# Transformation of surface waves over a bottom step

Article

Kurkin, A. A., Semin, S. V. and Stepanyants, Yu A.. 2015. "Transformation of surface waves over a bottom step." Russian Academy of Sciences, Izvestiya: Atmospheric and Oceanic Physics. 51 (2), pp. 214-223. https://doi.org/10.1134/S0001433815020097
Article Title Transformation of surface waves over a bottom step 1918 Article Kurkin, A. A. (Author), Semin, S. V. (Author) and Stepanyants, Yu A. (Author) Russian Academy of Sciences, Izvestiya: Atmospheric and Oceanic Physics 51 (2), pp. 214-223 10 2015 Russian Federation 0001-4338 1023-6317 1555-628X https://doi.org/10.1134/S0001433815020097 http://link.springer.com/article/10.1134%2FS0001433815020097 We analyze in detail the problem of the transformation of surface gravity waves over a bottom step in a basin of arbitrary depth in the linear approximation. We found that strict analytical results can be obtained only when a denumerable set of modes condensed near the step is taken into account. At the same time, one can use the formulas suggested in this work for the practical calculations. They provide an accuracy of 5% for the wave transmission coefficient. The specific peculiarities of transformation coefficients are discussed, including their nonmonotonic dependence on the parameters, asymptotic behavior at strong depth variations, etc. The data of a direct numerical simulation of wave transformation over a step are presented, which are compared with the exact and approximate formulas. The coefficients of excitation of modes condensed near the step by an incident quasi-monochromatic wave are found. A relationship between the transformation coefficients that follows from the conservation law of wave energy flux is found. surface waves, wave transformation, transmission coefficient, reflection coefficient, oceanic shelf, bottom step, evanescent modes 401207. Fundamental and theoretical fluid dynamics 370803. Physical oceanography 490109. Theoretical and applied mechanics Files associated with this item cannot be displayed due to copyright restrictions. Nizhny Novgorod State Technical University, Russia School of Agricultural, Computational and Environmental Sciences University of Southern Queensland

https://research.usq.edu.au/item/q309z/transformation-of-surface-waves-over-a-bottom-step

total views
• ##### 2
views this month

## Related outputs

##### Long wave propagation in canals with spatially varying cross-sections and currents
Churilov, Semyon and Stepanyants, Yury. 2024. "Long wave propagation in canals with spatially varying cross-sections and currents." Nonlinear and Modern Mathematical Physics (NMMP 2022). Tallahassee, United States 17 - 19 Jun 2022 United States. Springer. pp. 19-79 https://doi.org/10.1007/978-3-031-59539-4_2
##### Localized wave structures: Solitons and beyond
Ostrovsky, L., Pelinovsky, E., Shrira, V. and Stepanyants, Y.. 2024. "Localized wave structures: Solitons and beyond." Chaos: an interdisciplinary journal of nonlinear science. 34. https://doi.org/10.1063/5.0210903
##### Frequency downshifting in decaying wavetrains on the ocean surface covered by ice floes
Slunyaev, A. V. and Stepanyants, Y. A.. 2024. "Frequency downshifting in decaying wavetrains on the ocean surface covered by ice floes." Physics of Fluids. 36 (3). https://doi.org/10.1063/5.0200538
##### Solitons and lumps in the cylindrical Kadomtsev–Petviashvili equation. II. Lumps and their interactions
Zhang, Zhao, Hu, Wencheng, Guo, Qi and Stepanyants, Yury. 2024. "Solitons and lumps in the cylindrical Kadomtsev–Petviashvili equation. II. Lumps and their interactions." Chaos: an interdisciplinary journal of nonlinear science. 34 (1). https://doi.org/10.1063/5.0175716
##### Solitons and lumps in the cylindrical Kadomtsev–Petviashvili equation. I. Axisymmetric solitons and their stability
Hu, Wencheng, Zhang, Zhao, Guo, Qi and Stepanyants, Yury. 2024. "Solitons and lumps in the cylindrical Kadomtsev–Petviashvili equation. I. Axisymmetric solitons and their stability." Chaos: an interdisciplinary journal of nonlinear science. 34 (1). https://doi.org/10.1063/5.0175696
##### Scattering of gravity-capillary waves on a bottom step
Meylan, M.H. and Stepanyants, Y.A.. 2024. "Scattering of gravity-capillary waves on a bottom step." Physics of Fluids. 36 (1). https://doi.org/10.1063/5.0181237
##### Creation of weakly interacting lumps by degeneration of lump chains in the KP1 equation
Zhang, Zhao, Guo, Qi and Stepanyants, Yury. 2023. "Creation of weakly interacting lumps by degeneration of lump chains in the KP1 equation." Chaos, Solitons and Fractals. 170, pp. 1-13. https://doi.org/10.1016/j.chaos.2023.113398
##### Analysis of internal solitary waves in the Gulf of Oman and sources responsible for their generation
Koohestani, Kamran, Stepanyants, Yury and Allahdadi, Mohammad Nabi. 2023. "Analysis of internal solitary waves in the Gulf of Oman and sources responsible for their generation." Water: an open access journal. 15 (4), pp. 1-28. https://doi.org/10.3390/w15040746
