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## Динамика бризера на глубокой воде под действием ветра

Гл. 10. С. 46-48.

Abrashkin A. A., Oshmarina O. E.

Publication based on the results of:

### In book

Каз. : Издательство Казанcкого государственного университета, 2015

Abrashkin A. A., Якубович Е. И., Известия высших учебных заведений. Радиофизика 2015 Т. 58 № 11 С. 953-959

It is shown that the discrete frequency spectrum of the plane hydrodynamic flow of an ideal incompressible liquid with localized trajectories of liquid particles can contain only one harmonic, two harmonics, or an infinite number of the latter. ...

Added: March 2, 2016

Abrashkin A. A., Soloviev A., Fluid Dynamics 2013 Vol. 48 No. 5 P. 679-686

Plane periodic oscillations of an infinitely deep fluid are studied in the case of a nonuniform pressure distribution over its free surface. The fluid flow is governed by an exact solution of the Euler equations in the Lagrangian variables. The dynamics of an oscillating standing soliton are described, together with the scenario of the soliton ...

Added: November 19, 2013

Кечкин О. В., Mosharev P., Moscow University Physics Bulletin 2020 Vol. 75 No. 3 P. 192-197

The effective Lagrangian is derived and a group of hidden symmetries is determined for Maxwell’s theory with an axion in the stationary case. The general harmonic solution is constructed, and it is shown that a central source can have only a Coulomb-type magnetic field. The electric field of such a source has a complex potential, ...

Added: September 16, 2021

Abrashkin A. A., E.Н. Пелиновский, Теоретическая и математическая физика 2023 Т. 215 № 2 С. 165-175

A review of exact solutions for gravitational waves in deep water is given. All of them are obtained within the framework of the Lagrangian description and are generalizations of Gerstner waves (for cases of inhomogeneous pressure on the free surface and taking into account the rotation of the fluid). The Cauchy invariants are found for ...

Added: June 25, 2023

Abrashkin A. A., Pelinovsky E., Известия высших учебных заведений. Радиофизика 2023 Т. LXVI № 2-3 С. 130-144

By tradition, water waves are studied under the assumption of their potentiality. The vorticity is introduced by shear currents which are ubiquitous in the ocean. It is also generated in near-surface layer as a result of wind action. When these factors are taken into account, the models developed for pitential waves require refinement and generalization. ...

Added: September 12, 2023

Gromov E., Morozov V. P., Tyutin V. V., Труды НГТУ им. Р.Е. Алексеева 2010 № 4 (83) С. 40-49

The interaction of short single-component vector solitons in the frame of the coupled third–order nonlinear Schrodinger equations taking into account third–order linear dispersion, self–stepping, self–stimulated Ramanscattering, cross–stepping and cross–stimulated Raman-scattering terms is considered. Conditions of reflection and propagation of the solitons through each other and also the condition of oscillator interaction (vector breather) are obtained. ...

Added: May 21, 2012

Pelinovsky E., Abrashkin A. A., Theoretical and Mathematical Physics 2023 Vol. 215 No. 2 P. 599-608

We review exact solutions for gravity waves in deep water. All of them are obtained within the Lagrangian framework and are generalizations of Gerstner waves (to the cases of inhomogeneous pressure on the free surface and taking the rotation of the fluid into account). The Cauchy invariants are found for each type of waves. ...

Added: June 25, 2023

Mosharev P., Кечкин О. В., Moscow University Physics Bulletin 2020 Vol. 75 No. 5 P. 427-433

An exact expression is obtained for harmonic fields in Maxwell electrodynamics with dilatons in terms of elliptic Jacobi functions and elliptic Legendre integrals. The case of centrally symmetric fields is considered individually and effective charges of all three types, that is, electric, magnetic, and dilaton charges, are calculated. An expression is given for the generalized ...

Added: September 28, 2021

Rabinowitch A. S., RUDN Journal of Mathematics, Information Sciences and Physics 2013 No. 1 P. 274-283

Added: October 5, 2019

Abrashkin A. A., Soloviev A. G., Physical Review Letters 2013 Vol. 110 P. 014501-1-014501-4

A vertical model for freak wave formation in water is presented. The wind action is simulated by nonuniform pressure on the free surface. The motion of the fluid is described by exact solution of 2D hydrodynamic equations for ideal inviscid fluid in Lagrangian variables. Fluid particles rotate in circles of different radius. The model describes ...

