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## Морские волны-убийцы: наблюдения, физика и математика

Успехи физических наук. 2023. Т. 193. № 2. С. 155–181.

Rogue waves are anomalously high waves that may suddenly form on the sea surface. At the dawn of the 21st century, they attracted the interest of researchers, from oceanographers to mathematicians. The review discusses the results of their research: physical mechanisms leading to the generation of anomalously high waves and respective mathematical models, observational data, results of direct numerical simulations and laboratory experiments, and new approaches to modeling and forecasting extreme sea waves.

Chabchoub A., Hoffmann N., Onorato M. et al., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2012 Vol. 86 No. 5 P. 156601-1–156601-6

We present experimental observations of the hierarchy of rational breather solutions of the nonlinear Schrodinger equation (NLS) generated in a water wave tank. First, five breathers of the infinite hierarchy have been successfully generated, thus confirming the theoretical predictions of their existence. Breathers of orders higher than five appeared to be unstable relative to the ...

Added: January 18, 2013

He Y., Slunyaev A., Mori N. et al., Physical Review Letters 2022 Vol. 129 No. 14 Article 144502

Nonlinear wave focusing originating from the universal modulation instability (MI) is responsible for the formation of strong wave localizations on the water surface and in nonlinear wave guides, such as optical Kerr media and plasma. Such extreme wave dynamics can be described by breather solutions of the nonlinear Schrödinger equation (NLSE) like by way of example the famed ...

Added: October 13, 2022

Pelinovsky E., Ezersky A., Abha N., La Houille Blanche 2016 No. 1 P. 58–65

We have prepared two sets of experiments in a wave flume to model effects occurring in nature and to demonstrate resonance phenomena in laboratory conditions. The first set was performed to investigate non‑linear wave run‑up on the beach caused by harmonic wave maker located at some distance from the shore line. It is revealed that ...

Added: October 29, 2016

Switzerland: Springer, 2018

The present book gathers chapters from colleagues of A. Ezersky from Russia, especially
those from Nizhny Novgorod Institute of Applied Physics of the Russian Academy
of Science and from France, with whom he has been collaborating on experimental
and theoretical developments.
The book is subdivided into two parts. Part I contains eight chapters related to
nonlinear water waves and Part II ...

Added: October 21, 2018

Kurkina O., Rouvinskaya E., Talipova T. et al., Physica D: Nonlinear Phenomena 2016 Vol. 333 P. 222–234

Internal tidal wave entering shallow waters transforms into an undular bore and this process can be described in the framework of the Gardner equation (extended version of the Korteweg-de Vries equation with both quadratic and cubic nonlinear terms). Our numerical computations demonstrate the features of undular bore developing for different signs of the cubic nonlinear ...

Added: March 3, 2016

Didenkulova I., Pelinovsky E., Journal of Physics A: Mathematical and Theoretical 2016 Vol. 49 No. 19 P. 194001

Rogue wave formation in shallow water is often governed by dispersive focusing and wave-bottom interaction. In this study we try to combine these mechanisms by considering dispersive nonreflecting wave propagation in shallow strongly inhomogeneous channels. Nonreflecting wave propagation provides extreme wave amplification and the transfer of wave energy over large distances, while dispersive effects allow ...

Added: June 8, 2016

L. F. Calazans de Brito, A. M. Kamchatnov, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2024 Vol. 109 No. 1 Article 015102

We consider nonlinear wave structures described by the modified Korteweg–de Vries equation, taking into account a small Burgers viscosity for the case of steplike initial conditions. The Whitham modulation equations are derived, which include the small viscosity as a perturbation. It is shown that for a long enough time of evolution, this small perturbation leads to the ...

Added: February 1, 2024

Pelinovsky E., Slunyaev A., Soares C., Journal of Offshore Mechanics and Arctic Engineering 2014 Vol. 136 P. 011302

In this paper, some abnormal or rogue wave events registered in the North Sea by means of the surface elevation measurements are reconstructed with the help of theoretical models for water waves and numerical simulations of wave evolution. Time series of surface elevation, which are measured at a single point, provide incomplete information about the ...

Added: November 19, 2014

Isoard M., Kamchatnov A.M., Pavloff N., EPL 2020 Vol. 129 Article 64003

We consider the one-dimensional dynamics of nonlinear non-dispersive waves. The problem can be mapped onto a linear one by means of the hodograph transform. We propose an approximate scheme for solving the corresponding Euler-Poisson equation which is valid for any kind of nonlinearity. The approach is exact for monoatomic classical gas and agrees very well ...

Added: February 4, 2021

Kachulin D., Dyachenko A., Gelash A., Fluids 2019 Vol. 4 No. 2 Article 83

We numerically investigate pairwise collisions of solitary wave structures on the surface of deep water—breathers. These breathers are spatially localised coherent groups of surface gravity waves which propagate so that their envelopes are stable and demonstrate weak oscillations. We perform numerical simulations of breather mutual collisions by using fully nonlinear equations for the potential flow ...

Added: October 22, 2022

Dyachenko A., Studies in Applied Mathematics 2020 Vol. 144 No. 4 P. 493–503

One of the essential tasks of the theory of water waves is a construction of simplified mathematical models, which are applied to the description of complex events, such as wave breaking, appearing of freak waves in the assumption of weak nonlinearity. The Zakharov equation and its simplification, such as nonlinear Schrodinger equations and Dysthe equations, ...

