Freak wave in high-order weakly nonlinear wave evolution with bottom topography change

Lyu, Zuorui; Mori, Nobuhito; Kashima, Hiroaki

doi:10.1016/j.coastaleng.2021.103918

Cited by 13 publications

(12 citation statements)

References 18 publications

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“…In the 1-D problem of the unidirectional wave train, as in Lyu et al. (2021), the evolution equation of is numerically solved in a spatial step by the pseudo-spectral method. Based on the periodicity of the wave envelop in time and space, the partial differential term in the evolution equation can be transformed into a more concise form by using Fourier transform.…”

Section: Methodsmentioning

confidence: 99%

“…Similar to Lyu et al. (2021), we integrate in (2.19) at each step from offshore to onshore, assuming periodic boundary conditions in time, and construct the surface elevation in a discrete 2-D + T form. Equation (2.19) considers the contribution from first order to second order and second harmonic.…”

Section: Methodsmentioning

confidence: 99%

“…Several numerical studies of the different nonlinear evolution equations have been given, such as the NLS-like equation (Zeng & Trulsen 2012; Kimmoun et al. 2021; Lyu, Mori & Kashima 2021), the Korteweg–De Vries (KdV) equation (Sergeeva, Pelinovsky & Talipova 2011; Majda, Moore & Qi 2019), Boussinesq equations (Gramstad et al. 2013; Kashima, Hirayama & Mori 2014; Zhang et al.…”

Section: Introductionmentioning

confidence: 99%

“…To develop the freak wave analysis in 2-D wavefields, this study investigates the directional nonlinear modulated wave evolution in an uneven bottom as an expansion to the work of Lyu et al. (2021). The dNLS equation in 2-D form for a slow-varying bottom is applied to establish the numerical model.…”

Section: Introductionmentioning

confidence: 99%

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

2023

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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.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2023

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“…Wave focusing: Wave energy may be concentrated in a small area because of wave trapping, refraction, and re ection, such as wave-current interaction; wind force; bottom topography in uence, etc. [11][12][13]. e modulation instability, also known as Benjamin-Feir instability [14], has been accepted by many researchers to explain the occurrence of freak waves.…”

Section: Introductionmentioning

confidence: 99%

Study on Numerical Simulation and Electromagnetic Scattering of Time-Invariant Freak Waves

Han

Liu

2022

International Journal of Antennas and Propagation

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The occurrence probability of freak waves is related to the sea wave spectrum. In this paper, different wave spectrums are used to simulate time-invariant three-dimensional freak waves. Freak waves that meet the international standards are generated at fixed time and location by adjusting the energy of the wavelets. We studied the occurrence probability of freak waves under the conditions of different wave spectrums, different wind speeds, and different modulation ratios and optimized the calculation speed of the model. Simulation data show that the difference in the shape of the wave spectrum affects the probability of freak waves occurrence. The model conforms to the Benjamin–Feir index (BFI), and the ratio of wave steepness to spectrum bandwidth is the key. In this paper, the Kirchhoff approximation theory is used to study the electromagnetic scattering (EM scattering) properties of freak waves on the large scale. We ideally calculate the Normalized Radar Cross-Section (NRCS) from the sea surface with freak waves, under different wind speeds and different grazing angles. The NRCS of freak waves is extremely low, and the increase of wind speed and the decrease of the grazing angle will make the detection of freak waves more difficult. The possibility of detection of freak waves is higher at high grazing angles (low incidence angles). The numerical simulations provide reference for engineering.

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Experiments on uni-directional and nonlinear wave group shoaling

et al. 2021

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Freak wave in high-order weakly nonlinear wave evolution with bottom topography change

Cited by 13 publications

References 18 publications

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

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

Study on Numerical Simulation and Electromagnetic Scattering of Time-Invariant Freak Waves

Experiments on uni-directional and nonlinear wave group shoaling

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