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## Cauchy invariants and exact solutions of nonlinear equations of hydrodynamics

Theoretical and Mathematical Physics. 2023. Vol. 215. No. 2. P. 599-608.

Pelinovsky E., Abrashkin A. A.

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.

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., Deep-Sea Research Part II: Topical Studies in Oceanography 2019 Vol. 160 P. 3-6

Three Lagrangian invariants are shown to exist for flows in the equatorial region in the β - plane approximation.
They extend the Cauchy invariants to a non-rotating fluid. The relationship between these generalized invariants
and the results following from Kelvin's and Ertel's theorems is ascertained. Explicit expressions of the invariants
for equatorially trapped waves and equatorial Gerstner waves ...

Added: April 2, 2019

Abrashkin A. A., Pelinovsky E., Physics-Uspekhi 2022 Vol. 65 P. 453-467

To mark 220 years since the appearance of Gerstner's paper that proposed an exact solution to the hydrodynamic
equations, an overview of exact solutions for water waves is given, each of which is a generalization of the Gerstner wave. Additional factors are coastal geometry, fluid rotation, varying pressure on the free surface, stratification, fluid compressibility, and background flows. Waves on ...

Added: October 13, 2022

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., 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

Abrashkin A. A., Pelinovsky E., Izvestia, Atmospheric and Oceanic Physic 2018 Vol. 54 No. 1 P. 101-105

A nonlinear Schrцdinger equation (NSE) describing packets of weakly nonlinear waves in an inhomogeneously
vortical infinitely deep fluid 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. It is
shown that the modulational instability criteria for the weakly vortical waves and ...

Added: October 3, 2018

Abrashkin A. A., Chaos, Solitons and Fractals 2019 Vol. 118 P. 152-158

We present an analytical description of the class of unsteady vortex surface waves generated by non- uniformly distributed, time-harmonic pressure. The fluid motion is described by an exact solution of the equations of hydrodynamics generalizing the Gerstner solution. The trajectories of the fluid particles are circumferences. The particles on a free surface rotate around circumferences ...

Added: December 17, 2018

Abrashkin A. A., Pelinovsky E., Physics-Uspekhi 2018 Vol. 61 P. 307-312

We discuss the properties of two-dimensional, non
linear, potential, and vortex waves on the surface of an ideal
liquid of infinite depth. It is shown that in the quadratic order in
the amplitude, the vorticity of the Gerstner wave is equal in
magnitude to and different in sign from that of the Stokes drift
current in a surface layer. This ...

Added: October 3, 2018

Abrashkin A. A., Discrete and Continuous Dynamical Systems 2019 Vol. 39 No. 8 P. 4443-4453

A class of non-stationary surface gravity waves propagating in the
zonal direction in the equatorial region is described in the f -plane approx
imation. These waves are described by exact solutions of the equations of
hydrodynamics in Lagrangian formulation and are generalizations of Gerstner
waves. The wave shape and non-uniform pressure distribution on a free sur
face depend on two ...

Added: June 19, 2019

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

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., Успехи физических наук 2022 Т. 192 № 5 С. 491-506

Added: May 14, 2022

Abrashkin A. A., Pelinovsky E., Известия РАН. Физика атмосферы и океана 2018 № 1

The nonlinear Schrödinger (NLS) equation describing the propagation of inhomogeneous vertical wave packets in an infinitely deep fluid 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. It is shown that the modulation instability criteria of the considered ...

Added: October 16, 2017

Abrashkin A. A., Oshmarina O. E., В кн. : XI Всероссийский съезд по фундаментальным проблемам теоретической и прикладной механики, СБОРНИК ДОКЛАДОВ, Казань 20 — 24 августа 2015 г. : Каз. : Издательство Казанcкого государственного университета, 2015. Гл. 10. С. 46-48.

Предложена вихревая модель бризера, опрокидывающегося на глубокой воде. Действие ветра моделируется неоднородным распределением давления на свободной поверхности. Движение жидкости описывается точным решением уравнений двумерной гидродинамики для идеальной жидкости в лагранжевых координатах. Жидкие частицы вращаются по окружностям разного радиуса. Изучен процесс образования точки перегиба на профиле бризера. Обсуждается механизм обрушения волны и влияние завихренности течения на ...