##### Solitary waves and their interactions in the cylindrical Korteweg–de Vries equation
Hu, Wencheng, Ren, Jingli and Stepanyants, Y.. 2023. "Solitary waves and their interactions in the cylindrical Korteweg–de Vries equation." Symmetry. 15. https://doi.org/10.3390/sym15020413
##### Interaction of internal solitary waves with long periodic waves within the rotation modified Benjamin-Ono equation
Grimshaw, R. H. J., Smyth, N. F. and Stepanyants, Y. A.. 2021. "Interaction of internal solitary waves with long periodic waves within the rotation modified Benjamin-Ono equation." Physica D: Nonlinear Phenomena. 419, pp. 1-10. https://doi.org/10.1016/j.physd.2021.132867
##### Multi-lump formations from lump chains and plane solitons in the KP1 equation
Zhang, Zhao, Yang, Xiangyu, Li, Biao, Guo, Qi and Stepanyants, Yury. 2023. "Multi-lump formations from lump chains and plane solitons in the KP1 equation." Nonlinear Dynamics. 111 (2), p. 1625–1642. https://doi.org/10.1007/s11071-022-07903-8
##### Peculiarities of resonant interactions of lump chains within the KP1 equation
Zhang, Zhao, Li, Biao, Chen, Junchao, Guo, Qi and Stepanyants, Yury. 2022. "Peculiarities of resonant interactions of lump chains within the KP1 equation." Physica Scripta: an international journal for experimental and theoretical physics. 97 (11), pp. 1-14. https://doi.org/10.1088/1402-4896/ac99aa
##### Complex Dynamics of Solitons in Rotating Fluids
Ostrovsky, Lev A. and Stepanyants, Yury A.. 2022. "Complex Dynamics of Solitons in Rotating Fluids." Volchenkov, Dimitri and Machado, J. A. Tenreiro (ed.) Mathematical Methods in Modern Complexity Science. Switzerland. Springer. pp. 63-78
##### Lump Interactions with Plane Solitons
Stepanyants, Yu. A., Zakharov, D. V. and Zakharov, V. E.. 2022. "Lump Interactions with Plane Solitons." Radiophysics and Quantum Electronics. 64 (10), pp. 665-680. https://doi.org/10.1007/s11141-022-10169-0
##### Assessment and Prediction of Sea Level Trend in the South Pacific Region
Raj, Nawin, Gharineiat, Zahra, Ahmed, Abul Abrar Masrur and Stepanyants, Yury. 2022. "Assessment and Prediction of Sea Level Trend in the South Pacific Region." Remote Sensing. 14 (4), pp. 1-25. https://doi.org/10.3390/rs14040986
##### Modulation Instability of Hydro-Elastic Waves Blown by a Wind with a Uniform Vertical Profile
Boral, Susam, Sahoo, Trilochan and Stepanyants, Yury. 2021. "Modulation Instability of Hydro-Elastic Waves Blown by a Wind with a Uniform Vertical Profile." Fluids. 6 (12), pp. 1-18. https://doi.org/10.3390/fluids6120458
##### Dynamics of internal envelope solitons in a rotating fluid of a variable depth
Stepanyants, Yury. 2019. "Dynamics of internal envelope solitons in a rotating fluid of a variable depth." Fluids. 4 (1), pp. 1-12. https://doi.org/10.3390/fluids4010056
##### Modulation property of flexural-gravity waves on a water surface covered by a compressed ice sheet
Slunyaev, A. V. and Stepanyants, Y. A.. 2022. "Modulation property of flexural-gravity waves on a water surface covered by a compressed ice sheet." Physics of Fluids. 34, pp. 1-17. https://doi.org/10.1063/5.0100179
##### Symmetric interactions of plane solitons in two-dimensional nonlinear lattices
Nikitenkova, Svetlana and Stepanyants, Yury. 2022. "Symmetric interactions of plane solitons in two-dimensional nonlinear lattices." Communications in Nonlinear Science and Numerical Simulation. 114, pp. 1-10. https://doi.org/10.1016/j.cnsns.2022.106602
##### Degenerate lump interactions within the Kadomtsev-Petviashvili equation
Zhang, Zhao, Li, Biao, Chen, Junchao, Guo, Qi and Stepanyants, Yury. 2022. "Degenerate lump interactions within the Kadomtsev-Petviashvili equation." Communications in Nonlinear Science and Numerical Simulation. 112, pp. 1-14. https://doi.org/10.1016/j.cnsns.2022.106555
##### Reflectionless wave propagation on shallow water with variable bathymetry and current. Part 2
Churilov, Semyon M. and Stepanyants, Yury A.. 2022. "Reflectionless wave propagation on shallow water with variable bathymetry and current. Part 2." Journal of Fluid Mechanics. 939, pp. 1-12. https://doi.org/10.1017/jfm.2022.208
##### Reflectionless wave propagation on shallow water with variable bathymetry and current
Churilov, Semyon M. and Stepanyants, Yury A.. 2021. "Reflectionless wave propagation on shallow water with variable bathymetry and current." Journal of Fluid Mechanics. 931, pp. 1-25. https://doi.org/10.1017/jfm.2021.935
##### Hydrodynamic models of astrophysical wormholes: the general concept
Churilov, Semyon and Stepanyants, Yury. 2021. "Hydrodynamic models of astrophysical wormholes: the general concept." Physics of Fluids. 33 (7), pp. 1-23. https://doi.org/10.1063/5.0056877
##### Transformation of envelope solitons on a bottom step
Ducrozet, Guillaume, Slunyaev, Alexey and Stepanyants, Yury. 2021. "Transformation of envelope solitons on a bottom step." Physics of Fluids. 33. https://doi.org/10.1063/5.0054806
##### Modulation instability of surface waves in the model with the uniform wind profile
Boral, Susam, Sahoo, Trilochan and Stepanyants, Yury. 2021. "Modulation instability of surface waves in the model with the uniform wind profile." Symmetry. 13. https://doi.org/10.3390/sym13040651
