Wave scattering in spatially inhomogeneous currents

Article

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

Article Title	Wave scattering in spatially inhomogeneous currents
ERA Journal ID	1078
Article Category	Article
Authors	Churilov, Semyon (Author), Ermakov, Andrei (Author) and Stepanyants, Yury (Author)
Journal Title	Physical Review D
Journal Citation	96 (6), p. 064016
Number of Pages	25
Year	2017
Place of Publication	United States
ISSN	1550-2368
	1550-7998
	2470-0010
	2470-0029
Digital Object Identifier (DOI)	https://doi.org/10.1103/PhysRevD.96.064016
Web Address (URL)	https://journals.aps.org/prd/abstract/10.1103/PhysRevD.96.064016
Abstract	We analytically study a scattering of long linear surface waves on stationary currents in a duct (canal) of constant depth and variable width. It is assumed that the background velocity linearly increases or decreases with the longitudinal coordinate due to the gradual variation of duct width. Such a model admits an analytical solution of the problem in hand, and we calculate the scattering coefficients as functions of incident wave frequency for all possible cases of sub-, super-, and transcritical currents. For completeness we study both cocurrent and countercurrent wave propagation in accelerating and decelerating currents. The results obtained are analyzed in application to recent analog gravity experiments and shed light on the problem of hydrodynamic modeling of Hawking radiation.
Keywords	water wave; canal of variable width; non-uniform flow; wave scattering; transformation coefficients
ANZSRC Field of Research 2020	401207. Fundamental and theoretical fluid dynamics
	490109. Theoretical and applied mechanics
Public Notes	First prize winner of the USQ Publication Excellence Award for Journal Articles published during the period September - December 2017. Published version deposited in accordance with the copyright policy of the publisher.
Byline Affiliations	Russian Academy of Sciences, Russia
	School of Agricultural, Computational and Environmental Sciences
Institution of Origin	University of Southern Queensland

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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.

Transformation of surface waves over a bottom step

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

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

Wave scattering in spatially inhomogeneous currents

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