Added: March 2, 2016

Abrashkin A. A., Pelinovsky E., Успехи физических наук 2018 Т. 188 С. 329-334

It is shown in the quadratic approximation that the Gerstner wave vorticity is equal and of different sign to the vorticity of Stokes drift current in deep water. That gives an opportunity to interpret the Stokes wave as a superposition of the Gerstner wave and the Stokes drift and to explain, why the nonlinearity in ...

Added: October 17, 2017

Katushkina O. A., Quemerais E., Izmodenov V.V. et al., JOURNAL OF GEOPHYSICAL RESEARCH-SPACE PHYSICS 2017 Vol. 122 No. 11 P. 10921-10937

In this work, we present for the first time the Lyman α intensities measured by Voyager 1/UVS in 2003–2014 (at 90–130 AU from the Sun). During this period Voyager 1 measured the Lyman α emission in the outer heliosphere at an almost fixed direction close to the upwind (i.e.“ toward the interstellar flow). The data show an unexpected behavior in 2003–2009: the ...

Added: January 26, 2018

Aaij R., Abdelmotteleb A. S., Abellan Beteta C. et al., The European Physical Journal C - Particles and Fields 2023 Vol. 83 Article 543

https://link.springer.com/article/10.1140/epjc/s10052-023-11673-x#Abs1 ...

Added: December 4, 2023

Ружицкая Д. Д., САМОЙЛЕНКО А. А., Иванов А. Д. et al., Optoelectronics, Instrumentation and Data Processing 2017 Vol. 54 No. 1 P. 1-8

This paper presents an algorithm for processing the transmission spectra of whisperinggallery optical microcavities for use as a nanoparticle detector. The algorithm is based on the broadening of the microcavity resonance curve during precipitation of nanoparticles on the microcavity surface. Experimental results on the detection of particles are compared with Langmuir adsorption theory. The contribution ...

Added: May 25, 2018

М. : National Instruments Russia, 2017

Содержание сборника составляют доклады с результатами оригинальных исследований и технических решений, ранее не публиковавшиеся. Мы надеемся, что предлагаемый сборник окажется полезным для специалистов, работающих в различных областях науки и техники, для широкого круга преподавателей, аспирантов и студентов ВУЗов, а также для преподавателей средних школ и технических колледжей. ...

Added: May 10, 2017

Загорский Д. Л., Долуденко И. М., Каневский В. М. et al., Известия РАН. Серия физическая 2021 Т. 85 № 8 С. 1088-1094

FeCo and FeNi alloyed nanowires (NW) were obtained by the matrix synthesis method: the effect of the
growth voltage and the effect of using a reference electrode were studied. It is shown that the composition of
FeNi nanowires strongly depends on the growth potential (with its increase, the bcc structure is changing into
fcc), and it is also ...

Added: November 12, 2021

Panina I., Balandin S., Tsarev A. et al., International Journal of Molecular Sciences 2023 Vol. 24 No. 2 P. 1

To date, a number of lantibiotics have been shown to use lipid II — a highly conserved peptidoglycan precursor in the cytoplasmic membrane of bacteria — as their molecular target. The α-component (Lchα) of the two-component lantibiotic lichenicidin (Lchα), previously isolated from the Bacillus licheniformis VK21 strain, seems to contain two putative lipid II binding ...

Added: February 21, 2023

Alfimov M., Litvinov A., Journal of High Energy Physics 2022 No. 01 Article 43

We study regularization scheme dependence of beta-function for sigma models with two-dimensional target space. Working within four-loop approximation, we conjecture the scheme in which the beta-function retains only two tensor structures up to certain terms containing zeta_3. Using this scheme, we provide explicit solutions to RG flow equation corresponding to Yang-Baxter- and lambda-deformed SU(2)/U(1) sigma ...

Added: February 1, 2022

Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18

Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...

Added: November 16, 2020

Kuzmichev S. A., Kuzmicheva T. E., Tchesnokov S. N. et al., Journal of Superconductivity and Novel Magnetism 2016 Vol. 29 No. 4 P. 1111-1116

We present temperature dependences of the large and the small superconducting gaps measured directly by SnS-Andreev spectroscopy in various Fe-based superconductors and MgB2. The experimental L,S(T ) are wellfitted with a two-gap model based on Moskalenko and Suhl system of equations (supplemented with a BCS integral renormalization). From the fitting procedure, we estimate the key ...

Added: March 19, 2016