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Papers by Yury Stepanyants

Research paper thumbnail of Transformation of envelope solitons on a bottom step

Physics of Fluids, 2021

In this paper, we study the transformation of surface envelope solitons traveling over a bottom s... more In this paper, we study the transformation of surface envelope solitons traveling over a bottom step in water of a finite depth. Using the transformation coefficients earlier derived in the linear approximation, we find the parameters of transmitted pulses and subsequent evolution of the pulses in the course of propagation. Relying on the weakly nonlinear theory, the analytic formulas are derived which describe the maximum attainable wave amplitude in the neighborhood of the step and in the far zone. Solitary waves may be greatly amplified (within the weakly nonlinear theory formally, even without a limit) when propagating from relatively shallow water to the deeper domain due to the constructive interference between the newly emerging envelope solitons and the residual quasi-linear waves. The theoretical results are in good agreement with the data of direct numerical modeling of soliton transformation. In particular, more than double wave amplification is demonstrated in the perfor...

Research paper thumbnail of A conceptual model for the description of oxidation and transport processes in sulphidic waste rock dumps

Applied Mathematical Modelling, Jul 1, 2002

Research paper thumbnail of Referee’s report on the paper by T. Talipova, E. Pelinovsky, O. Kurkina, A. Giniyatullin, A. Kurkin “Exceedance frequency of appearance of extreme internal waves in the World Ocean”

Research paper thumbnail of Dynamics of particles in the steady flows of an inviscid fluid

Research paper thumbnail of Reflectionless wave propagation on shallow water with variable bathymetry and current

Journal of Fluid Mechanics, Nov 24, 2021

Research paper thumbnail of Interaction of multi-lumps within the Kadomtsev–Petviashvili equation

Research paper thumbnail of Nonlinear spectra of shallow water waves

HAL (Le Centre pour la Communication Scientifique Directe), 2013

The problem of spectra interpretation of nonlinear shallow water waves is studied in terms of int... more The problem of spectra interpretation of nonlinear shallow water waves is studied in terms of interacting Korteweg-de Vries (KdV) solitons and quasi-linear wavetrains. The method of data processing of random wave field is suggested and illustrated by an example. The soliton component obscured in the random wave field can be determined either on the basis of the inverse scattering method or by direct numerical solution of the KdV equation. The distribution function of number of solitons on amplitudes was constructed for the illustrative example. The relevance of the suggested approach to field measurements is discussed.

Research paper thumbnail of Generalized Korteweg–de Vries equation for internal waves in two-layer fluid

Research paper thumbnail of Burgers–Rott vortices with surface tension

Zeitschrift für Angewandte Mathematik und Physik, May 31, 2008

Research paper thumbnail of Stationary bathtub vortices and a critical regime of liquid discharge

Journal of Fluid Mechanics, May 14, 2008

Research paper thumbnail of Complex Dynamics of Solitons in Rotating Fluids

Research paper thumbnail of Localized nonlinear optical modes and the corresponding support structures: Exact solutions to the nonlinear Schrödinger equation with external potentials

Research paper thumbnail of Stationary Gravity Waves with the Zero Mean Vorticity in Stratified Fluid

Studies in Applied Mathematics, Dec 16, 2011

Research paper thumbnail of Solitary wave instability in the positive-dispersion media described by the two-dimensional Boussinesq equations

Journal of Experimental and Theoretical Physics, Jul 1, 1994

Research paper thumbnail of Nanoparticle Dynamics in a Viscous Fluid at Small Reynolds Numbers

Proceedings of the 6th Australasian Congress on Applied Mechanics, Dec 1, 2010

Dynamics of small size solid particles in viscous density stratified fluid is studied analyticall... more Dynamics of small size solid particles in viscous density stratified fluid is studied analytically and numerically within the framework of the creeping flow approximation corresponding to very small Reynolds numbers. The equation of motion for a particle includes a consideration of the gravity/buoyancy force, Stokes drag force and the Bossinesq-Basset drag (BBD) force. The problem studied is applicable to many practical situations where particle motion may be experienced in viscous fluid of variable density. Exact analytical solutions describing particle motion are obtained both for the buoyant and heavy particles. It is shown that for a non-stationary motion of a particle, the consideration of the BBD force is principally important, resulting in much slower decay of the particle velocity compared to the case when only the Stokes drag force is accounted. A heavy particle motion in piece-homogeneous multilayered fluid and in smoothly stratified fluid is also studied. The results obtained are relevant in particular to the physical processes occurring in the cooling systems of nuclear reactors such as the Open Pool Australian Light-water research reactor OPAL at Lucas Heights, Sydney.

Research paper thumbnail of Evolution of non-stationary pulses in a cold magnetized quark-gluon plasma

Communications in Nonlinear Science and Numerical Simulation, Apr 1, 2020

Research paper thumbnail of Structure of two-dimensional solitons in the context of a generalized Kadomtsev-Petviashvili equation

Radiophysics and Quantum Electronics, Oct 1, 1987

Research paper thumbnail of On the connections between solutions of one-dimensional and quasi-one-dimensional evolution equations

Russian Mathematical Surveys, Feb 28, 1989

Research paper thumbnail of Reflectionless wave propagation on shallow water with variable bathymetry and current. Part 2

Journal of Fluid Mechanics, Mar 24, 2022

Research paper thumbnail of Transformation of Narrowband Wavetrains of Surface Gravity Waves Passing over a Bottom Step

