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## Effects of coherent dynamics of stochastic deep-water waves

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 waves. In this situation the free wave stochastic dynamics is strongly non-Gaussian, and the kinetic equation for sea surface waves fails. 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.

Laurie J., Boffetta G., Falkovich G. et al., Physical Review Letters 2014 Vol. 113 No. 25 P. 254503-1-254503-5

An inverse turbulent cascade in a restricted two-dimensional periodic domain creates a condensate-a pair of coherent system-size vortices. We perform extensive numerical simulations of this system and carry out theoretical analysis based on momentum and energy exchanges between the turbulence and the vortices. We show that the vortices have a universal internal structure independent of ...

Added: October 15, 2016

Kamchatnov A.M., Chaos 2020 Vol. 30 Article 123148

The theory of motion of edges of dispersive shock waves generated after wave breaking of simple waves is developed. It is shown that this motion obeys Hamiltonian mechanics complemented by a Hopf-like equation for evolution of the background flow, which interacts with the edge wave packets or the edge solitons. A conjecture about the existence ...

Added: February 4, 2021

I.V.Kolokolov, V.V.Lebedev, Journal of Fluid Mechanics 2016 Vol. 809 No. paper R2 P. 1-11

We analyze velocity fluctuations inside coherent vortices generated as a result of the inverse cascade in the two-dimensional ($2d$) turbulence in a finite box. As we demonstrated in \citep{16KL}, the universal velocity profile, established in \citep{14LBFKL}, corresponds to the passive regime of the flow fluctuations. The property enables one to calculate correlation functions of the ...

Added: October 23, 2016

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

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

Kamchatnov A.M., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2019 Vol. 99 No. 1 Article 012203

We suggest a method for calculation of parameters of dispersive shock waves in the framework of Whitham modulation theory applied to nonintegrable wave equations with a wide class of initial conditions corresponding to propagation of a pulse into a medium at rest. The method is based on universal applicability of Whitham’s “number of waves conservation ...

Added: February 4, 2021

I.V.Kolokolov, V.V. Lebedev, JETP Letters 2015 Vol. 101 No. 3 P. 181-184

The inverse cascade of two-dimensional turbulence in a restricted domain leads to creating a coherent flow containing a number of system-size vortices. We examine the case of forcing turbulence with zero bottom friction where the final statistically steady state is determined by viscosity. We analytically establish structure of the coherent vortices in the state. ...

Added: October 15, 2016

Kolokolov I., Lebedev V., Письма в Журнал экспериментальной и теоретической физики 2017 Т. 106 № 10 С. 633-636

Two dimensional turbulence has the striking tendency to self-organize into large-scale, coherent structures due to the inverse energy cascade \cite{67Kra,68Lei,69Bat}. Here we theoretically examine the case of a static pumping where the exciting force is independent of time, the case corresponds to the experimental setup of the works . We establish dependence of the large-scale ...

Added: November 12, 2017

Doludenko A., Fortova S., Kolokolov I. et al., Physics of Fluids 2021 Vol. 33 No. 011704 P. 1-6

We investigate the coherent vortex produced by two-dimensional turbulence excited in a finite box. We establish analytically the mean velocity
profile of the vortex for the case where the bottom friction is negligible and express its characteristics via the parameters of pumping. Our
theoretical predictions are verified and confirmed by direct numerical simulations in the framework of ...

Added: January 20, 2021

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

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

I.V.Kolokolov, V.V. Lebedev, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2016 Vol. 93 No. 3 P. 033104-1-033104-7

We discuss the structure and geometrical characteristics of coherent vortices appearing as a result of the inverse cascade in two-dimensional turbulence in a finite box.We demonstrate that the universal velocity profile, established by J. Laurie et al. [Phys. Rev. Lett. 113, 254503 (2014)], corresponds to the passive regime of flow fluctuations.We find the vortex core ...

Added: October 15, 2016

Kolokolov I., Lebedev V., Chertkov M. et al., Physical Review Letters 2007 Vol. 99 P. 084501-1-084501-4

We report a numerical study, supplemented by phenomenological explanations, of ‘‘energy condensation’’
in forced 2D turbulence in a biperiodic box. Condensation is a finite size effect which occurs after
the standard inverse cascade reaches the size of the system. It leads to the emergence of a coherent vortex
dipole. We show that the time growth of the dipole ...

Added: February 10, 2017

Kolokolov I., Lebedev V., Chertkov M., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2010 Vol. 81 P. 015302R

Two-dimensional turbulence generated in a finite box produces large-scale coherent vortices coexisting with
small-scale fluctuations. We present a rigorous theory explaining the =1/4 scaling in the Vr− law of the
velocity spatial profile within a vortex, where r is the distance from the vortex center. This scaling, consistent
with earlier numerical and laboratory measurements, is universal in ...

Added: February 7, 2017

Камчатнов А. М., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2022 Vol. 105 Article 044204

Equations for contour dynamics of trough-shaped dark solitons are obtained for the general form of the nonlinearity function. Their self-similar solution which describes the nonlinear stage of the bending instability of dark solitons is studied in detail. ...

Added: October 20, 2022

Камчатнов А. М., Иванов С. К., Nonlinear Dynamics 2022 Vol. 108 P. 2505-2512

We consider the modulationally stable version of the Kaup–Boussinesq system which models propagation of onlinear waves in various physical situations. It is shown that the Whitham modulation equations for this model have a new type of solutions which describe trigonometric shock waves. In the Gurevich–Pitaevskii problem of evolution of an initial discontinuity, these solutions correspond to a ...

Added: October 20, 2022

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

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

Kolokolov I., Kostenko M., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2020 Vol. 101 No. 033108 P. 1-3

We consider two-dimensional turbulence in the presence of a condensate. The nondiagonal correlation
functions of the Lagrangian accelerations are calculated, and it is shown that they have the same universality
properties as the nondiagonal correlation functions of the velocity fluctuations. ...

Added: March 25, 2020

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

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

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

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