arXiv subjects

Alexey Slunyaev

Publications and source records attributed to Alexey Slunyaev.

14 recordsLinked to original sources

arXiv2023

Nonlinear waves, modulations and rogue waves in the modular Korteweg-de Vries equation

Effects of nonlinear dynamics of solitary waves and wave modulations within the modular (also known as quadratically cubic) Korteweg - de Vries equation are studied analytically and numerically. Large wave events can occur in the course of interaction between solitons of different signs. Stable and unstable (finite-time-lived) breathers can be generated in inelastic collisions of solitons and from perturbations of two polarities. A nonlinear evolution equation on long modulations of quasi-sinusoidal waves is derived, which is the modular or quadratically cubic nonlinear Schrödinger equation. Its solutions in the form of envelope solitons describe breathers of the modular Korteweg - de Vries equation. The instability conditions are obtained from the linear stability analysis of periodic wave perturbations. Rogue-wave-type solutions emerging due to the modulational instability in the modular Korteweg - de Vries equation are simulated numerically. They exhibit similar wave amplification, but develop faster than in the Benjamin - Feir instability described by the cubic nonlinear Schrödinger equation.

nlin.PS↗

arXiv2022

Experimental evidence of nonlinear focusing in standing water waves

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 doubly-localized Peregrine breathers (PB), which typify particular cases of MI. On the other hand, it has been suggested that the MI relevance weakens when the wave field becomes broadband or directional. Here, we provide experimental evidence of nonlinear and distinct PB-type focusing in standing water waves describing the scenario of two counter-propagating wave trains. The collected collinear wave measurements are in excellent agreement with the hydrodynamic coupled NLSE (CNLSE) and suggest that MI can undisturbedly prevail during the interplay of several wave systems and emphasize the potential role of exact NLSE solutions in extreme wave formation beyond the formal narrowband and uni-directional limits. Our work may inspire further experimental investigations in various nonlinear wave guides governed by CNLSE frameworks as well as theoretical progress to predict strong wave coherence in directional fields.

physics.flu-dyn↗

arXiv2021

Persistence of hydrodynamic envelope solitons: detection and rogue wave occurrence

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. The group is identified by the solution of the associated scattering problem for the nonlinear Schrödinger equation as the intense envelope soliton with remarkably stable parameters. Most of extreme waves occur on top of this group, resulting in higher and longer rogue wave events.

nlin.PS↗

arXiv2020

The Peregrine breather on the zero-background limit as the two-soliton degenerate solution: An experimental study

Solitons are coherent structures that describe the nonlinear evolution of wave localizations in hydrodynamics, optics, plasma and Bose-Einstein condensates. While the Peregrine breather is known to amplify a single localized perturbation of a carrier wave of finite amplitude by a factor of three, there is a counterpart solution on zero background known as the degenerate two-soliton which also leads to high amplitude maxima. In this study, we report several observations of such multi-soliton with doubly-localized peaks in a water wave flume. The data collected in this experiment confirm the distinctive attainment of wave amplification by a factor of two in good agreement with the dynamics of the nonlinear Schrödinger equation solution. Advanced numerical simulations solving the problem of nonlinear free water surface boundary conditions of an ideal fluid quantify the physical limitations of the degenerate two-soliton in hydrodynamics.

physics.flu-dyn↗

arXiv2020

Effects of coherent dynamics of stochastic deep-water waves

A method of windowed spatio-temporal 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 waves. In this situation the free wave stochastic dynamics is strongly non-Gaussian, and the kinetic approach is inapplicable. Traces of coherent wave patterns are found in the Fourier transform of the directional irregular sea waves; they may form 'jets' in the Fourier domain which strongly violate the classic dispersion relation.

nlin.PS↗

arXiv2019

Account of occasional wave breaking in numerical simulations of irregular water waves in the focus of the rogue wave problem

The issue of accounting of the wave breaking phenomenon in direct numerical simulations of oceanic waves is discussed. It is emphasized that this problem is crucial for the deterministic description of waves, and also for the dynamical calculation of extreme wave statistical characteristics, such as rogue wave height probability, asymmetry, etc. The conditions for reproducible simulations of irregular steep waves within the High Order Spectral Method for the potential Euler equations are identified. Such non-dissipative simulations are considered as the reference when comparing with the simulations which use two kinds of wave breaking regularization. It is shown that the perturbations caused by the wave breaking attenuation may be noticeable within 20 min of the wave evolution.

