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J. Mar. Sci. Eng. 2019, 7(1), 9; https://doi.org/10.3390/jmse7010009

A Mild-Slope System for Bragg Scattering of Water Waves by Sinusoidal Bathymetry in the Presence of Vertically Sheared Currents

1
School of Naval Architecture and Marine Engineering, National Technical University of Athens, Zografos, 15773 Athens, Greece
2
Univ Toulon, Aix Marseille Univ., CNRS/INSU, IRD, MIO UM 110, Mediterranean Institute of Oceanography, La Garde, France
*
Author to whom correspondence should be addressed.
Received: 12 October 2018 / Revised: 21 December 2018 / Accepted: 29 December 2018 / Published: 7 January 2019
(This article belongs to the Section Ocean Engineering)
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Abstract

Extended mild-slope models (MMSs) are examined for predicting the characteristics of normally incident waves propagating over sinusoidal bottom topography in the presence of opposing shearing currents. It is shown that MMSs are able to provide quite good predictions in the case of Bragg scattering of waves over rippled bathymetry without a current, but fail to provide good predictions concerning the resonant frequency in the additional presence of a current. In order to resolve the above mismatch, a two-equation mild-slope system (CMS2) is derived from a variational principle based on the representation of the wave potential expressed as a superposition of the forward and backward components. The latter system is compared against experimentally measured data collected in a wave flume and is shown to provide more accurate predictions concerning both the resonant frequency and the amplitude of the reflection coefficient. Future work will be devoted to the examination of the derived model for a more general wave system over realistic seabed topography. View Full-Text
Keywords: wave-current interaction; sinusoidal bathymetry; resonant reflection; mild-slope equation; coupled-mode system wave-current interaction; sinusoidal bathymetry; resonant reflection; mild-slope equation; coupled-mode system
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Belibassakis, K.; Touboul, J.; Laffitte, E.; Rey, V. A Mild-Slope System for Bragg Scattering of Water Waves by Sinusoidal Bathymetry in the Presence of Vertically Sheared Currents. J. Mar. Sci. Eng. 2019, 7, 9.

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