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Extreme Waves in Crossing Sea States

Joseph Brennan

School of Mathematics and Statistics, University College Dublin, Belfield Dublin 4, Ireland

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John M. Dudley

Institut FEMTO-ST CNRS, Université de Franche-Comté, UMR 6174, France

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Frédéric Dias

http://orcid.org/0000-0002-5123-4929

School of Mathematics and Statistics, University College Dublin, Belfield Dublin 4, Ireland

E-mail Address: frederic.dias@ucd.ie

Corresponding author.

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https://doi.org/10.1142/S252980701850001XCited by:13 (Source: Crossref)

Abstract

The evolution of crossing sea states and the emergence of rogue waves in such systems are studied via numerical simulations performed using a higher order spectral (HOS) method to solve the free surface Euler equations with a flat bottom. Two classes of crossing sea states are analyzed: one using directional spectra from the Draupner wave crossing at different angles, another considering a Draupner-like spectra crossed with a narrowband JONSWAP state to model spectral growth between wind sea and swell. These two classes of crossing sea states are constructed using the spectral output of a WAVEWATCH III hindcast on the Draupner rogue wave event. We measure ensemble statistical moments as functions of time, finding that although the crossing angle influences the statistical evolution to some degree, there are no significant third-order effects present. Additionally, we pay particular attention to the mean sea level measured beneath extreme crest heights, the elevation of which (set up or set down) is shown to be related to the spectral content in the low wavenumber region of the corresponding spectrum.

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