physics.flu-dyn↗

arXiv2019

Lifetimes of rogue wave events in direct numerical simulations of deep-water irregular sea waves

The issue of rogue wave lifetimes is addressed in this study, which helps to detail the general picture of this dangerous oceanic phenomenon. The direct numerical simulations of irregular wave ensembles are performed to obtain the complete accurate data on the rogue wave occurrence and evolution. The simulations are conducted by means of the HOS scheme for the potential Euler equations; purely collinear wave systems, moderately crested and short-crested sea states have been simulated. We join instant abnormally high waves in close locations and close time moments to new objects, rogue events, what helps to retrieve the abnormal occurrences more stably and more consistently from the physical point of view. The rogue wave event probability distributions are built based on the simulated wave data. They show the distinctive difference between rough sea states with small directional bandwidth on the one part, and small-amplitude states and short-crested states on the other part. The former support long-living rogue wave patterns (the corresponding probability distributions have heavy tails), though the latter possess exponential probability distributions of rogue event lifetimes and produce much shorter rogue wave events.

physics.ao-ph↗

arXiv2018

On the optimal focusing of solitons and breathers in long wave models

Conditions of optimal (synchronized) collisions of any number of solitons and breathers are studied within the framework of the Gardner equation with positive cubic nonlinearity, which in the limits of small and large amplitudes tends to other long-wave models, the classic and the modified Korteweg -- de Vries equations. The local solution for an isolated soliton or breather within the Gardner equation is obtained. The wave amplitude in the focal point is calculated exactly. It exhibits a linear superposition of partial amplitudes of the solitons and breathers. The crucial role of the choice of proper soliton polarities and breather phases on the cumulative wave amplitude in the focal point is demonstrated. Solitons are most synchronized when they have alternating polarities. The straightforward link to the problem of synchronization of envelope solitons and breathers in the focusing nonlinear Schrödinger equation is discussed (then breathers correspond to envelope solitons propagating above a condensate).

nlin.PS↗

arXiv2017

On the incomplete recurrence of modulationally unstable deep-water surface gravity waves

The issue of a recurrence of the modulationally unstable water wave trains within the framework of the fully nonlinear potential Euler equations is addressed. It is examined, in particular, if a modulation which appears from nowhere (i.e., is infinitesimal initially) and generates a rogue wave which then disappears with no trace. If so, this wave solution would be a breather solution of the primitive hydrodynamic equations. It is shown with the help of the fully nonlinear numerical simulation that when a rogue wave occurs from a uniform Stokes wave train, it excites other waves which have different lengths, what prevents the complete recurrence and, eventually, results in a quasi-periodic breathing of the wave envelope. Meanwhile the discovered effects are rather small in magnitude, and the period of the modulation breathing may be thousands of the dominant wave periods. Thus, the obtained solution may be called a quasi-breather of the Euler equations.

physics.flu-dyn↗

arXiv2016

Rogue events in spatio-temporal numerical simulations of unidirectional waves in basins of different depth

The evolution of unidirectional nonlinear sea surface waves is calculated numerically by means of solutions of the Euler equations. The wave dynamics corresponds to quasi-equilibrium states characterized by JONSWAP spectra. The spatio-temporal data are collected and processed providing information about the wave height probability and typical appearance of abnormally high waves (rogue waves). The waves are considered at different water depths ranging from deep to relatively shallow cases ($k_p h > 0.8$, where $k_p$ is the peak wavenumber, and $h$ is the local depth). The asymmetry between front and rear rogue wave slopes is identified; it becomes apparent for sufficiently high waves in rough sea states at all considered depths. The lifetimes of rogue events may reach up to 30-60 wave periods depending on the water depth. The maximum observed wave has height of about 3 significant wave heights. A few randomly chosen in-situ time series from the Baltic Sea are in agreement with the general picture of the numerical simulations.

