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Research Papers: CFD and VIV

The Effect of Third-Order Nonlinearities on the Statistical Distributions of Wave Heights, Crests and Troughs in Bimodal Crossing Seas

[+] Author and Article Information
Petya G. Petrova

Centre for Marine Technology and Engineering (CENTEC),
Instituto Superior Técnico,
Technical University of Lisbon,
Av. Rovisco Pais 1049-001,
Lisboa, Portugal

M. Aziz Tayfun

College of Engineering and Petroleum,
Kuwait University,
Safat 13060, Kuwait

C. Guedes Soares

Centre for Marine Technology and Engineering (CENTEC),
Instituto Superior Técnico,
Technical University of Lisbon,
Av. Rovisco Pais 1049-001,
Lisboa, Portugal
e-mail: guedess@mar.ist.utl.pt

1Corresponding author.

Contributed by the Ocean Offshore and Arctic Engineering Division of ASME for publication in the Journal of Offshore Mechanics and Arctic Engineering. Manuscript received May 1, 2011; final manuscript received October 9, 2011; published online February 25, 2013. Assoc. Editor: Arvid Naess.

J. Offshore Mech. Arct. Eng 135(2), 021801 (Feb 25, 2013) (9 pages) Paper No: OMAE-11-1038; doi: 10.1115/1.4007381 History: Received May 01, 2011; Revised October 09, 2011

This paper investigates the effect of third-order nonlinearities on the statistical distributions of wave heights, crests, and troughs of waves mechanically generated in a deep-water basin and simulating two crossing systems characterized by bimodal spectra. The observed statistics exhibits various effects of third-order nonlinearities, in a manner dependent on both the distance from the wave-maker and the angle between the mean directions of the component wave systems. In order to isolate and demonstrate the effects of third-order nonlinearities by themselves, the vertically asymmetric distortions induced by second-order bound waves are removed from the observed time series. It appears then that the distributions of wave crests, troughs and heights extracted from the nonskewed records clearly deviate from the Rayleigh distribution, suggesting that the waves are characterized by nonlinear corrections of higher-order than the typical of second-order waves. Nonetheless, some models developed for weakly nonlinear second-order waves can still be used in describing wave heights, crests and troughs in mixed seas, provided that the relevant distribution parameters are modified, so as to reflect the effects of third-order corrections and some basic characteristics of the mixed seas.

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Copyright © 2013 by ASME
Topics: Waves , Seas , Gages
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Figures

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Fig. 1

Definition sketch illustrating various properties of ACF for bimodal seas with prevalent low-frequency spectral energy or comparable low-high frequency energies

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Fig. 2

Test equipment in the MARINTEK basin

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Fig. 3

Exceedance distributions of wave heights along the tank for θ = 60 deg

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Fig. 4

Exceedance distributions of wave heights along the tank for θ = 120 deg

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Fig. 5

Empirical dependence rm(h) versus the theoretical model from Eq. (12)

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Fig. 6

Exceedance distributions of wave crests and troughs along the tank for θ = 60 deg

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Fig. 7

Exceedance distributions of wave crests and troughs along the tank for θ = 120 deg

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Fig. 8

(a) and (b) Nonlinear surface profile, second-order corrections and the resulting nonskew profile; (c) and (d) the exceedance distributions of crests, troughs, and heights extracted from the nonskew surface series

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