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Attenuation of long interfacial waves over a randomly rough seabed

Published online by Cambridge University Press:  31 August 2007

MOHAMMAD-REZA ALAM  and
CHIANG C. MEI
MOHAMMAD-REZA ALAM
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
CHIANG C. MEI
Affiliation:
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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Abstract

The effects of randomly irregular bathymetry on the propagation of interfacial gravity waves are studied. Modelling sea water by a two-layer fluid of different densities, weakly nonlinear waves much longer than the sea depth but comparable to the horizontal scale of bathymetry are treated by Boussinesq approximation and multiple-scale analysis. For transient wave pulses, the governing equation for the pulse profile is shown to be an integro-differential equation combining KdV and Burgers terms. Quantitative and qualitative effect of disorder on the attenuation of wave amplitude, reduction of wave speed and change of wave profile are examined numerically and analytically based on the asymptotic approximation. For time-harmonic waves, mode-coupling equations are derived and examined for the competition between diffusion by random scattering, steepening by nonlinearityand frequency dispersion for a broad range of depth ratios.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 587 , 25 September 2007 , pp. 73 - 96
Copyright
Copyright © Cambridge University Press 2007

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