George, Australia. A direct comparison of experimental and numerical data shows that, as long as the nonlinearity is small, the second-order model describes the statistical properties of field data very accurately. By low-pass filtering the Lake George time series, there is evidence that some energetic wave groups are accompanied by a setup instead of a setdown. A numerical study of the coupling coefficient of the second-order model reveals that such an experimental result is consistent with the second-order theory, provided directional spreading is included in the wave spectrum. In particular, the coupling coefficient of the second-order difference contribution predicts a setup as a result of the interaction of two waves with the same frequency but with different directions. This result is also confirmed by numerical simulations. Bispectral analysis, furthermore, indicates that this setup is a statistically significant feature of the observed wave records.

& Current affiliation: Det Norske Veritas, Høvik, Norway

Corresponding author address: Alessandro Toffoli, Det Norske Veritas, Veritasveien 1, 1322 Høvik, Norway. Email: alessandro.toffoli@dnv.com

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