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Why rogue waves occur atop abrupt depth transitions

Published online by Cambridge University Press:  26 May 2021

Yan Li Open the ORCID record for Yan Li [Opens in a new window] ,
Samuel Draycott Open the ORCID record for Samuel Draycott [Opens in a new window] ,
Yaokun Zheng ,
Zhiliang Lin ,
Thomas A.A. Adcock Open the ORCID record for Thomas A.A. Adcock [Opens in a new window]  and
Ton S. van den Bremer Open the ORCID record for Ton S. van den Bremer [Opens in a new window]
Yan Li*
Affiliation:
Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK Department of Energy and Process Engineering, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
Samuel Draycott
Affiliation:
Department of Mechanical, Aerospace and Civil Engineering, University of Manchester, Manchester M13 9PL, UK
Yaokun Zheng
Affiliation:
State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China
Zhiliang Lin
Affiliation:
State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China
Thomas A.A. Adcock
Affiliation:
Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK
Ton S. van den Bremer
Affiliation:
Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK Faculty of Civil Engineering and Geosciences, Delft University of Technology, 2628 CD Delft, The Netherlands
*
†Email address for correspondence: yan.li@ntnu.no
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Abstract

Abrupt depth transitions (ADTs) have recently been identified as potential causes of ‘rogue’ ocean waves. When stationary and (close-to-) normally distributed waves travel into shallower water over an ADT, distinct spatially localized peaks in the probability of extreme waves occur. These peaks have been predicted numerically, observed experimentally, but not explained theoretically. Providing this theoretical explanation using a leading-order-physics-based statistical model, we show, by comparing to new experiments and numerical simulations, that the peaks arise from the interaction between linear free and second-order bound waves, also present in the absence of the ADT, and new second-order free waves generated due to the ADT.

JFM classification

Waves/Free-surface Flows: Surface gravity waves

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JFM Rapids
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Journal of Fluid Mechanics , Volume 919 , 25 July 2021 , R5
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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