Scattering of Oceanic Internal Gravity Waves off Random Bottom Topography

Peter Müller Department of Oceanography, School of Ocean and Earth Science and Technology, University of Hawaii, Honolulu, Hawaii

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Naihuai Xu Department of Oceanography, School of Ocean and Earth Science and Technology, University of Hawaii, Honolulu, Hawaii

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Abstract

The scattering of oceanic internal gravity waves off random bottom topography is analyzed under the assumptions that (i) the height of the topography is smaller than the vertical wavelength and (ii) the slope of the topography is smaller than the wave slope. For each frequency, scattering redistributes the incoming energy flux in horizontal wavenumber space. The scattered wave field approaches an equilibrium state where the energy flux is equipartitioned in horizontal wavenumber space. For incoming red spectra, this implies a transfer from low to high wavenumbers. For typical internal wave and bottom spectra, about 6.8% of the incoming energy flux is redistributed. While this might be less than the flux redistribution caused by reflection off a critical slope, the scattering process transfers the energy flux to higher wavenumbers than the reflection process. Scattering might thus be equally or more efficient than reflection in causing high shears and mixing near the bottom.

Abstract

The scattering of oceanic internal gravity waves off random bottom topography is analyzed under the assumptions that (i) the height of the topography is smaller than the vertical wavelength and (ii) the slope of the topography is smaller than the wave slope. For each frequency, scattering redistributes the incoming energy flux in horizontal wavenumber space. The scattered wave field approaches an equilibrium state where the energy flux is equipartitioned in horizontal wavenumber space. For incoming red spectra, this implies a transfer from low to high wavenumbers. For typical internal wave and bottom spectra, about 6.8% of the incoming energy flux is redistributed. While this might be less than the flux redistribution caused by reflection off a critical slope, the scattering process transfers the energy flux to higher wavenumbers than the reflection process. Scattering might thus be equally or more efficient than reflection in causing high shears and mixing near the bottom.

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