Topographical Scattering of Waves: Spectral Approach
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 131, Issue 6
Abstract
The topographical scattering of gravity waves is investigated using a spectral energy balance equation that accounts for first-order wave-bottom Bragg scattering. This model represents the bottom topography and surface waves with spectra, and evaluates a Bragg scattering source term that is theoretically valid for small bottom and surface slopes and slowly varying spectral properties. The robustness of the model is tested for a variety of topographies uniform along one horizontal dimension including nearly sinusoidal, linear ramp, and step profiles. Results are compared with reflections computed using an accurate method that applies integral matching along vertical boundaries of a series of steps. For small bottom amplitudes, the source term representation yields accurate reflection estimates even for a localized scatterer. This result is proved for small bottom amplitudes relative to the mean water depth . Wave reflection by small amplitude bottom topography thus depends primarily on the bottom elevation variance at the Bragg resonance scales, and is insensitive to the detailed shape of the bottom profile. Relative errors in the energy reflection coefficient are found to be typically .
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Acknowledgments
This research is supported by a joint grant from the Centre National de la Recherche Scientifique (CNRS) and Délégation Générale pour l’Armement (DGA). Additional funding is provided by the U.S. Office of Naval Research,ONR and the U.S. National Science Foundation in the framework of the 2003 Nearshore Canyon Experiment (NCEX). Fruitful discussions with Kostas Belibassakis are gratefully acknowledged.NSF
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Information
Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 131 • Issue 6 • November 2005
Pages: 311 - 320
Copyright
© 2005 ASCE.
History
Received: Feb 5, 2004
Accepted: Apr 14, 2005
Published online: Nov 1, 2005
Published in print: Nov 2005
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