##### Can a submarine be perished by internal waves?
Stepanyants, Yu. A.. 2021. "Can a submarine be perished by internal waves?" Priroda (in Russian).
##### Hydrodynamic Forces Exerting on an Oscillating Cylinder under Translational Motion in Water Covered by Compressed Ice
Stepanyants Yury and Sturova, Izolda. 2021. "Hydrodynamic Forces Exerting on an Oscillating Cylinder under Translational Motion in Water Covered by Compressed Ice ." Water: an open access journal. 13 (6). https://doi.org/10.3390/w13060822
##### Description of Nonlinear Vortical Flows of Incompressible Fluid in Terms of a Quasi-Potential
Ermakov, Andrei and Stepanyants, Yury. 2021. "Description of Nonlinear Vortical Flows of Incompressible Fluid in Terms of a Quasi-Potential ." Physics. 3 (4), pp. 799-913. https://doi.org/10.3390/physics3040050
##### Waves on a compressed floating ice plate caused by motion of a dipole in water
Stepanyants, Yury and Sturova, Izolda V.. 2020. "Waves on a compressed floating ice plate caused by motion of a dipole in water." Journal of Fluid Mechanics. 907, pp. A7-1. https://doi.org/10.1017/jfm.2020.764
##### Emergence of envelop solitary waves from initial localised pulses within the Ostrovsky equation
Grimshaw, R. H. J. and Stepanyants, Y. A.. 2020. "Emergence of envelop solitary waves from initial localised pulses within the Ostrovsky equation." Radiophysics and Quantum Electronics. 63 (1), pp. 21-28. https://doi.org/10.1007/s11141-020-10031-1
##### The asymptotic approach to the description of two-dimensional symmetric soliton patterns
Stepanyants, Yury. 2020. "The asymptotic approach to the description of two-dimensional symmetric soliton patterns." Symmetry. 12 (10). https://doi.org/10.3390/sym12101586
##### A geometric model for estimating the volume and surface area of apples
Scarmana, Gabriel, McDougall, Kevin and Stepanyants, Yury. 2020. "A geometric model for estimating the volume and surface area of apples." Smart Surveyors for Land and Water Management (2020). Amsterdam, Netherlands 10 - 14 May 2020 Copenhagen, Denmark.
##### Kinematics of interacting solitons in two-dimensional space
Ostrovsky, L.A. and Stepanyants, Y. A.. 2020. "Kinematics of interacting solitons in two-dimensional space." Russian Journal of Earth Science. 20, pp. 1-11. https://doi.org/10.2205/2020ES000735
##### Nonlinear Models of Finite Amplitude Interfacial Waves in Shallow Two-Layer Fluid
Kurkina, Oxana, Kurkin, Andrey, Pelinovsky, Efim, Stepanyants, Yury and Talipova, Tatiana. 2019. "Nonlinear Models of Finite Amplitude Interfacial Waves in Shallow Two-Layer Fluid." Berezovski, Arkadi and Soomere, Tarmo (ed.) Applied Wave Mathematics II: Selected Topics in Solids, Fluids, and Mathematical Methods and Complexity. Cham, Switzerland. Springer. pp. 61-87
##### Nonlinear Waves in a Rotating Ocean (The Ostrovsky Equation and Its Generalizations and Applications)
Stepanyants, Yury. 2020. "Nonlinear Waves in a Rotating Ocean (The Ostrovsky Equation and Its Generalizations and Applications)." Russian Academy of Sciences, Izvestiya: Atmospheric and Oceanic Physics. 56 (1), pp. 16-32. https://doi.org/10.1134/S0001433820010077
##### Evolution of non-stationary pulses in a cold magnetized quark-gluon plasma
Fogaca, D. A., Fariello, R., Navarra, F. S. and Stepanyants, Y. A.. 2020. "Evolution of non-stationary pulses in a cold magnetized quark-gluon plasma." Communication on Nonlinear Sciences and Numerical Simulation. 83. https://doi.org/10.1016/j.cnsns.2019.105144
##### Transformation of Long Surface and Tsunami-Like Waves in the Ocean with a Variable Bathymetry
Ermakov, Andrei and Stepanyants, Yury. 2020. "Transformation of Long Surface and Tsunami-Like Waves in the Ocean with a Variable Bathymetry." Pure and Applied Geophysics. 177 (3), pp. 1675-1693. https://doi.org/10.1007/s00024-019-02259-4
