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Ocean Engineering

Nonlinear Crest, Trough, and Wave Height Distributions in Sea States With Double-Peaked Spectra

[+] Author and Article Information
Felice Arena

Department of Mechanics and Materials, ‘Mediterranea’ University of Reggio Calabria, Localita Feo di Vito, 89100 Reggio Calabria, Italyarena@unirc.it

C. Guedes Soares

Unit of Marine Technology and Engineering, Instituto Superior Técnico, Technical University of Lisbon, Avenida Rovisco Pais, 1049-001 Lisboa, Portugalguedess@mar.ist.utl.pt

J. Offshore Mech. Arct. Eng 131(4), 041105 (Sep 30, 2009) (8 pages) doi:10.1115/1.3160657 History: Received July 03, 2007; Revised May 25, 2008; Published September 30, 2009

The peak to trough distributions of nonlinear high sea waves in bimodal sea states in deep water are investigated. The statistical distribution of wave height is first analyzed by considering the Boccotti’s expression, where the parameters of the distribution are calculated for some bimodal spectra of sea states recorded in the Atlantic Ocean. The nonlinear crest and trough distributions are then obtained, particularizing for two peaked spectra the second-order Fedele and Arena expression, which depends on two parameters. The results have been finally validated by means of Monte Carlo simulations of second-order random waves with bimodal spectra.

Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Bimodal spectrum recorded at Sines (Portugal) in December 2000

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Figure 2

Bimodal spectrum recorded at Sines (Portugal) in December 2000

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Figure 3

Bimodal spectrum recorded in North Atlantic Ocean (see Ref. 1)

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Figure 4

Bimodal spectrum recorded in North Atlantic Ocean (see Ref. 1)

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Figure 5

Spectrum A. Distribution of crest-to-trough wave heights: Comparison among the Rayleigh distribution (Eq. 1), the theoretical complete distribution with K=1 (Eq. 2), and the data from simulations (upper panel: data of linear simulations; lower panel: data of nonlinear simulations).

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Figure 6

Spectrum A. Upper panel: Comparison among the Rayleigh distribution (Eq. 8), the theoretical nonlinear distribution (Eq. 9), and the crest data from nonlinear simulations. Lower panel: Comparison among the Rayleigh distribution (Eq. 8), the theoretical nonlinear distribution (Eq. 10), and the trough data from nonlinear simulations.

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Figure 7

Spectrum A. Comparison among the Rayleigh (Eq. 8) and the theoretical crest and trough distributions from linear simulations

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Figure 8

Spectrum B. Distribution of crest-to-trough wave heights: Comparison among the Rayleigh distribution (Eq. 1), the theoretical complete distribution with K=1 (Eq. 2), and the data from simulations (upper panel: data of linear simulations; lower panel: data of nonlinear simulations).

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Figure 9

Spectrum B. Upper panel: comparison among the Rayleigh distribution (Eq. 8), the theoretical nonlinear distribution (Eq. 9), and the crest data from nonlinear simulations. Lower panel: comparison among the Rayleigh distribution (Eq. 8), the theoretical nonlinear distribution (Eq. 10), and the trough data from nonlinear simulations.

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Figure 10

Spectrum B. Comparison among the Rayleigh (Eq. 8) and the theoretical crest and trough distributions from linear simulations.

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Figure 11

Spectrum C. Distribution of crest-to-trough wave heights: comparison among the Rayleigh distribution (Eq. 1), the theoretical complete distribution with K=1 (Eq. 2), and the data from simulations (upper panel: data of linear simulations; lower panel: data of nonlinear simulations).

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Figure 12

Spectrum C. Upper panel: comparison among the Rayleigh distribution (Eq. 8), the theoretical nonlinear distribution (Eq. 9), and the crest data from nonlinear simulations. Lower panel: comparison among the Rayleigh distribution (Eq. 8), the theoretical nonlinear distribution (Eq. 10), and the trough data from nonlinear simulations.

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Figure 13

Spectrum C. Comparison among the Rayleigh (Eq. 8) and the theoretical crest and trough distributions from linear simulations.

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Figure 14

Spectrum D. Distribution of crest-to-trough wave heights: Comparison among the Rayleigh distribution (Eq. 1), the theoretical complete distribution and with K=1 (Eq. 2), and the data from simulations (upper panel: data of linear simulations; lower panel: data of nonlinear simulations).

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Figure 15

Spectrum D. Upper panel: comparison among the Rayleigh distribution (Eq. 8), the theoretical nonlinear distribution (Eq. 9), and the crest data from nonlinear simulations. Lower panel: comparison among the Rayleigh distribution (Eq. 8), the theoretical nonlinear distribution (Eq. 10), and the trough data from nonlinear simulations.

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Figure 16

Spectrum D. Comparison among the Rayleigh (Eq. 8) and the theoretical crest and trough distributions from linear simulations.

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