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Freak wave in a two-dimensional directional wavefield with bottom topography change. Part 1. Normal incidence wave

Published online by Cambridge University Press:  17 March 2023

Zuorui Lyu Open the ORCID record for Zuorui Lyu [Opens in a new window] ,
Nobuhito Mori Open the ORCID record for Nobuhito Mori [Opens in a new window]  and
Hiroaki Kashima
Zuorui Lyu
Affiliation:
Coastal Engineering Laboratory, Department of Civil Engineering, School of Engineering, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan
Nobuhito Mori*
Affiliation:
Disaster Prevention Research Institute, Kyoto University, Gokasho, Uji, Kyoto 611-0011, Japan Swansea University, Bay Campus, Skewen, Swansea SA1 8EN, UK
Hiroaki Kashima
Affiliation:
Coastal and Ocean Engineering Department, Port and Airport Research Institute, 3-1-1 Nagase, Yokosuka, Kanagawa 239-0826, Japan
*
†Email address for correspondence: mori@oceanwave.jp
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Abstract

In the propagation and evolution of sea waves, previous studies pointed out that the occurrence of the freak wave height is significantly related to the quasi-resonant four-wave interaction in the modulated waves. From numerical--experimental study over an uneven bottom, the nonlinear effect caused by the bathymetry change also contributes to the occurrence of extreme events in unidirectional waves. To comprehensively analyse the two-dimensional wavefield, this study develops an evolution model for a directional random wavefield based on the depth-modified nonlinear Schrödinger equation, which considers the nonlinear resonant interactions and the wave shoaling the shallow water. Through Monte Carlo simulation, we discuss the directional effect on the four-wave interaction in the wave train and the maximum wave height distribution from deep to shallow water with a slow varying slope. The numerical result indicates that the directional spreading has a dispersion effect on the freak wave height. In a shallow-water environment, this effect becomes weak, and the bottom topography change is the main influencing factor in the wave evolution.

JFM classification

Geophysical and Geological Flows: Coastal engineering Instability: Nonlinear instability Geophysical and Geological Flows: Shallow water flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 959 , 25 March 2023 , A19
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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