##### Rossby waves in the ocean covered by compressed ice
Stepanyants, Y. A. and Sturova, I. V.. 2020. "Rossby waves in the ocean covered by compressed ice." Geophysical and Astrophysical Fluid Dynamics. 114 (3), pp. 306-316. https://doi.org/10.1080/03091929.2020.1712716
##### Soliton interaction with external forcing within the Korteweg–de Vries equation
Ermakov, Andrei and Stepanyants, Yury. 2019. "Soliton interaction with external forcing within the Korteweg–de Vries equation." Chaos: an interdisciplinary journal of nonlinear science. 29 (1). https://doi.org/10.1063/1.5063561
##### The effects of interplay between the rotation and shoaling for a solitary wave on variable topography
Stepanyants, Yury. 2019. "The effects of interplay between the rotation and shoaling for a solitary wave on variable topography." Studies in Applied Mathematics. 142 (4 (Special Issue)), pp. 465-486. https://doi.org/10.1111/sapm.12255
##### Helical solitons in vector modified Korteweg-de Vries equations
Pelinovsky, Dmitry E. and Stepanyants, Yury A.. 2018. "Helical solitons in vector modified Korteweg-de Vries equations." Physics Letters A. 382 (44), pp. 3165-3171. https://doi.org/10.1016/j.physleta.2018.08.015
##### Dynamics of particles and bubbles under the action of acoustic radiation force
Ostrovsky, Lev A. and Stepanyants, Yury A.. 2018. "Dynamics of particles and bubbles under the action of acoustic radiation force." Edelman, Mark, Macau, Elbert E. N. and Sanjuan, Miguel A. F. (ed.) Chaotic, fractional, and complex dynamics: New insights and perspectives. Germany. Springer. pp. 205-230
##### Modeling of Bose–Einstein condensation in a water tank
Rousseaux, Germain and Stepanyants, Yury. 2018. "Modeling of Bose–Einstein condensation in a water tank." Abcha, Nizar, Pelinovsky, Efim and Mutabazi, Innocent (ed.) Nonlinear waves and pattern dynamics. Cham, Switzerland. Springer. pp. 91-102
##### Adiabatic decay of internal solitons due to Earth’s rotation within the framework of the Gardner–Ostrovsky equation
Obregon, Maria, Raj, Nawin and Stepanyants, Yury. 2018. "Adiabatic decay of internal solitons due to Earth’s rotation within the framework of the Gardner–Ostrovsky equation." Chaos: an interdisciplinary journal of nonlinear science. 28 (3), pp. 1-11. https://doi.org/10.1063/1.5021864
##### Decay of Benjamin–Ono solitons under the influence of dissipation
Grimshaw, Roger H., Smyth, Noel F. and Stepanyants, Yury A.. 2018. "Decay of Benjamin–Ono solitons under the influence of dissipation." Wave Motion. 78, pp. 98-115. https://doi.org/10.1016/j.wavemoti.2018.01.005
##### Resonance properties of forced oscillations of particles and gaseous bubbles in a viscous fluid at small Reynolds numbers
Hassan, H. K. and Stepanyants, Y. A.. 2017. "Resonance properties of forced oscillations of particles and gaseous bubbles in a viscous fluid at small Reynolds numbers." Physics of Fluids. 29 (10), pp. 1-5. https://doi.org/10.1063/1.5002152
##### Particle dynamics in a viscous fluid under the action of acoustic radiation force
Hassan, Hassan K., Ostrovsky, Lev A. and Stepanyants, Yury A.. 2017. "Particle dynamics in a viscous fluid under the action of acoustic radiation force." Interdisciplinary Journal of Discontinuity, Nonlinearity, and Complexity. 6 (3), pp. 317-327. https://doi.org/10.5890/DNC.2017.09.006
##### Internal solitary waves in two-layer fluids at near-critical situation
Kurkina, O., Singh, N. and Stepanyants, Y.. 2014. "Internal solitary waves in two-layer fluids at near-critical situation." 19th Australasian Fluid Mechanics Conference (AFMC 2014). Melbourne, Australia 08 - 11 Dec 2014 Australia.
