From modulational instability to focusing dam breaks in water waves

作者: Félicien Bonnefoy , Alexey Tikan , François Copie , Pierre Suret , Guillaume Ducrozet

DOI: 10.1103/PHYSREVFLUIDS.5.034802

关键词:

摘要: We report water wave experiments performed in a long tank where we consider the evolution of nonlinear deep-water surface gravity waves with envelope form large-scale rectangular barrier. Our reveal that, for range initial parameters, packet is not disintegrated by Benjamin-Feir instability but exhibits specific, strongly modulation, which propagates from edges toward center finite speed. Using numerical tools spectral analysis experimental data, identify observed structures focusing dispersive dam break flows, peculiar type shock recently described framework semiclassical limit 1D Schrodinger equation (1D-NLSE). results are shown to be good quantitative agreement predictions 1D-NLSE theory. This first observation persisting dynamics modulationally unstable system.

参考文章(87)
D. J. Benney, A. C. Newell, The Propagation of Nonlinear Wave Envelopes Journal of Mathematics and Physics. ,vol. 46, pp. 133- 139 ,(1967) , 10.1002/SAPM1967461133
V. E. Zakharov, A. A. Gelash, Nonlinear stage of modulation instability. Physical Review Letters. ,vol. 111, pp. 054101- ,(2013) , 10.1103/PHYSREVLETT.111.054101
Alexander Tovbis, Gennady A. El, Eduardo G. Khamis, Dam break problem for the focusing nonlinear Schr\"odinger equation and the generation of rogue waves arXiv: Pattern Formation and Solitons. ,(2015) , 10.1088/0951-7715/29/9/2798
Thomas Brooke Benjamin, Michael James Lighthill, On cnoidal waves and bores Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences. ,vol. 224, pp. 448- 460 ,(1954) , 10.1098/RSPA.1954.0172
Efim Pelinovsky, Anna Sergeeva (Kokorina), Numerical modeling of the KdV random wave field European Journal of Mechanics B-fluids. ,vol. 25, pp. 425- 434 ,(2006) , 10.1016/J.EUROMECHFLU.2005.11.001
M. V. Pavlov, Nonlinear Schrödinger equation and the bogolyubov-whitham method of averaging Theoretical and Mathematical Physics. ,vol. 71, pp. 584- 588 ,(1987) , 10.1007/BF01017090
L. I. Zagryadskaya, L. A. Ostrovskii, Observed self-influence of modulated waves in a nonlinear line Radiophysics and Quantum Electronics. ,vol. 11, pp. 548- 550 ,(1968) , 10.1007/BF01033372
V.E. Zakharov, L.A. Ostrovsky, Modulation instability: The beginning Physica D: Nonlinear Phenomena. ,vol. 238, pp. 540- 548 ,(2009) , 10.1016/J.PHYSD.2008.12.002
Miro Erkintalo, Kamal Hammani, Bertrand Kibler, Christophe Finot, Nail Akhmediev, John M. Dudley, Goëry Genty, Higher-order modulation instability in nonlinear fiber optics international conference on transparent optical networks. ,vol. 107, pp. 253901- ,(2011) , 10.1103/PHYSREVLETT.107.253901