Added: October 21, 2022

Slunyaev A., Кокорина А. В., Известия РАН. Физика атмосферы и океана 2020 Т. 56 № 2 С. 210–223

Выполнено прямое численное моделирование гравитационных волн ветрового диапазона на двумерной поверхности моря в рамках исходных потенциальных уравнений гидродинамики. Обсуждаются результаты обработки полученных данных для условий глубокого моря, спектра JONSWAP и
разных интенсивностей волнения, ширин углового спектра и пиковатости. Статистические и спектральные характеристики волн эволюционируют в течение длительного времени. Показана специфическая асимметрия характерных профилей аномально высоких волн. ...

Added: June 5, 2020

Kamchatnov A.M., L. F. Calazans de Brito, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2021 Vol. 104 Article 054203

We show that the number of solitons produced from an arbitrary initial pulse of the simple wave type can be calculated analytically if its evolution is governed by a generalized nonlinear Schroedinger equation provided this number is large enough. The final result generalizes the asymptotic formula derived for completely integrable nonlinear wave equations like the standard NLS equation ...

Added: January 17, 2022

Didenkulova I., Nikolkina I., Pelinovsky E., JETP Letters 2013 Vol. 97 No. 4 P. 221–225

Properties of rogue waves in the basin of intermediate depth are discussed in comparison with known properties of rogue waves in deep waters. Based on observations of rogue waves in the ocean of intermediate depth we demonstrate that the modulational instability can still play a significant role in their formation for basins of 20m and ...

Added: February 26, 2013

Bienaime T., Isoard M., Fontaine Q. et al., Physical Review Letters 2021 Vol. 126 Article 183901

We report on the formation of a dispersive shock wave in a nonlinear optical medium. We monitor the evolution of the shock by tuning the incoming beam power. The experimental observations for the position and intensity of the solitonic edge of the shock, as well as the location of the nonlinear oscillations are well described ...

Added: October 14, 2021

Камчатнов А. М., Успехи физических наук 2021 Т. 191 № 1 С. 52–87

We present an introduction to the theory of dispersive shock waves in the framework of the approach proposed by Gurevich and Pitaevskii (Zh. Eksp. Teor. Fiz., Vol. 65, p. 590 (1973) [Sov. Phys. JETP, Vol. 38, p. 291 (1974)]) based on Whitham’s theory of modulation of nonlinear waves. We explain how Whitham equations for a ...

Added: October 14, 2021

Kamchatnov A.M., Chaos 2019 Vol. 29 Article 023106

We discuss the problem of breaking of a nonlinear wave in the process of its propagation into a medium at rest. It is supposed that the profile of the wave is described at the breaking moment by the function (−x) 1/n (x < 0, positive pulse) or −x 1/n (x > 0, negative pulse) of ...

Added: February 4, 2021

Slunyaev A., Physics of Fluids 2021 Vol. 33 Article 036606

The observation of a wave group persisting for more than 200 periods in the direct numerical simulation of nonlinear unidirectional irregular water waves in deep water is discussed. The simulation conditions are characterized by parameters realistic for broad-banded waves in the sea. Through solution of the associated scattering problem for the nonlinear Schr€odinger equation, the group is ...

Added: March 19, 2021

Slunyaev A., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2020 Vol. 101 Article 062214

A method of windowed spatiotemporal spectral filtering is proposed to segregate different nonlinear wave components and to calculate the surface of free waves. The dynamic kurtosis (i.e., produced by the free wave component) is shown able to contribute essentially to the abnormally large values of the surface displacement kurtosis, according to the direct numerical simulations of realistic sea ...

Added: June 28, 2020

Kartashova E., Talipova T., Pelinovsky E., Nonlinear Processes in Geophysics 2013 Vol. 20 No. 4 P. 571–580

The nonlinear deformation of long internal waves in the ocean is studied using the dispersionless Gardner equation. The process of nonlinear wave deformation is determined by the signs of the coefficients of the quadratic and cubic nonlinear terms; the breaking time depends only on their absolute values. The explicit formula for the Fourier spectrum of ...

Added: October 15, 2013

Gurbatov S., Pelinovsky E., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2020 Vol. 102 No. 1 P. 012207

The paper considers the probability distributions of the nonlinear wave characteristics in nondispersive media
that satisfy the Riemann- and the Kardar-Parisi-Zhang-type equations. By using the Lagrangian and Euler
relations of statistical descriptions, expressions are obtained for the probability density of the Riemann wave
(displacement) integral through the initial probability density of displacement, velocity, and acceleration. The
case of Gaussian ...

Added: July 24, 2020

Didenkulova E., Physica D: Nonlinear Phenomena 2022 Vol. 432 Article 133130

Breathers or oscillating wave packets, along with solitons, are the most energy-carrying waves in various physical media, i.e. surface and internal waves, optical networks, and Josephson junctions. Breathers largely determine the overall wave dynamics of wave fields. In this work, the dynamics of a set of breathers or the so-called breather turbulence or breather gas ...

Added: January 26, 2022

Slunyaev A., Кокорина А. В., Journal of Ocean Engineering and Marine Energy 2017 Vol. 3 P. 395–408

The results of the probabilistic analysis of the direct numerical simulations of irregular unidirectional deep
water waves are discussed. It is shown that an occurrence of large-amplitude soliton-like groups represents an extraordinary case, which is able to increase noticeably the probability of high waves even in moderately rough sea conditions. The ensemble of wave realizations should be large enough to take these ...

Added: March 1, 2019

Didenkulova E., Slunyaev A., Pelinovsky E., European Journal of Mechanics - B/Fluids 2019 Vol. 78 P. 21–31

Direct numerical simulations of irregular unidirectional nonlinear wave evolution are performed within the framework of the Korteweg–de Vries equation for bimodal wave spectra model cases. The additional wave system co-existence effect on the evolution of the wave statistical characteristics and spectral shapes, and also on the attained equilibrium state is studied. The concerned problem describes, for example, the interaction ...

Added: June 15, 2019