##### Soliton solutions to the fifth-order Korteweg–de Vries equation and their applications to surface and internal water waves
Khusnutdinova, K. R., Stepanyants, Y. A. and Tranter, M. R.. 2018. "Soliton solutions to the fifth-order Korteweg–de Vries equation and their applications to surface and internal water waves." Physics of Fluids. 30 (2), pp. 1-20. https://doi.org/10.1063/1.5009965
##### Decay of Kadomtsev–Petviashvili lumps in dissipative media
Clarke, S., Gorshkov, K., Grimshaw, R. and Stepanyants, Y.. 2018. "Decay of Kadomtsev–Petviashvili lumps in dissipative media." Physica D: Nonlinear Phenomena. 366, pp. 43-50. https://doi.org/10.1016/j.physd.2017.11.009
##### Multi-lump structures in the Kadomtsev–Petviashvili equation
Stepanyants, Yury. 2017. "Multi-lump structures in the Kadomtsev–Petviashvili equation." Aronson, Igor S., Pikovsky, Arkady, Rulkov, Nikolai F. and Tsimring, Lev S. (ed.) Advances in dynamics, patterns, cognition: challenges in complexity. Cham, Switzerland. Springer. pp. 307-324
##### Soliton spectra of random water waves in shallow basins
Giovanangeli, J.-P., Kharif, C. and Stepanyants, Y.A.. 2018. "Soliton spectra of random water waves in shallow basins." Mathematical Modelling of Natural Phenomena (MMNP). 13 (4), pp. 1-20. https://doi.org/10.1051/mmnp/2018018
##### Obliquely propagating skew KP lumps
Singh, N. and Stepanyants, Y.. 2016. "Obliquely propagating skew KP lumps." Wave Motion. 64, pp. 92-102. https://doi.org/10.1016/j.wavemoti.2016.03.005
##### Wave scattering in spatially inhomogeneous currents
Churilov, Semyon, Ermakov, Andrei and Stepanyants, Yury. 2017. "Wave scattering in spatially inhomogeneous currents." Physical Review D. 96 (6), p. 064016. https://doi.org/10.1103/PhysRevD.96.064016
##### Scattering of long water waves in a canal with rapidly varying cross-section in the presence of a current
Churilov, Semyon, Ermakov, Andrei, Rousseaux, Germain and Stepanyants, Yury. 2017. "Scattering of long water waves in a canal with rapidly varying cross-section in the presence of a current." Physcial Review Fluids. 2 (9), p. 094805. https://doi.org/10.1103/PhysRevFluids.2.094805
##### Adiabatic decay of internal solitons in a rotating ocean
Obregon, M. A., Raj, N. and Stepanyants, Y. A.. 2016. "Adiabatic decay of internal solitons in a rotating ocean." 20th Australasian Fluid Mechanics Conference (AFMC 2016). Perth, Australia 05 - 08 Dec 2016 Australia.
##### Modulational instability of wave trains in a rotating ocean
Nikitenkova, S. P., Singh, N. N. and Stepanyants, Y. A.. 2016. "Modulational instability of wave trains in a rotating ocean." 20th Australasian Fluid Mechanics Conference (AFMC 2016). Perth, Australia 05 - 08 Dec 2016 Australia.
##### Transformation of internal waves at the bottom ledge
Churaev, E. N., Semin, S. V. and Stepanyants, Y. A.. 2014. "Transformation of internal waves at the bottom ledge." 19th Australasian Fluid Mechanics Conference (AFMC 2014). Melbourne, Australia 08 - 11 Dec 2014 Australia.
##### Description of vortical flows of incompressible fluid in terms of quasi-potential function
Ermakov, A. M. and Stepanyants, Y. A.. 2016. "Description of vortical flows of incompressible fluid in terms of quasi-potential function." 20th Australasian Fluid Mechanics Conference (AFMC 2016). Perth, Australia 05 - 08 Dec 2016 Australia.
##### Interaction of solitons with long waves in a rotating fluid
Ostrovsky, L. A. and Stepanyants, Y. A.. 2016. "Interaction of solitons with long waves in a rotating fluid." Physica D: Nonlinear Phenomena. 333, pp. 266-275. https://doi.org/10.1016/j.physd.2016.02.008
##### Wave blocking phenomenon of surface waves on a shear flow with a constant vorticity
Maissa, Philippe, Rousseaux, Germain and Stepanyants, Yury. 2016. "Wave blocking phenomenon of surface waves on a shear flow with a constant vorticity." Physics of Fluids. 28 (3), pp. 1-18. https://doi.org/10.1063/1.4942116
##### Negative energy waves in shear flow with a linear profile
Maissa, Philippe, Rousseaux, Germain and Stepanyants, Yury. 2016. "Negative energy waves in shear flow with a linear profile." European Journal of Mechanics B: Fluids. 56, pp. 192-199. https://doi.org/10.1016/j.euromechflu.2016.01.003
##### Formation of wave packets in the Ostrovsky equation for both normal and anomalous dispersion
Grimshaw, Roger, Stepanyants, Yury and Alias, Azwani. 2016. "Formation of wave packets in the Ostrovsky equation for both normal and anomalous dispersion." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 472 (2185), pp. 1-20. https://doi.org/10.1098/rspa.2015.0416
##### Transformation of surface and internal waves on a bottom step
Kurkin, Andrey, Semin, Sergey and Stepanyants, Yury. 2015. "Transformation of surface and internal waves on a bottom step." Fundamental and Applied Hydrophysics (in Russian). 8 (3), pp. 3-19.
