If waves travel over a random bathymetry, strong spatial attenuation occurs due to multiple scattering (c.f. Anderson localization in solid-state physics). Unlike Bragg scattering where strong resonance occurs for a discrete set of frequencies satisfying the Bragg resonance condition, spatial attenuation takes place at nearly all wave frequencies in disordered media. Our consideration of localization in stratified waters was motivated by the need of Ormen-Lange gas extraction project in North Sea to estimate the impact of long-period internal waves on gas pipelines. Evolution of internal solitary waves and the effect of harmonic-generation in time-periodic waves traveling over random topography were studied.
– Alam, M.-R. and Mei, C.C., “Ships advancing near the critical speed in a shallow channel with a randomly uneven bed”, J. Fluid Mechanics, Volume 616 (2008), pages 397-417. [PDF]