ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


For citation:

Ezerskij A. B., Polukhina O. E., Brossard J., Marin F., Mutabazi I. Dynamics of solitons excited in resonators on the surface of shallow water: theory and experiment. Izvestiya VUZ. Applied Nonlinear Dynamics, 2004, vol. 12, iss. 1, pp. 138-158. DOI: 10.18500/0869-6632-2004-12-1-138-158

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Language: 
Russian
Article type: 
Article
UDC: 
532.59

Dynamics of solitons excited in resonators on the surface of shallow water: theory and experiment

Autors: 
Ezerskij Aleksandr Borisovich, Institute of Applied Physics of the Russian Academy of Sciences
Polukhina Oksana Evgenievna, Nizhny Novgorod State Technical University named after RE Alekseev
Brossard Jerome, Le Havre Normandy University
Marin Francois, Le Havre Normandy University
Mutabazi Innocent, Le Havre Normandy University
Abstract: 

Excitation of solitons of surface waves in resonators is investigated. It was found that solitons may be generated on the shallow water surface against the background of a large-scale resonator mode. Multistability and period doubling of nonlinear waves excited in the resonator were found. Spatio-temporal diagrams were ploited for different regimes of wave excitation. Spatio-temporal dynamics of nonlinear fields of soliton excitation in a resonator and in an unbounded system were compared. Two approaches were used for theoretical description of solitons excitation. The first one was based on searching solutions of ordinary differential equations for phase and amplitude of soliton propagating against the background of harmonic wave and the second one was based оп direct numerical calculations of Euler equations in the Boussinesq approximation. Qualitative investigation of equation for amplitude and phase of solitons and numerical simulation allowed us to explain the characteristics of solitons observed in the experiment.

Key words: 
Reference: 

1. Leibovich S. Seebass АВ. (ed.). Nonlinear Waves. Ithaca, NY: Cornell University Press; 1974.

2. Remoissenet M. Waves called solitons: concepts and experiments. Berlin, Heibelberg, New-York: Springer-Verlag, 1996. 260 p.

3. Maxworthy Т. Experiments оn collision between solitary waves. Journal of Fluid Mechanics. 1976;76:177–185.

4. Weidman PD, Maxworthy T. Experiments on strong interaction between solitary waves. Journal of Fluid Mechanics. 1978;85(3):417–431.

5. Bettini А, Minelli TA, Pascoli D. Solitons in Undergraduate Laboratory. American Journal of Physics. 1983;51:977–984.

6. Olsen M, Smith H, Scott AC. Solitons in а Tank. American Journal of Physics. 1984;54:826–830.

7. Feng Z. Travelling Solitary Wave Solutions to the Generalized Boussinesq Equation. Wave motion. 2003;37:17–23.

8. Renouard DP, Seabra Santos FJ, Temperville AM. Experimental Study of the Generation, Damping, and Reflexion оf а Solitary Wave. Dynamics of Atmosphere and Oceans. 1985;9:341–358.

9. Dingemans MW. Water Wave Propagation over Uneven Bottoms Part 2-Nonlinear Wave Propagation. Singapore: World Scientific; 1997. 471 p.

10. Cooker MJ, Weidman PD, Bale DS. Reflection of High Amplitude Wave at a Vertical Wall. Journal of Fluid Mechanics. 1997;342:141–158.

11. Temperville А. Interaction оf Solitary Waves in Shallow Water Theory. Archives of Mechanics (Archiwum Mechaniki Stosowanej). 1979;31(2):177–184.

12. Oikawa M, Yajima N. Interactions of Solitary Waves – a Perturbation Approach to Nonlinear systems. Journal of the Physical Society of Japan. 1973;34:1093–1099.

13. Su CH, Rida MM. On Head-on Collision between Solitary Waves. Journal of Fluid Mechanics. 1980;98(3):509–525.

14. Power H, Chwang AT. On Reflection of a Planar Solitary Wave at a Vertical Wall. Wave motion. 1984;6:183–195.

15. Hammack JL, Segur H. The Korteveg – de Vries Equation and Water Wave. Part 2. Comparison with experiments. Journal of Fluid Mechanics. 1974;60;769–800.

16. Chester W, Borns JA. Resonant Oscillations of Water Waves. II. Experiment. Proceedings of the Royal Society A. 1968;А306:23–39.

17. Chester W. Resonant Oscillations оf Water Waves. I. Theory // Proceedings of the Royal Society A. 1968;A306:1–22.

18. Wu J, Keolian R, Rudnik I. Observation оf Nonpropagating Hydrodynamic Soliton. Physical Review Letters. 1984;52(16):1421–1424.

19. Gorshkov KA, Ostrovsky LA, Papko VV. Parametric Amplification and Pulse Generation in Nonlinear Distributed Systems. Radiophysics and Quantum Electronics. 1973;16(8):1195–1204.

20. Potapov AI, Vesnitsky AI. Interaction of Solitary Waves under Head-on Collisions. Experimental investigation. Wave motion. 1994;19:29–35.

21. Grimshow R, Pelinovsky EN, Talipova TG. Damping of Large-amplitude Solitary Waves. Wave motion. 2003;37:351–364.

22. Ostrovsky LA, Soustova IA. The Upper Mixed Layer of the Ocean as an Energy Sink of Internal Waves. Okeanologiya. 1979; 19(6):973–981.

23. Pelinovski EN. The Hydrodynamics of the Tsunami Waves. Nejny Novgorod: IPF RAS press; 1996. 276 p.

Received: 
29.08.2003
Accepted: 
16.01.2004
Published: 
20.06.2004