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Two-dimensional localization of surface gravity waves in finite water depth

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We extend the homogenization theory to study nonlinear waves in a finite depth sea where the bathymetry is random over a large area. Evolution for the envelope of a nearly sinusoidal progressive wavetrain is derived and is used to study the nonlinear diffraction by a two-dimensional bathymetry. It is found that randomness prohibits the intrusion of waves through multiple scattering. However, in the wake of the random region the wavefield recovers and dark solitons emerge.

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