Mathematical Modelling of Natural Phenomena, 2014

Research paper thumbnail of Transformation of envelope solitons on a bottom step

Physics of Fluids, 2021

In this paper, we study the transformation of surface envelope solitons traveling over a bottom s... more In this paper, we study the transformation of surface envelope solitons traveling over a bottom step in water of a finite depth. Using the transformation coefficients earlier derived in the linear approximation, we find the parameters of transmitted pulses and subsequent evolution of the pulses in the course of propagation. Relying on the weakly nonlinear theory, the analytic formulas are derived which describe the maximum attainable wave amplitude in the neighborhood of the step and in the far zone. Solitary waves may be greatly amplified (within the weakly nonlinear theory formally, even without a limit) when propagating from relatively shallow water to the deeper domain due to the constructive interference between the newly emerging envelope solitons and the residual quasi-linear waves. The theoretical results are in good agreement with the data of direct numerical modeling of soliton transformation. In particular, more than double wave amplification is demonstrated in the perfor...

Research paper thumbnail of A conceptual model for the description of oxidation and transport processes in sulphidic waste rock dumps

Applied Mathematical Modelling, Jul 1, 2002

Research paper thumbnail of Referee’s report on the paper by T. Talipova, E. Pelinovsky, O. Kurkina, A. Giniyatullin, A. Kurkin “Exceedance frequency of appearance of extreme internal waves in the World Ocean”

Research paper thumbnail of Dynamics of particles in the steady flows of an inviscid fluid

Research paper thumbnail of Reflectionless wave propagation on shallow water with variable bathymetry and current

Journal of Fluid Mechanics, Nov 24, 2021

Research paper thumbnail of Interaction of multi-lumps within the Kadomtsev–Petviashvili equation

Research paper thumbnail of Nonlinear spectra of shallow water waves

HAL (Le Centre pour la Communication Scientifique Directe), 2013

The problem of spectra interpretation of nonlinear shallow water waves is studied in terms of int... more The problem of spectra interpretation of nonlinear shallow water waves is studied in terms of interacting Korteweg-de Vries (KdV) solitons and quasi-linear wavetrains. The method of data processing of random wave field is suggested and illustrated by an example. The soliton component obscured in the random wave field can be determined either on the basis of the inverse scattering method or by direct numerical solution of the KdV equation. The distribution function of number of solitons on amplitudes was constructed for the illustrative example. The relevance of the suggested approach to field measurements is discussed.

Research paper thumbnail of Generalized Korteweg–de Vries equation for internal waves in two-layer fluid

Research paper thumbnail of Burgers–Rott vortices with surface tension

Zeitschrift für Angewandte Mathematik und Physik, May 31, 2008

Research paper thumbnail of Stationary bathtub vortices and a critical regime of liquid discharge

Journal of Fluid Mechanics, May 14, 2008

Research paper thumbnail of Complex Dynamics of Solitons in Rotating Fluids

Research paper thumbnail of Localized nonlinear optical modes and the corresponding support structures: Exact solutions to the nonlinear Schrödinger equation with external potentials

Research paper thumbnail of Stationary Gravity Waves with the Zero Mean Vorticity in Stratified Fluid

Studies in Applied Mathematics, Dec 16, 2011

Research paper thumbnail of Solitary wave instability in the positive-dispersion media described by the two-dimensional Boussinesq equations

Journal of Experimental and Theoretical Physics, Jul 1, 1994

Research paper thumbnail of Nanoparticle Dynamics in a Viscous Fluid at Small Reynolds Numbers

Proceedings of the 6th Australasian Congress on Applied Mechanics, Dec 1, 2010

Dynamics of small size solid particles in viscous density stratified fluid is studied analyticall... more Dynamics of small size solid particles in viscous density stratified fluid is studied analytically and numerically within the framework of the creeping flow approximation corresponding to very small Reynolds numbers. The equation of motion for a particle includes a consideration of the gravity/buoyancy force, Stokes drag force and the Bossinesq-Basset drag (BBD) force. The problem studied is applicable to many practical situations where particle motion may be experienced in viscous fluid of variable density. Exact analytical solutions describing particle motion are obtained both for the buoyant and heavy particles. It is shown that for a non-stationary motion of a particle, the consideration of the BBD force is principally important, resulting in much slower decay of the particle velocity compared to the case when only the Stokes drag force is accounted. A heavy particle motion in piece-homogeneous multilayered fluid and in smoothly stratified fluid is also studied. The results obtained are relevant in particular to the physical processes occurring in the cooling systems of nuclear reactors such as the Open Pool Australian Light-water research reactor OPAL at Lucas Heights, Sydney.

Research paper thumbnail of Evolution of non-stationary pulses in a cold magnetized quark-gluon plasma

Communications in Nonlinear Science and Numerical Simulation, Apr 1, 2020

Research paper thumbnail of Structure of two-dimensional solitons in the context of a generalized Kadomtsev-Petviashvili equation

Radiophysics and Quantum Electronics, Oct 1, 1987

Research paper thumbnail of On the connections between solutions of one-dimensional and quasi-one-dimensional evolution equations

Russian Mathematical Surveys, Feb 28, 1989

Research paper thumbnail of Reflectionless wave propagation on shallow water with variable bathymetry and current. Part 2

Journal of Fluid Mechanics, Mar 24, 2022

Research paper thumbnail of Transformation of Narrowband Wavetrains of Surface Gravity Waves Passing over a Bottom Step

Mathematical Modelling of Natural Phenomena, 2014

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