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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.
Motivation: Ormen Lange (gas field) pipeline
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
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.
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