##### Modulational stability of weakly nonlinear wave-trains in media with small- and large-scale dispersions
Nikitenkova, S., Singh, N. and Stepanyants, Y.. 2015. "Modulational stability of weakly nonlinear wave-trains in media with small- and large-scale dispersions." Chaos: an interdisciplinary journal of nonlinear science. 25 (12), pp. 123113-1. https://doi.org/10.1063/1.4937362
##### Transient free surface flow past a two-dimensional flat stern
Ogilat, Osama and Stepanyants, Yury. 2015. "Transient free surface flow past a two-dimensional flat stern." Discontinuity, Nonlinearity and Complexity. 4 (3), pp. 353-369. https://doi.org/10.5890/DNC.2015.09.010
##### The Bernoulli integral for a certain class of non-stationary viscous vortical flows of incompressible fluid
Stepanyants, Y. A. and Yakubovich, E. I.. 2015. "The Bernoulli integral for a certain class of non-stationary viscous vortical flows of incompressible fluid." Studies in Applied Mathematics. 135 (3), pp. 295-309. https://doi.org/10.1111/sapm.12087
##### Transformation of waves over a bottom step
Kurkin, Andrey, Semin, Sergey and Stepanyants, Yury. 2015. Transformation of waves over a bottom step. Nizhny Novgorod (Russia). Nizhny Novgorod State Technical University.
##### Modeling of transformation of surface wave packets interacting with abrupt bottom change
Brovchenko, Igor, Maderich, Vladimir, Semin, Sergey, Stepanyants, Yury and Terletska, Kateryna. 2015. "Modeling of transformation of surface wave packets interacting with abrupt bottom change." Applied Hydromechanics. 17 (1), pp. 3-9.
##### Dynamics of two charged particles in a creeping flow
Hassan, H. K. and Stepanyants, Y. A.. 2015. "Dynamics of two charged particles in a creeping flow." Journal of Physical Mathematics. 6 (2). https://doi.org/10.4172/2090-0902.1000145
##### Beyond the KdV: post-explosion development
Ostrovsky, L., Pelinovsky, E., Shrira, V. and Stepanyants, Y.. 2015. "Beyond the KdV: post-explosion development." Chaos: an interdisciplinary journal of nonlinear science. 25 (9), pp. 1-13. https://doi.org/10.1063/1.4927448
##### Generalized Korteweg–de Vries equation for internal waves in two-layer fluid
Giniyatullin, A. R., Kurkin, A. A., Kurkina, O. E. and Stepanyants, Y. A.. 2014. "Generalized Korteweg–de Vries equation for internal waves in two-layer fluid." Fundamental and Applied Hydrophysics (in Russian). 7 (4), pp. 16-28.
##### Transformation of internal waves passing over a bottom step
Churaev, Egor N., Semin, Sergey V. and Stepanyants, Yuri A.. 2015. "Transformation of internal waves passing over a bottom step." Journal of Fluid Mechanics. 768, pp. R3-1. https://doi.org/10.1017/jfm.2015.92
##### Structure of internal solitary waves in two-layer fluid at near-critical situation
Kurkina, O., Singh, N. and Stepanyants, Y.. 2015. "Structure of internal solitary waves in two-layer fluid at near-critical situation." Communications in Nonlinear Science and Numerical Simulation. 22 (1-3), pp. 1235-1242. https://doi.org/10.1016/j.cnsns.2014.09.018
##### Dispersion properties of waves on a surface of viscous fluid covered by an elastic film
Averbukh, E. L., Kurkin, A. A., Stepanyants, Y. A. and Talipova, T. G.. 2014. "Dispersion properties of waves on a surface of viscous fluid covered by an elastic film." Fluid Dynamics. 49 (6), pp. 796-803. https://doi.org/10.1134/S0015462814060118
##### Transformation of narrowband wavetrains of surface gravity waves passing over a bottom step
Giniyatullin, A. R., Kurkin, A. A., Semin, S. V. and Stepanyants, Y. A.. 2014. "Transformation of narrowband wavetrains of surface gravity waves passing over a bottom step." Mathematical Modelling of Natural Phenomena (MMNP). 9 (5), pp. 73-82. https://doi.org/10.1051/mmnp/20149505
##### On stationary solutions of the reduced Gardner–Ostrovsky equation
Obregon, Maria and Stepanyants, Yury. 2014. "On stationary solutions of the reduced Gardner–Ostrovsky equation." Discontinuity, Nonlinearity and Complexity. 3 (4), pp. 445-456. https://doi.org/10.5890/DNC.2014.12.007
##### Nonlinear vector waves of a flexural mode in a chain model of atomic particles
Nikitenkova, S. P., Raj, N. and Stepanyants, Y. A.. 2015. "Nonlinear vector waves of a flexural mode in a chain model of atomic particles." Communications in Nonlinear Science and Numerical Simulation. 20 (3), pp. 731-742. https://doi.org/10.1016/j.cnsns.2014.05.031
##### Interaction of gaseous bubbles under the action of radiation modified Bjerknes force
Stepanyants, Yury and Yeoh, Guan. 2008. "Interaction of gaseous bubbles under the action of radiation modified Bjerknes force." 22nd International Congress of Theoretical and Applied Mechanics (IC-TAM2008). Adelaide, Australia 24 - 29 Aug 2008
##### Recent results on the problem of wave-current interaction including water depth, surface tension/amplitude and vorticity effects
Maissa, Philippe, Rousseaux, Germain and Stepanyants, Yury. 2013. "Recent results on the problem of wave-current interaction including water depth, surface tension/amplitude and vorticity effects." 7th International Conference on Coastal Dynamics. Arcachon, France 24 - 28 Jun 2013 Arcachon, France.
