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Nonlinear Crest Height Distribution in Three-Dimensional Ocean Waves

[+] Author and Article Information
Felice Arena

Department of Mechanics and Materials, Mediterranea University of Reggio Calabria, Feo di Vito, 89122 Reggio Calabria, Italyarena@unirc.it

Alfredo Ascanelli1

Department of Mechanics and Materials, Mediterranea University of Reggio Calabria, Feo di Vito, 89122 Reggio Calabria, Italyalfredo.ascanelli@unirc.it

1

Also at Impresa Pietro Cidonio S.p.A., Viale Mazzini, 88-00195 Rome, Italy.

J. Offshore Mech. Arct. Eng 132(2), 021604 (Mar 10, 2010) (6 pages) doi:10.1115/1.4000394 History: Received October 17, 2008; Revised February 21, 2009; Published March 10, 2010; Online March 10, 2010

The interest and studies on nonlinear waves are increased recently for their importance in the interaction with floating and fixed bodies. It is also well-known that nonlinearities influence wave crest and wave trough distributions, both deviating from the Rayleigh law. In this paper, a theoretical crest distribution is obtained, taking into account the extension of Boccotti’s quasideterminism theory (1982, “On Ocean Waves With High Crests,” Meccanica, 17, pp. 16–19), up to the second order for the case of three-dimensional waves in finite water depth. To this purpose, the Fedele and Arena (2005, “Weakly Nonlinear Statistics of High Random Waves,” Phys. Fluids, 17(026601), pp. 1–10) distribution is generalized to three-dimensional waves on an arbitrary water depth. The comparison with Forristall’s second order model (2000, “Wave Crest Distributions: Observations and Second-Order Theory,” J. Phys. Oceanogr., 30(8), pp. 1931–1943) shows the theoretical confirmation of his conclusion: The crest distribution in deep water for long-crested and short-crested waves are very close to each other; in shallow water the crest heights in three-dimensional waves are greater than values given by the long-crested model.

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Figures

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Figure 4

Comparison among the Rayleigh, Forristall (either 2D and 3D formulation), and theoretical (Eq. 15) distributions for different values of the water depth, either for short-crested or long-crested waves

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Figure 3

Parameter α of the crest and trough distributions, as a function of the Phillips parameter of the spectrum: short-crested waves

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Figure 2

Parameter α of the crest and trough distributions, as a function of the Phillips parameter of the spectrum: long-crested waves

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Figure 1

Parameter α of the crest and trough distributions, as a function of the relative water depth for the Phillips parameter of the spectrum equal to 0.01. Upper panel: long-crested waves. Lower panes: short-crested waves.

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