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## Two Models for 2D Deep Water Waves

Fluids. 2022. Vol. 7. No. 6. Article 204.

Dremov S., Kachulin D., Dyachenko A.

In this paper we propose two Hamiltonian models to describe two-dimensional deep water waves propagating on the surface of an ideal incompressible three-dimensional fluid. The idea is based on taking advantage of the Zakharov equation for one-dimensional waves which can be written in the form of so-called compact equations. We generalize these equations to the case of two-dimensional waves. As a test of our models, we perform numerical simulations of the dynamics of standing waves in a channel with smooth vertical walls. The results obtained in the proposed models are comparable, indicating that the models are similar to the original Zakharov equation.

Kachulin D., Dyachenko A., Dremov S., Fluids 2020 Vol. 5 No. 2 Article 65

The paper presents the long-time dynamics with multiple collisions of breathers in the super compact Zakharov equation for unidirectional deep water waves. Solutions in the form of breathers were found numerically by the Petviashvili method. In the terms of envelope and the assumption of the narrow spectral width the super compact equation turns into the ...

Added: October 22, 2022

Dyachenko A., Fluids 2019 Vol. 4 No. 1 Article 47

The waves on a free surface of 2D deep water can be split into two groups: the waves moving to the right, and the waves moving to the left. A specific feature of the four-wave interactions of water waves allows to describe the evolution of the two groups as a system of two equations. The ...

Added: October 20, 2022

Kachulin D., Dyachenko A., Zakharov V., Fluids 2020 Vol. 5 No. 2 Article 67

We investigate and compare soliton turbulence appearing as a result of modulational
instability of the homogeneous wave train in three nonlinear models for surface gravity waves:
the nonlinear Schrödinger equation, the super compact Zakharov equation, and the fully nonlinear
equations written in conformal variables. We show that even at a low level of energy and average
wave steepness, the ...

Added: October 22, 2022

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

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

Kachulin D., Dremov S., Dyachenko A., Fluids 2021 Vol. 6 No. 3 Article 115

This article presents a study of bound periodically oscillating coherent structures arising on the free surface of deep water. Such structures resemble the well known bi-soliton solution of the nonlinear Schrödinger equation. The research was carried out in the super-compact Dyachenko-Zakharov equation model for unidirectional deep water waves and the full system of nonlinear equations ...

Added: October 22, 2022

Dyachenko A., Kachulin D., Zakharov V., Lobachevskii Journal of Mathematics 2017 Vol. 38 No. 5 P. 888-892

Presented are the results of experiments on calculation of Probability Distribution Functions for elevations of waters waves in numerical tank. Statistics of waves of anomalous amplitude, or freak-waves were compared both for nonlinear and linear models. Obviously, linear model demonstrates the exact Rayleigh distribution of surface elevations while PDFs for nonlinear equation have tails (for ...

Added: October 22, 2022

Tararushkin E., Smirnov G., Kalinichev A. G., Minerals 2023 Vol. 13 No. 8 Article 1018

The 10-Å phase is an important member of the family of dense hydrous magnesium silicates (DHMSs) that play a major role in the water budget in the Earth’s upper mantle. Its nominal composition is usually written as Mg3Si4O10(OH)2·xH2O, and its structure is often described as layers of talc with some amount of water present in ...

Added: August 1, 2023

М. : Энциклопедия, Инфра-М, 2017

The New Russian Encyclopedia is a fundamental reference publication in 18 volumes that characterizes nature, population, economy, history, science, art, technology and other important aspects. Contains about 60,000 articles, about 30,000 biographies, about 15,000 color illustrations, maps, charts, diagrams, tables. Leaves since 2003. ...

Added: October 29, 2018

Чугунин Д. В., Клименко М. В., Chernyshov A. et al., Геомагнетизм и аэрономия 2018 Т. 58 № 1 С. 53-65

In this paper, measurements of thermal and superthermal ions on the Interball-2 satellite are compared with the results of numerical simulation based on geomagnetic disturbances on December 7, 1996. It is shown that kinetic processes at small scales can have a significant effect on large-scale processes in high latitudes, leading to heating and the formation ...

Added: November 28, 2019

Садовничий В. А., Панасюк М. И., Липунов В. М. et al., Космические исследования 2019 Т. 57 № 1 С. 46-56

The article discusses the results of experiments on the Lomonosov satellite to observe natural and man-made space threats, including electromagnetic transients, space debris. A new space project of the Moscow State University named after M.V. Lomonosov Univesat-SOCRAT on the creation of a constellation of satellites for real-time monitoring in near-earth space: radiation situation; potentially dangerous ...

Added: October 15, 2021

Pyrkova D. V., Tarasova N. K., Krylov N. et al., Journal of Biomolecular Structure and Dynamics 2013 Vol. 31 No. 1 P. 87-95

Delineation and analysis of lateral clustering of lipids in model bilayers is an important step toward understanding of the physical processes underlying formation of lipid domains and rafts in cell membranes. Computer modeling methods represent a powerful tool to address the problem since they can detect clusters of only few lipid molecules – this issue ...

Added: November 14, 2013

Egor Stadnichuk, Свечникова Е., Atmospheric Research 2022 Vol. 277 Article 106329

Relativistic runaway electron avalanches (RREA) occurring in thunderstorm large-scale electric fields are one of the sources of atmospheric gamma radiation. Relativistic feedback is the generation of RREAs by positrons or backscattered gamma rays of the previously produced RREAs. In strong electric fields, relativistic feedback can make RREAs self-sustainable that hypothetically can cause a terrestrial gamma-ray flash (TGF). This paper introduces ...

