Articles | Volume 22, issue 3
Nonlin. Processes Geophys., 22, 313–324, 2015
https://doi.org/10.5194/npg-22-313-2015
Nonlin. Processes Geophys., 22, 313–324, 2015
https://doi.org/10.5194/npg-22-313-2015

Research article 21 May 2015

Research article | 21 May 2015

An analytical model of the evolution of a Stokes wave and its two Benjamin–Feir sidebands on nonuniform unidirectional current

I. V. Shugan et al.

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Subject: Nonlinear Waves, Pattern Formation, Turbulence | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere
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Cited articles

Benjamin, T. B. and Feir, J. E.: Instability of periodic wavetrains in nonlinear dispersive systems, J. Fluid Mech., 27, 417–430, 1967.
Bridges, T. and Dias, F.: Enhancement of the Benjamin-Feir instability with dissipation, Phys. Fluids, 19, 104–104, 2007.
Chavla, A. and Kirby, J.: Experimental study of breaking waves on a blocking current, Proc. 26th International Conference on Coastal Engineering, Copenhagen, 22–26 June, 759–772, 1998.
Chavla, A. and Kirby, J.: Monochromatic and random wave breaking at block points, J. Geophys. Res., 107, 4.1–4.19, 2002.
Chabchoub, A., Akhmediev, N., and Hoffmann, N.: Experimental study of spatiotemporally localized surface gravity water waves, Phys. Rev. E., 86, 016311, https://doi.org/10.1103/PhysRevE.86.016311, 2012.
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Short summary
An analytical weakly nonlinear model of Benjamin–Feir instability of a Stokes wave on nonuniform unidirectional current is presented. In contrast to the models based on versions of the cubic Schrodinger equation the current variations could be strong, which allows us to examine the blockage of waves. Waves may overpass the blocking barrier produced by strong adverse current. We find reasonable correspondence between the results of model simulations and available experimental results.