Nonlinear random wave field in shallow water: variable Korteweg-de Vries framework
TLDR
In this paper, the transformation of a random wave field in shallow water of variable depth is analyzed within the framework of the variable-coefficient Korteweg-de Vries equation.Abstract:
. The transformation of a random wave field in shallow water of variable depth is analyzed within the framework of the variable-coefficient Korteweg-de Vries equation. The characteristic wave height varies with depth according to Green's law, and this follows rigorously from the theoretical model. The skewness and kurtosis are computed, and it is shown that they increase when the depth decreases, and simultaneously the wave state deviates from the Gaussian. The probability of large-amplitude (rogue) waves increases within the transition zone. The characteristics of this process depend on the wave steepness, which is characterized in terms of the Ursell parameter. The results obtained show that the number of rogue waves may deviate significantly from the value expected for a flat bottom of a given depth. If the random wave field is represented as a soliton gas, the probabilities of soliton amplitudes increase to a high-amplitude range and the number of large-amplitude (rogue) solitons increases when the water shallows.read more
Citations
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Laboratory evidence of freak waves provoked by non-uniform bathymetry
TL;DR: In this article, the authors show experimental evidence that as relatively long unidirectional waves propagate over a sloping bottom, from a deeper to a shallower domain, there can be a local maximum of kurtosis and skewness close to the shallower side of the slope.
Journal ArticleDOI
Numerical simulation of a solitonic gas in KdV and KdV–BBM equations
TL;DR: In this paper, the collective behavior of soliton ensembles is studied using the methods of the direct numerical simulation, and some high resolution numerical results are presented in both integrable and nonintegrable cases.
Journal ArticleDOI
Evolution of skewness and kurtosis of weakly nonlinear unidirectional waves over a sloping bottom
H. Zeng,Karsten Trulsen +1 more
TL;DR: In this article, the effect of slowly varying depth on the values of skewness and kurtosis of weakly nonlinear irregular waves propagating from deeper to shallower water is considered.
Journal ArticleDOI
Freak waves in weakly nonlinear unidirectional wave trains over a sloping bottom in shallow water
TL;DR: Trulsen et al. as mentioned in this paper showed numerical evidence that bottom non-uniformity can provoke significantly increased probability of freak waves as a wave field propagates into shallower water, in agreement with recent experimental results.
Journal ArticleDOI
Extreme waves induced by strong depth transitions: Fully nonlinear results
TL;DR: In this article, a random, one-directional wave field with prescribed statistics propagating over a submerged step is considered, up to an almost deep-to-shallow transition (kpH ≈ 1.8 − 0.78).
References
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Book
A practical guide to pseudospectral methods
TL;DR: In this article, the authors introduce spectral methods via orthogonal functions and finite differences, and compare computational cost of spectral methods with FD and PS methods in polar and spherical geometries.
Book
Solitons: An Introduction
P. G. Drazin,Robin Johnson +1 more
TL;DR: In this article, the authors introduce the Inverse Scattering Transform (IST) and its application in the theory of solitons and its applications to nonlinear systems that arise in the physical sciences.
Solitons: An introduction
P. G. Drazin,Robin Johnson +1 more
TL;DR: In this paper, the authors introduce the Inverse Scattering Transform (IST) and its application in the theory of solitons and its applications to nonlinear systems that arise in the physical sciences.
Journal ArticleDOI
Oceanic Rogue Waves
TL;DR: In most circumstances, the properties of rogue waves and their probability of occurrence appear to be consistent with second-order random-wave theory as mentioned in this paper, although it is unclear whether these represent measurement errors or statistical flukes, or are caused by physical mechanisms not covered by the model.