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Parameterizing Surface and Internal Tide Scattering and Breaking on Supercritical Topography: The One- and Two-Ridge Cases

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  • 1 School of Earth and Ocean Sciences, and Department of Physics, University of Victoria, Victoria, British Columbia, Canada
  • | 2 Navy Research Laboratory, Ocean Dynamics and Prediction Branch, Stennis Space Center, Mississippi
  • | 3 Program in Atmosphere and Ocean Sciences, Princeton University, Princeton, New Jersey
  • | 4 Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California
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Abstract

A parameterization is presented for turbulence dissipation due to internal tides generated at and impinging upon topography steep enough to be “supercritical” with respect to the tide. The parameterization requires knowledge of the topography, stratification, and the remote forcing—either barotropic or baroclinic. Internal modes that are arrested at the crest of the topography are assumed to dissipate, and faster modes assumed to propagate away. The energy flux into each mode is predicted using a knife-edge topography that allows linear numerical solutions. The parameterization is tested using high-resolution two-dimensional numerical models of barotropic and internal tides impinging on an isolated ridge, and for the generation problem on a two-ridge system. The recipe is seen to work well compared to numerical simulations of isolated ridges, so long as the ridge has a slope steeper than twice the critical steepness. For less steeply sloped ridges, near-critical generation becomes more dominant. For the two-ridge case, the recipe works well when compared to numerical model runs with very thin ridges. However, as the ridges are widened, even by a small amount, the recipe does poorly in an unspecified manner because the linear response at high modes becomes compromised as it interacts with the slopes.

Corresponding author address: Jody Klymak, School of Earth and Ocean Sciences, University of Victoria, P.O. Box 3055, STN CSC, Victoria, BC V8W 3P6, Canada. E-mail: jklymak@uvic.ca

Abstract

A parameterization is presented for turbulence dissipation due to internal tides generated at and impinging upon topography steep enough to be “supercritical” with respect to the tide. The parameterization requires knowledge of the topography, stratification, and the remote forcing—either barotropic or baroclinic. Internal modes that are arrested at the crest of the topography are assumed to dissipate, and faster modes assumed to propagate away. The energy flux into each mode is predicted using a knife-edge topography that allows linear numerical solutions. The parameterization is tested using high-resolution two-dimensional numerical models of barotropic and internal tides impinging on an isolated ridge, and for the generation problem on a two-ridge system. The recipe is seen to work well compared to numerical simulations of isolated ridges, so long as the ridge has a slope steeper than twice the critical steepness. For less steeply sloped ridges, near-critical generation becomes more dominant. For the two-ridge case, the recipe works well when compared to numerical model runs with very thin ridges. However, as the ridges are widened, even by a small amount, the recipe does poorly in an unspecified manner because the linear response at high modes becomes compromised as it interacts with the slopes.

Corresponding author address: Jody Klymak, School of Earth and Ocean Sciences, University of Victoria, P.O. Box 3055, STN CSC, Victoria, BC V8W 3P6, Canada. E-mail: jklymak@uvic.ca
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