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

[+] Author Affiliations
Petya G. Petrova, C. Guedes Soares

Technical University of Lisbon, Lisbon, Portugal

M. Aziz Tayfun

Kuwait University, Safat, Kuwait

Paper No. OMAE2011-50313, pp. 923-933; 11 pages
  • ASME 2011 30th International Conference on Ocean, Offshore and Arctic Engineering
  • Volume 2: Structures, Safety and Reliability
  • Rotterdam, The Netherlands, June 19–24, 2011
  • ISBN: 978-0-7918-4434-2
  • Copyright © 2011 by ASME


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, simulating two crossing systems characterized by bimodal spectra. Observed statistics exhibit 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, 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 non-skewed series clearly deviate from the Rayleigh distribution, suggesting that 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 relevant distribution parameters are modified so as to reflect the effects of third-order corrections and some basic characteristics of mixed seas.

Copyright © 2011 by ASME



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