{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T19:30:19Z","timestamp":1774294219551,"version":"3.50.1"},"reference-count":48,"publisher":"ASME International","issue":"2","content-domain":{"domain":["asmedigitalcollection.asme.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2013,5,1]]},"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.1115\/1.4007381","type":"journal-article","created":{"date-parts":[[2013,4,24]],"date-time":"2013-04-24T20:49:39Z","timestamp":1366836579000},"update-policy":"https:\/\/doi.org\/10.1115\/crossmarkpolicy-asme","source":"Crossref","is-referenced-by-count":18,"title":["The Effect of Third-Order Nonlinearities on the Statistical Distributions of Wave Heights, Crests and Troughs in Bimodal Crossing Seas"],"prefix":"10.1115","volume":"135","author":[{"given":"Petya G.","family":"Petrova","sequence":"first","affiliation":[{"name":"Centre for Marine Technology and Engineering (CENTEC), Instituto Superior T\u00e9cnico, Technical University of Lisbon, Av. Rovisco Pais 1049-001, Lisboa, Portugal"}]},{"given":"M.","family":"Aziz Tayfun","sequence":"additional","affiliation":[{"name":"College of Engineering and Petroleum, Kuwait University, Safat 13060, Kuwait"}]},{"given":"C.","family":"Guedes Soares","sequence":"additional","affiliation":[{"name":"Centre for Marine Technology and Engineering (CENTEC), Instituto Superior T\u00e9cnico, Technical University of Lisbon, Av. 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