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Exact solutions for wave propagation over a patch of large bottom corrugations

Published online by Cambridge University Press:  17 October 2012

Jie Yu  and
Guangfu Zheng
Jie Yu*
Affiliation:
Department of Civil, Construction and Environmental Engineering, North Carolina State University, Raleigh, NC 27695-7908, USA
Guangfu Zheng
Affiliation:
Department of Civil, Construction and Environmental Engineering, North Carolina State University, Raleigh, NC 27695-7908, USA
*
†Email address for correspondence: [email protected]
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Abstract

Applying the Floquet theory for linear motions (Howard & Yu, J. Fluid Mech., vol. 593, 2007, pp. 209–234) to the problem of wave propagation over a patch of periodic bottom corrugations in an otherwise flat seabed, we show that exact solutions to this scattering problem can be constructed without any constraint on the bottom amplitude and/or slope. These solutions are able to describe both the slowly and fast varying aspects of the flow, in contrast to the analyses based on the general ideas of slowly varying waves. We use as an example the well-studied Bragg scattering by a patch of bottom corrugations to present some quantitative results and comparisons with experimental data.

JFM classification

Geophysical and Geological Flows: Coastal engineering Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Wave scattering
Type
Papers
Information
Journal of Fluid Mechanics , Volume 713 , 25 December 2012 , pp. 362 - 375
Copyright
©2012 Cambridge University Press

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