##### Nonlinear spectra of shallow water waves
Giovanangeli, J. -P., Kharif, C., Raj, N. and Stepanyants, Y.. 2013. "Nonlinear spectra of shallow water waves." Oceans - San Diego, 2013. San Diego, United States 23 - 26 Sep 2013 United States. IEEE (Institute of Electrical and Electronics Engineers). https://doi.org/10.23919/OCEANS.2013.6741132
##### Numerical study of nonlinear wave processes by means of discrete chain models
Obregon, M., Raj, N. and Stepanyants, Y.. 2012. "Numerical study of nonlinear wave processes by means of discrete chain models." Gu, Y. T. and Saha, Suvash C. (ed.) 4th International Conference on Computational Methods (ICCM 2012). Gold Coast, Australia 25 - 28 Nov 2012 Brisbane, Australia.
##### On numerical solution of the Gardner Ostrovsky equation
Obregon, M. A. and Stepanyants, Y. A.. 2012. "On numerical solution of the Gardner Ostrovsky equation." Mathematical Modelling of Natural Phenomena (MMNP). 7 (2), pp. 113-130. https://doi.org/10.1051/mmnp/20127210
##### Stationary gravity waves with the zero mean vorticity in stratified fluid
Clamond, D. and Stepanyants, Y.. 2012. "Stationary gravity waves with the zero mean vorticity in stratified fluid." Studies in Applied Mathematics. 128 (1), pp. 59-85. https://doi.org/10.1111/j.1467-9590.2011.00530.x
##### Measuring rate of change of oxygen concentration and intrinsic oxidation rate in a pile of material
Bennett, John, Stepanyants, Yury and Ritchie, Ian. 2004. Measuring rate of change of oxygen concentration and intrinsic oxidation rate in a pile of material. WO 2004/072636 A1
##### Internal solitons in laboratory experiments: Comparison with theoretical models
Ostrovsky, L A. and Stepanyants, Y. A.. 2005. "Internal solitons in laboratory experiments: Comparison with theoretical models." Chaos: an interdisciplinary journal of nonlinear science. 15. https://doi.org/10.1063/1.2107087
##### Measurement of hydraulic conductivity using a radioactive or activatable tracer
Waring, Christopher Leslie, Airey, Peter Lewis and Stepanyants, Yury A.. 2007. Measurement of hydraulic conductivity using a radioactive or activatable tracer. AU2007231556
##### Measurement of hydraulic conductivity, porosity and lithology by neutron activation borehole logging at high spatial resolution increments
Waring, C. L., Stepanyants, Y. A., Hankin, S. I., Airey, P. L. and Peterson, M. A.. 2009. "Measurement of hydraulic conductivity, porosity and lithology by neutron activation borehole logging at high spatial resolution increments." Milne-Home, William A. (ed.) IAH Groundwater in The Sydney Basin Symposium (2009). Sydney, Australia 04 - 05 Aug 2009 Sydney, NSW, Australia.
##### Internal solitons in the ocean and their effect on underwater sound
Apel, John R., Ostrovsky, Lev A., Stepanyants, Yury A. and Lynch, James F.. 2007. "Internal solitons in the ocean and their effect on underwater sound." The Journal of the Acoustical Society of America. 121 (2), pp. 695-722. https://doi.org/10.1121/1.2395914
##### Influence of bottom boundary conditions for temperature on the heat distribution within oxidising heaps
Crawford, Jagoda and Stepanyants, Yury. 2005. "Influence of bottom boundary conditions for temperature on the heat distribution within oxidising heaps." Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal. 46, pp. C1104-C1125.
##### Propagation of waves in shear flows
Fabrikant, Anatoly and Stepanyants, Yury. 1998. Propagation of waves in shear flows. Singapore. World Scientific Publishing.
##### Dispersion of long gravity-capillary surface waves and asymptotic equations for solitons
Stepanyants, Yury. 2005. "Dispersion of long gravity-capillary surface waves and asymptotic equations for solitons." Proceedings of the Russian Academy of Engineering Sciences Series: Applied Mathematics and Mechanics. 14, pp. 33-40.
##### Scalar description of three-dimensional vortex flows of incompressible fluid
Stepanyants, Yu. A. and Yakubovich, Evsey. 2011. "Scalar description of three-dimensional vortex flows of incompressible fluid." Doklady Physics. 56 (2), pp. 130-133. https://doi.org/10.1134/S1028335811020169
##### The inverse problem for the Gross-Pitaevskii equation
Malomed, Boris A. and Stepanyants, Yury A.. 2010. "The inverse problem for the Gross-Pitaevskii equation." Chaos: an interdisciplinary journal of nonlinear science. 20 (1). https://doi.org/10.1063/1.3367776
##### Dynamics of two charged particles in viscous fluid at small Reynolds numbers
Stepanyants, Y. A. and Strunin, D. V.. 2011. "Dynamics of two charged particles in viscous fluid at small Reynolds numbers." de Oliveira, Cassiano (ed.) 2011 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Enginnering (MC 2011). Rio de Janeiro, Brazil 08 - 12 May 2011 Rio de Janeiro.