physics.ao-ph↗

arXiv2015

Wave amplification in the framework of forced nonlinear Schrodinger equation: the rogue wave context

Irregular waves which experience the time-limited external forcing within the framework of the nonlinear Schrodinger (NLS) equation are studied numerically. It is shown that the adiabatically slow pumping (the time scale of forcing is much longer than the nonlinear time scale) results in selective enhancement of the solitary part of the wave ensemble. The slow forcing provides eventually wider wavenumber spectra, larger values of kurtosis and higher probability of large waves. In the opposite case of rapid forcing the nonlinear waves readjust passing through the stage of fast surges of statistical characteristics. Single forced envelope solitons are considered with the purpose to better identify the role of coherent wave groups. An approximate description on the basis of solutions of the integrable NLS equation is provided. Applicability of the Benjamin - Feir Index to forecasting of conditions favourable for rogue waves is discussed.

physics.flu-dyn↗

arXiv2014

Nonlinear dynamics of trapped waves on jet currents and rogue waves

Nonlinear dynamics of surface gravity waves trapped by an opposing jet current is studied analytically and numerically. For wave fields narrowband in frequency but not necessarily with narrow angular distributions the developed asymptotic weakly nonlinear theory based on the modal approach of (V. Shrira, A. Slunyaev, J. Fluid. Mech, 738, 65, 2014) leads to the one-dimensional modified nonlinear Schrödinger equation of self-focusing type for a single mode. Its solutions such as envelope solitons and breathers are considered to be prototypes of rogue waves; these solutions, in contrast to waves in the absence of currents, are robust with respect to transverse perturbations, which suggests potentially higher probability of rogue waves. Robustness of the long-lived analytical solutions in form of the modulated trapped waves and solitary wave groups is verified by direct numerical simulations of potential Euler equations.

physics.flu-dyn↗

arXiv2013

Simulations and experiments of short intense envelope solitons of surface water waves

The problem of existence of stable nonlinear groups of gravity waves in deep water is revised by means of laboratory and numerical simulations with the focus on intense waves. Wave groups with steepness up to $A_{cr} ω_m^2 /g \approx 0.30$ are reproduced in laboratory experiments ($A_{cr}$ is the wave crest amplitude, $ω_m$ is the mean angular frequency and $g$ is the gravity acceleration). We show that the groups remain stable and exhibit neither noticeable radiation nor structural transformation for more than 60 wave lengths or about 15-30 group lengths. These solitary wave patterns differ from the conventional envelope solitons, as only a few individual waves are contained in the group. Very good agreement is obtained between the laboratory results and strongly nonlinear numerical simulations of the potential Euler equations. The envelope soliton solution of the nonlinear Schrödinger equation is shown to be a reasonable first approximation for specifying the wavemaker driving signal. The short intense envelope solitons possess vertical asymmetry similar to regular Stokes waves with the same frequency and crest amplitude. Nonlinearity is found to have remarkably stronger effect on the speed of envelope solitons in comparison to the nonlinear correction to the Stokes wave velocity.

physics.flu-dyn↗

arXiv2011

Rogue waters

In this essay we give an overview on the problem of rogue or freak wave formation in the ocean. The matter of the phenomenon is a sporadic occurrence of unexpectedly high waves on the sea surface. These waves cause serious danger for sailing and sea use. A number of huge wave accidents resulted in damages, ship losses and people injuries and deaths are known. Now marine researchers do believe that these waves belong to a specific kind of sea waves, not taken into account by conventional models for sea wind waves. This paper addresses to the nature of the rogue wave problem from the general viewpoint based on the wave process ideas. We start introducing some primitive elements of sea wave physics with the purpose to pave the way for the further discussion. We discuss linear physical mechanisms which are responsible for high wave formation, at first. Then, we proceed with description of different sea conditions, starting from the open deep sea, and approaching the sea cost. Nonlinear effects which are able to cause rogue waves are emphasised. In conclusion we briefly discuss the generality of the physical mechanisms suggested for the rogue wave explanation; they are valid for rogue wave phenomena in other media such as solid matters, superconductors, plasmas and nonlinear optics

physics.ao-ph↗