Added: May 24, 2023

Logvenkov S. A., Moiseeva I., Stein A., Biofizika 2016 Vol. 61 No. 6 P. 989-995

Invagination of epithelial sheets is an important type of morphogenetic deformation. Primary
invagination during gastrulation in the sea urchin provides one of the simplest and best-studied examples.
The specific mechanisms of invagination remain unclear in spite of numerous observations. The problem of
plane-stress deformation of an initially circular layer exposed to a constant internal pressure is considered.
Active forces ...

Added: February 14, 2017

Dyachenko A., Kachulin D., Zakharov V., Journal of Ocean Engineering and Marine Energy 2017 Vol. 3 No. 4 P. 409-415

Water waves have long been a subject of attention of both mathematicians and physicists. The formulation of the problem is simple enough to be considered fundamental, but as of yet many questions still remain unanswered and many phenomena associated with wind-driven turbulence remain puzzling. We consider a “unidirectional” motion of weakly nonlinear gravity waves, i.e., ...

Added: October 22, 2022

Klein M., Clauss G., Slunyaev A., Physics of Fluids 2017 Vol. 29 P. 047103-1-047103-17

The investigation of dynamics of intense solitary wave groups of collinear surface waves is performed by means of numerical simulations of the Euler equations and laboratory experiments. The processes of solitary wave generation, reflection from a wall and collisions are considered. Steep solitary wave groups with characteristic steepness up to kAcr ~ 0.3 (where k is the ...

Added: February 14, 2019

Zelenyi L., Malova H., Grigorenko E. et al., 2019 Vol. 61 P. 1-12

In this article we aim to highlight the problems related to the structure and stability of the
comparatively thin current sheets that were relatively recently discovered by space missions in
the magnetospheres of the Earth and planets, as well as in the solar wind. These magnetoplasma
structures are universal in collisionless cosmic plasmas and can play a key ...

Added: March 22, 2019

Abrashkin A. A., Journal of Physics A: Mathematical and Theoretical 2022 Vol. 55 No. 41 Article 415701

An analytical description of unsteady edge waves over a uniform slope is proposed. It is assumed that the waves are excited by time-harmonic external pressure with inhomogeneous spatial distribution. The problem is considered in Lagrangian variables. An exact solution of the hydrodynamic equations is obtained. It generalizes the stationary Gerstner–Constantin solution. The proposed model describes the dynamics of coastal splashes ...

Added: October 13, 2022

Kolokolov I., Lebedev V., Gamba A. et al., Physical Review Letters 2007 Vol. 99 P. 158101-1-158101-4

Eukaryotic cells possess a sensible chemical compass allowing them to orient toward sources of soluble chemicals. The extracellular chemical signal triggers separation of the cell membrane into two domains populated by different phospholipid molecules and oriented along the signal anisotropy. We propose a theory of this polarization process, which is articulated into subsequent stages of ...

Added: February 10, 2017

Могилевский М. М., Чугунин Д. В., Chernyshov A. et al., Письма в Журнал экспериментальной и теоретической физики 2021 Т. 114 № 1 С. 18-23

According to measurements of the electric component of the electromagnetic field in the frequency range from 2 kHz to 10 MHz by the Japanese ERG satellite, generation regions of kilometric continuum radiation and new hectometric continuum radiation have been determined. It is demonstrated that the kilometric continuum is mainly observed on the dayside of the ...

Added: January 21, 2022

A. A. Abrashkin, Constantin A., Journal of Differential Equations 2023 Vol. 374 P. 632-641

We investigate steady flow moving purely in the azimuthal direction on rotating sphere and having a meridionally localized jet structure. An exact solution for a stratified invicsid fluid, which admits a depth-dependent velocity profile below the surface, is constructed in spherical coordinates. This soluton is relevant to the modelling of the Antarctic Circumpolar Current. We ...

Added: September 14, 2023

Стадничук Е. М., Хамитов Т. М., Нозик А. А. et al., EPL 2020 Vol. 132 No. 3 Article 35001

The connection between thunderstorms and relativistic runaway electron avalanches is an important topic that has attracted the attention of many researchers. Among other things, there are a lot of various simulations of the dynamics of electron avalanches. This article was written mostly in response to the article The critical avalanche of runaway electrons by Evgeny ...

Added: May 24, 2023

Parkhomenko E., Malova H., Grigorenko E. et al., Physics of Plasmas 2019 Vol. 26 No. 4 P. 1-9

This work is devoted to the investigation of particle acceleration during magnetospheric dipolarizations. A numerical model is presented
taking into account the four scenarios of plasma acceleration that can be realized: (A) total dipolarization with characteristic time scales of
3 min; (B) single peak value of the normal magnetic component Bz occurring on the time scale of ...

Added: April 16, 2019

Адушкин В. В., Нифадьев В. И., Чен Б. Б. et al., Doklady Earth Sciences 2019 Т. 487 № 3 С. 299-303

Based on the data of experimental studies of wave disturbances in the Earth's atmosphere before and after the earthquakes in Uzbekistan (May 26, 2013) and Kyrgyzstan (January 8, 2007), earlier unknown changes in the parameters of internal gravity waves are revealed. These changes were manifested during the period of five days before the earthquake and in certain cases ...

Added: August 28, 2019