##### Nanoparticle dynamics in a viscous fluid at small Reynolds numbers
Stepanyants, Yury A. and Yeoh, Guan H.. 2010. "Nanoparticle dynamics in a viscous fluid at small Reynolds numbers." Teh, Kian, Davies, Ian and Howard, Ian (ed.) 6th Australasian Congress on Applied Mechanics (ACAM 6). Perth, Western Australia 12 - 15 Dec 2010 Perth, Australia.
##### Localised nonlinear optical modes and the corresponding support structures: exact solutions to the nonlinear Schrodinger equation with external potentials
Malomed, B. A. and Stepanyants, Y. A.. 2010. "Localised nonlinear optical modes and the corresponding support structures: exact solutions to the nonlinear Schrodinger equation with external potentials." ICEAA 2010: International Conference on Electromagnetics in Advanced Applications. Sydney, Australia 20 - 24 Sep 2010 Sydney, Australia. https://doi.org/10.1109/ICEAA.2010.5651681
##### Lump solutions of 2D generalized Gardner equation
Stepanyants, Y. A., Ten, I. K. and Tomita, H.. 2006. "Lump solutions of 2D generalized Gardner equation." Luo, Albert C. J., Dai, Liming and Hamidzadeh, Hamid R. (ed.) Conference on Nonlinear Science and Complexity (2006). Beijing, China 07 - 12 Aug 2006 Singapore.
##### Internal solitons in the ocean
Apel, John R., Ostrovsky, Lev A., Stepanyants, Yury A. and Lynch, James F.. 2006. Internal solitons in the ocean. Woods Hole, MA. United States. Woods Hole Oceanographic Institution.
##### Tsunami surge in a river: a hydraulic jump in an inhomogeneous channel
Caputo, Jean-Guy and Stepanyants, Y. A.. 2007. "Tsunami surge in a river: a hydraulic jump in an inhomogeneous channel." Kundu, Anjan (ed.) Tsunami and nonlinear waves. Berlin, Germany. Springer. pp. 97-112
##### Solutions classification to the extended reduced Ostrovsky equation
Stepanyants, Yury A.. 2008. "Solutions classification to the extended reduced Ostrovsky equation." Symmetry, Integrability and Geometry: Methods and Applications. 4. https://doi.org/10.3842/SIGMA.2008.073
##### Mechanisms of particle transport acceleration in porous media
Panfilov, M., Panfilova, I. and Stepanyants, Y.. 2008. "Mechanisms of particle transport acceleration in porous media." Transport in Porous Media. 74 (1), pp. 49-71. https://doi.org/10.1007/s11242-007-9201-9
##### Particle and bubble dynamics in a creeping flow
Stepanyants, Yury and Yeoh, Guan. 2009. "Particle and bubble dynamics in a creeping flow." European Journal of Mechanics B: Fluids. 28 (5), pp. 619-629. https://doi.org/10.1016/j.euromechflu.2009.04.004
##### On stationary solutions of the reduced Ostrovsky equation: periodic waves, compactons and compound solitons
Stepanyants, Yury. 2006. "On stationary solutions of the reduced Ostrovsky equation: periodic waves, compactons and compound solitons." Chaos, Solitons and Fractals. 28 (1), pp. 193-204. https://doi.org/10.1016/j.chaos.2005.05.020
##### The motion of a cylindrical body in a stratified fluid under the action of a radiation force
Kozyrev, O. R., Reznik, S. N. and Stepanyants, Yu. A.. 2009. "The motion of a cylindrical body in a stratified fluid under the action of a radiation force." Journal of Applied Mathematics and Mechanics. 73 (2), pp. 188-195. https://doi.org/10.1016/j.jappmathmech.2009.04.008
##### Front solutions of Richards' equation
Caputo, Jean-Guy and Stepanyants, Yury. 2008. "Front solutions of Richards' equation." Transport in Porous Media. 74 (1), pp. 1-20. https://doi.org/10.1007/s11242-007-9180-x
##### Burgers-Rott vortices with surface tension
Stepanyants, Yury A. and Yeoh, Guan H.. 2008. "Burgers-Rott vortices with surface tension." Zeitschrift fuer Angewandte Mathematik und Physik. 59 (6), pp. 1057-1068. https://doi.org/10.1007/s00033-008-7071-9
##### Stationary bathtub vortices and a critical regime of liquid discharge
Stepanyants, Yury and Yeoh, Guan. 2008. "Stationary bathtub vortices and a critical regime of liquid discharge." Journal of Fluid Mechanics. 604 (1), pp. 77-98. https://doi.org/10.1017/S0022112008001080
##### Modelling internal solitary waves on the Australian North West Shelf
Grimshaw, Roger, Pelinovsky, Efim, Stepanyants, Yury and Talipova, Tatiana. 2006. "Modelling internal solitary waves on the Australian North West Shelf." Marine and Freshwater Research. 57 (3), pp. 265-272. https://doi.org/10.1071/MF05016