### ?

## Rogue wave formation under the action of quasi-stationary pressure

Communications in Nonlinear Science and Numerical Simulation. 2016. Vol. 34. P. 66-76.

Abrashkin A. A., Oshmarina O. E.

The process of rogue wave formation on deep water is considered. A wave of extreme amplitude is born against the background of uniform waves (Gerstner waves) under the action of external pressure on free surface. The pressure distribution has a form of a quasi-stationary “pit”. The fluid motion is supposed to be a vortex one and is described by an exact solution of equations of 2D hydrodynamics for an ideal fluid in Lagrangian coordinates. Liquid particles are moving around circumferences of different radii in the absence of drift flow. Values of amplitude and wave steepness optimal for rogue wave formation are found numerically. The influence of vorticity distribution and pressure drop on parameters of the fluid is investigated.

Priority areas:
mathematics

Language:
English

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., Yakubovich E. I., Radiophysics and Quantum Electronics 2016 Vol. 58 No. 11 P. 852-857

We show that the discrete frequency spectrum of a plane hydrodynamic flow of ideal incompressible liquid with localized trajectories of the liquid particles can contain only one, two, or an infinite number of harmonics. ...

Added: November 17, 2016

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., 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., 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

Abrashkin A. A., Pelinovsky E., Journal of Physics A: Mathematical and Theoretical 2021 Vol. 54 No. 39 Article 395701

To study stationary periodic weakly vortical waves on water (the Gouyon waves), the method of the modified Lagrangian variables is suggested. The wave vorticity Ω is specified as a series in the small steepness parameter ε in
the form: Ω =\sum( ε^n · Ω_n (b)), where Ω_n are arbitrary functions of the vertical Lagrangian coordinate b. Earlier Gouyon (1958) studied ...

Added: October 5, 2021

A. A. Abrashkin, Monatshefte fur Mathematik 2022 Vol. 199 No. 4 P. 717-732

Propagation of periodic stationaryweakly vortical gravitationalwaves on the freewater surface is considered. Similar wave motion was studied by Gouyon (Ann de la Fac des Sci de l’Université de Toulouse Sér 4(22):1–55, 1958) in linear and quadratic approximations in small parameter of the wave’s steepness ε for the deep water conditions.
In this paper this result is considered for the ...

Added: October 13, 2022

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

Tamm M., Stadnichuk V., Ilyina A. et al., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2014 Vol. 89 P. 042137

We consider two random walkers starting at the same time t = 0 from different points in space separated by a given distance R. We compute the average volume of the space visited by both walkers up to time t as a function of R and t and dimensionality of space d. For d < 4, this volume, after proper renormalization, is shown to be ...

Added: May 23, 2014

Pelinovsky E., Slunyaev A., Soares C., Journal of Offshore Mechanics and Arctic Engineering 2014 Vol. 136 P. 011302

In this paper, some abnormal or rogue wave events registered in the North Sea by means of the surface elevation measurements are reconstructed with the help of theoretical models for water waves and numerical simulations of wave evolution. Time series of surface elevation, which are measured at a single point, provide incomplete information about the ...

Added: November 19, 2014

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., 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

Pelinovsky E., Talipova T., Slunyaev A. et al., Natural Hazards and Earth Science Systems 2014 Vol. 14 P. 861-870

Spatio-temporal evolution of rogue waves measured in Taiwanese coastal waters is reconstructed by means of numerical simulations. Their lifetimes are up to 100 s. The time series used for reconstructions were measured at dimensionless depths within the range of kh = 1.3−4.0, where k is the wave number and h is the depth. All identified ...

Added: November 19, 2014

Rulkov N., Hunt A. M., Rulkov P. et al., American Journal of Engineering and Applied Sciences 2016 Vol. 9 No. 4 P. 973-984

The discreet-time (map-based) approach to modeling nonlinear dynamics of spiking and spiking-bursting activity of neurons has demonstrated its very high efficiency in simulations of neuro-biologically realistic behavior both in large-scale network models for brain activity studies and in real-time operation of Central Pattern Generator network models for biomimetic robotics. This paper studies the next step ...

