dorsal/arxiv
View SchemaCurrent effects on scattering of surface gravity waves by bottom topography
| Authors | Rudy Magne, Fabrice Ardhuin |
|---|---|
| Categories | |
| ArXiv ID | physics/0510150 |
| URL | https://arxiv.org/abs/physics/0510150 |
Abstract
Scattering of random surface gravity waves by small amplitude topography in the presence of a uniform current is investigated theoretically. This problem is relevant to ocean waves propagation on shallow continental shelves where tidal currents are often significant. A perturbation expansion of the wave action to second order in powers of the bottom amplitude yields an evolution equation for the wave action spectrum. A scattering source term gives the rate of exchange of the wave action spectrum between wave components, with conservation of the total action at each absolute frequency. With and without current, the scattering term yields reflection coefficients for the amplitudes of waves that converge, to the results of previous theories for monochromatic waves propagating in one dimension over sinusoidal bars. Over sandy continental shelves, tidal currents are known to generate sandwaves with scales comparable to those of surface waves. Application of the theory to such a real topography suggests that scattering mainly results in a broadening of the directional wave spectrum, due to forward scattering, while the back-scattering is generally weaker. The current may strongly influence surface gravity wave scattering by selecting different bottom scales with widely different spectral densities due the sharp bottom spectrum roll-off.
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"abstract": "Scattering of random surface gravity waves by small amplitude topography in\nthe presence of a uniform current is investigated theoretically. This problem\nis relevant to ocean waves propagation on shallow continental shelves where\ntidal currents are often significant. A perturbation expansion of the wave\naction to second order in powers of the bottom amplitude yields an evolution\nequation for the wave action spectrum. A scattering source term gives the rate\nof exchange of the wave action spectrum between wave components, with\nconservation of the total action at each absolute frequency. With and without\ncurrent, the scattering term yields reflection coefficients for the amplitudes\nof waves that converge, to the results of previous theories for monochromatic\nwaves propagating in one dimension over sinusoidal bars. Over sandy continental\nshelves, tidal currents are known to generate sandwaves with scales comparable\nto those of surface waves. Application of the theory to such a real topography\nsuggests that scattering mainly results in a broadening of the directional wave\nspectrum, due to forward scattering, while the back-scattering is generally\nweaker. The current may strongly influence surface gravity wave scattering by\nselecting different bottom scales with widely different spectral densities due\nthe sharp bottom spectrum roll-off.",
"arxiv_id": "physics/0510150",
"authors": [
"Rudy Magne",
"Fabrice Ardhuin"
],
"categories": [
"physics.ao-ph"
],
"title": "Current effects on scattering of surface gravity waves by bottom topography",
"url": "https://arxiv.org/abs/physics/0510150"
},
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