Added: February 15, 2013

Abrashkin A. A., Pelinovsky E., Nonlinear Processes in Geophysics 2017 Vol. 24 P. 255-264

The nonlinear Schrödinger (NLS) equation describing the propagation of weakly rotational wave packets in an infinitely deep fluid in Lagrangian coordinates has been derived. The vorticity is assumed to be an arbitrary function of Lagrangian coordinates and quadratic in the small parameter proportional to the wave steepness. The vorticity effects manifest themselves in a shift ...

Added: June 26, 2017

Didenkulova E., Pelinovsky E., Fluids 2020 Vol. 5 P. 205

Oscillating wave packets (breathers) are a significant part of the dynamics of internal gravity
waves in a stratified ocean. The formation of these waves can be provoked, in particular, by the decay
of long internal tidal waves. Breather interactions can significantly change the dynamics of the wave
fields. In the present study, a series of numerical experiments on ...

Added: November 10, 2020

Abrashkin A. A., Бодунова Ю. П., Известия РАН. Механика жидкости и газа 2012 № 6 С. 50-59

Изучаются стоячие поверхностные волны в вязкой жидкости бесконечной глубины. Дано решение задачи в линейном и квадратичном приближениях. Подробно проанализирован случай длинных по сравнению с толщиной пограничного слоя волн. Определены траектории жидких частиц и выражение для завихренности. ...

Added: November 19, 2013

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

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

Abrashkin A. A., Bodunova Y., Fluid Dynamics 2012 Vol. 47 No. 6 P. 725-734

Standing surface waves in a viscous infinite-depth fluid are studied. The solution of the problem is obtained in the linear and quadratic approximations. The case of long, as compared with the boundary layer thickness, waves is analyzed in detail. The trajectories of fluid particles are determined and an expression for the vorticity is derived. ...

Added: February 25, 2014

Abrashkin A. A., Oshmarina O. E., Physics Letters A 2014 Vol. 378 P. 2866-2871

A vortical model of breather overturning on deep water is proposed. The action of wind is simulated by nonuniform pressure on the free surface. The fluid motion is described by an exact solution of 2D hydrodynamic equations for an inviscid fluid in Lagrangian variables. Fluid particles rotate in circles of different radii. Formation of contraflexure ...

Added: September 16, 2014

Abrashkin A. A., Bodunova Y., Fluid Dynamics 2013 Vol. 48 No. 2 P. 223-231

Within the framework of the Lagrangian approach a method for describing a wave packet on the surface of an infinitely deep, viscous fluid is developed. The case, in which the inverse Reynolds number is of the order of the wave steepness squared is analyzed. The expressions for fluid particle trajectories are determined, accurate to the ...

Added: February 25, 2014

L I Kuzmina, Osipov Y. V., , in : IOP Conference Series: Materials Science and Engineering. Vol. 913: International Scientific Conference "Construction and Architecture: Theory and Practice of Innovative Development" (CATPID-2020) - Part 1 26-30 September 2020, Nalchik, Russian Federation.: IOP Publishing, 2020. Ch. 032066. P. 1-8.

Chemical reactions in a porous medium are found in many natural phenomena and
technological processes. Reactive substances dissolved in groundwater can significantly
change the soil strength. The precipitate formed as a result of the reaction changes the porous
medium structure and affects the porosity and permeability. A one-dimensional model of the
reaction of two reagents in a homogeneous porous ...

Added: January 7, 2021

Колпаков И. Ю., Князев Д. В., Нелинейная динамика 2015 Т. 11 № 1 С. 89-97

In the frameworks of a class of exact solutions of the Navier–Stokes equations with linear dependence of part the speed components on one spatial variablethe axisymmetricalnonselfsimilar ﬂows of viscous ﬂuid in the cylindrical area which radius changes over the time under some law calculated during the solution are considered. The problem is reduced to two-parametrical ...

Added: April 7, 2015

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

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

Rabinowitch A. S., Applied Mathematics 2010 Vol. 1 P. 1-7

Added: October 5, 2019

Abrashkin A. A., Соловьев А. Г., Известия РАН. Механика жидкости и газа 2013 № 5 С. 125-133

Изучены плоские периодические колебания бесконечно глубокой жидкости при неоднородном распределении давления на ее свободной поверхности. Движение жидкости описывается точным решением уравнения Эйлера в лагранжевых переменных. Исследованы динамика колеблющегося стоячего солитона, а также сценарий эволюции солитона и возникновение волны аномально большой амплитуды на фоне однородного герстнеровского волнения (модель волны-убийцы). Все течения являются неоднородно завихренными. ...

Added: November 19, 2013