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Scattering of Internal Waves at Finite Topography in Two Dimensions. Part II: Spectral Calculations and Boundary Mixing

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  • 1 Department of Oceanography, University of Hawaii at Manoa, Honolulu, Hawaii
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Abstract

The scattering of internal gravity waves at finite topography is studied theoretically and numerically for a two-dimensional finite-depth ocean. In Part I a single incident plane wave was considered. Here a random superposition of incident waves is considered with a spectrum derived from the Garrett and Munk spectrum. The topography is either a slope–shelf or ridge configuration with the bottom being flat in the far fields. The incident energy flux is partitioned into reflected and transmitted waves and redistributed in modenumber space. The scattering is irreversible. In frequency space topography acts like a filter. Waves with frequencies lower than the critical frequency are reflected. Waves with frequencies higher than the critical frequency are transmitted onto the shelf or across the ridge. In modenumber space, both the reflected and transmitted flux spectra are flatter than the incident spectrum, indicating a transfer from low to high modenumbers. This transfer is accompanied by an increase in the energy spectrum and, even more so, in the shear spectrum. A critical modenumber is determined such that the cumulative inverse Richardson number up to this modenumber is one. The flux scattered to modenumbers beyond this critical modenumber is calculated and is assumed to be available for internal wave induced boundary mixing. Various topographic profiles are compared. Convex profiles are more efficient than linear or concave profiles in scattering waves to high modenumbers.

Corresponding author address: Dr. Peter Müller, Department of Oceanography, University of Hawaii at Manoa, 1000 Pope Road, MSB 429, Honolulu, HI 96822.

Email: pmuller@iniki.soest.hawaii.edu

Abstract

The scattering of internal gravity waves at finite topography is studied theoretically and numerically for a two-dimensional finite-depth ocean. In Part I a single incident plane wave was considered. Here a random superposition of incident waves is considered with a spectrum derived from the Garrett and Munk spectrum. The topography is either a slope–shelf or ridge configuration with the bottom being flat in the far fields. The incident energy flux is partitioned into reflected and transmitted waves and redistributed in modenumber space. The scattering is irreversible. In frequency space topography acts like a filter. Waves with frequencies lower than the critical frequency are reflected. Waves with frequencies higher than the critical frequency are transmitted onto the shelf or across the ridge. In modenumber space, both the reflected and transmitted flux spectra are flatter than the incident spectrum, indicating a transfer from low to high modenumbers. This transfer is accompanied by an increase in the energy spectrum and, even more so, in the shear spectrum. A critical modenumber is determined such that the cumulative inverse Richardson number up to this modenumber is one. The flux scattered to modenumbers beyond this critical modenumber is calculated and is assumed to be available for internal wave induced boundary mixing. Various topographic profiles are compared. Convex profiles are more efficient than linear or concave profiles in scattering waves to high modenumbers.

Corresponding author address: Dr. Peter Müller, Department of Oceanography, University of Hawaii at Manoa, 1000 Pope Road, MSB 429, Honolulu, HI 96822.

Email: pmuller@iniki.soest.hawaii.edu

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