Localization over a Random Bottom

 

Localization of Internal Waves by Random Topography

 

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.

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Motivation: Ormen Lange (gas field) pipeline

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Ormen-Lange pipeline is the world’s longest underwater pipeline 1,200 km (746 mi) and is from Nyhamna to Easington in England. Typical height of roughness: 20m and length: 200-1000 m and the pipeline will be suspended between and anchored at successive crests

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Fission of soliton-like pulses after a soliton passes a finite strip of random seabed

 

References:

– 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]