Added: January 15, 2017

М. : Институт прикладной математики им. М.В. Келдыша РАН, 2018

Содержит материалы, представленные к рассмотрению на научно-практический семинар “Новые информационные технологии в автоматизированных системах”, проводившейся в Москве 20 апреля 2018 г.
Представляет интерес для научных сотрудников, преподавателей, аспирантов и студентов, работающих по указанным научным направлениям. ...

Added: April 20, 2018

Zlotnik Alexander, Zlotnik Ilya, Computational Methods in Applied Mathematics 2015 Vol. 15 No. 2 P. 233-245

We consider the Cauchy problem for the 1D generalized Schrὅdinger equation on the whole axis. To solve it, any order finite element in space and the Crank-Nicolson in time method with the discrete transpa\-rent boundary conditions (TBCs) has recently been constructed. Now we engage the global Richardson extrapolation in time to derive the high order ...

Added: March 3, 2015

Koltsov S., Physica A: Statistical Mechanics and its Applications 2018 Vol. 512 P. 1192-1204

This study proposes to minimize Rényi and Tsallis entropies for finding the optimal number of topics T in topic modeling (TM). A promising tool to obtain knowledge about large text collections, TM is a method whose properties are underresearched; in particular, parameter optimization in such models has been hindered by the use of monotonous quality ...

Added: October 11, 2018

М. : Физический факультет МГУ им. М.В. Ломоносова, 2014

Сборник тезисов докладов Международного научного семинара Актуальные проблемы математической физики. МГу им. М.В. Ломоносова, 28-29 ноября 2014 г. ...

Added: November 28, 2014

Madera A. G., Компьютерные исследования и моделирование 2019 Т. 11 № 4 С. 613-630

A hierarchical method of mathematical and computer modeling of interval-stochastic thermal processes in complex electronic systems for various purposes is developed. The developed concept of hierarchical structuring reflects both the constructive hierarchy of a complex electronic system and the hierarchy of mathematical models of heat exchange processes. Thermal processes that take into account various physical ...

Added: November 1, 2019

Seul : World Scientific and Engineering Academy and Society, 2015

This year the 12th International Conference on E-Activities (E-ACTIVITIES '15) and the 4th International Conference on Applied and Computational Mathematics (ICACM '15) were held in Seoul, South Korea, September 5-7, 2015. The conferences provided a platform to discuss elearning, e-management, e-marketing, numerical analysis and applications, probabilities, statistics, operational research, algorithms, discrete mathematics, systems, communications, control ...

Added: October 13, 2015

М. : МИЭМ НИУ ВШЭ, 2013

The materials of The Second International Scientific – Practical Conference is presented below. The Conference reflects the modern state of innovation in education, science, industry and social-economic sphere, from the standpoint of introducing new information technologies.
Digest of Conference materials is presented in 4 parts. It is interesting for a wide range of researchers, teachers, graduate ...

Added: April 18, 2013

M. : Association of graduates and employees of AFEA named after prof. Zhukovsky, 2018

The materials of The International Scientific – Practical Conference is presented below.
The Conference reflects the modern state of innovation in education, science, industry and social-economic sphere, from the standpoint of introducing new information technologies.
It is interesting for a wide range of researchers, teachers, graduate students and professionals in the field of innovation and information technologies. ...

Added: May 24, 2018

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

Tamm M., Majumdar S., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2012 Vol. 86 P. 021135

We compute analytically the mean number of common sites, WN(t), visited by N independent random walkers each of length t and all starting at the origin at t=0 in d dimensions. We show that in the (N−d) plane, there are three distinct regimes for the asymptotic large-t growth of WN(t). These three regimes are separated by two critical lines d=2 and d=dc(N)=2N/(N−1) in the (N-d) plane. For d<2, WN(t)∼td/2 for large t (the N dependence is ...

Added: November 18, 2013