dorsal/arxiv
View SchemaTopographical scattering of waves: a spectral approach
| Authors | Rudy Magne, Fabrice Ardhuin, Vincent Rey, Thomas H. C. Herbers |
|---|---|
| Categories | |
| ArXiv ID | physics/0504148 |
| URL | https://arxiv.org/abs/physics/0504148 |
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 $h$ 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 $2h/H$.
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"abstract": "The topographical scattering of gravity waves is investigated using a\nspectral energy balance equation that accounts for first order wave-bottom\nBragg scattering. This model represents the bottom topography and surface waves\nwith spectra, and evaluates a Bragg scattering source term that is\ntheoretically valid for small bottom and surface slopes and slowly varying\nspectral properties. The robustness of the model is tested for a variety of\ntopographies uniform along one horizontal dimension including nearly\nsinusoidal, linear ramp and step profiles. Results are compared with\nreflections computed using an accurate method that applies integral matching\nalong vertical boundaries of a series of steps. For small bottom amplitudes,\nthe source term representation yields accurate reflection estimates even for a\nlocalized scatterer. This result is proved for small bottom amplitudes $h$\nrelative to the mean water depth $H$. Wave reflection by small amplitude bottom\ntopography thus depends primarily on the bottom elevation variance at the Bragg\nresonance scales, and is insensitive to the detailed shape of the bottom\nprofile. Relative errors in the energy reflection coefficient are found to be\ntypically $2h/H$.",
"arxiv_id": "physics/0504148",
"authors": [
"Rudy Magne",
"Fabrice Ardhuin",
"Vincent Rey",
"Thomas H. C. Herbers"
],
"categories": [
"physics.ao-ph"
],
"title": "Topographical scattering of waves: a spectral approach",
"url": "https://arxiv.org/abs/physics/0504148"
},
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