2005/04/21 by Rudy Magne, Fabrice Ardhuin, Magne, Rudy +6
Earth and Planetary Sciences · Physics and Astronomy · #Atmospheric and Oceanic Physics (physics.ao-ph) #Coastal and Marine Dynamics #FOS: Physical sciences #Ocean Waves and Remote Sensing #Oceanographic and Atmospheric Processes #physics.ao-ph
paper · pdf · doi:10.48550/arxiv.physics/0504148
Second revision for Journal of Waterways Ports and Coastal Engineering
arxiv created 2005/04/21 · openalex publication_date 2005/04/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 h relative to the mean water depth H. 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 2h/H.