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A Simple Parameterization of Turbulent Tidal Mixing near Supercritical Topography

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  • 1 School of Earth and Ocean Sciences, and Department of Physics, University of Victoria, Victoria, British Columbia, Canada
  • | 2 Program in Atmosphere and Ocean Sciences, Princeton University, Princeton, New Jersey
  • | 3 Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California
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Abstract

A simple parameterization for tidal dissipation near supercritical topography, designed to be applied at deep midocean ridges, is presented. In this parameterization, radiation of internal tides is quantified using a linear knife-edge model. Vertical internal wave modes that have nonrotating phase speeds slower than the tidal advection speed are assumed to dissipate locally, primarily because of hydraulic effects near the ridge crest. Evidence for high modes being dissipated is given in idealized numerical models of tidal flow over a Gaussian ridge. These idealized models also give guidance for where in the water column the predicted dissipation should be placed. The dissipation recipe holds if the Coriolis frequency f is varied, as long as hN/Wf, where N is the stratification, h is the topographic height, and W is a width scale. This parameterization is not applicable to shallower topography, which has significantly more dissipation because near-critical processes dominate the observed turbulence. The parameterization compares well against simulations of tidal dissipation at the Kauai ridge but predicts less dissipation than estimated from observations of the full Hawaiian ridge, perhaps because of unparameterized wave–wave interactions.

Corresponding author address: J. Klymak, School of Earth and Ocean Sciences, and Department of Physics, University of Victoria, P.O. Box 3055 STN CSC, Victoria BC V8W 4A3, Canada. Email: jklymak@uvic.ca

Abstract

A simple parameterization for tidal dissipation near supercritical topography, designed to be applied at deep midocean ridges, is presented. In this parameterization, radiation of internal tides is quantified using a linear knife-edge model. Vertical internal wave modes that have nonrotating phase speeds slower than the tidal advection speed are assumed to dissipate locally, primarily because of hydraulic effects near the ridge crest. Evidence for high modes being dissipated is given in idealized numerical models of tidal flow over a Gaussian ridge. These idealized models also give guidance for where in the water column the predicted dissipation should be placed. The dissipation recipe holds if the Coriolis frequency f is varied, as long as hN/Wf, where N is the stratification, h is the topographic height, and W is a width scale. This parameterization is not applicable to shallower topography, which has significantly more dissipation because near-critical processes dominate the observed turbulence. The parameterization compares well against simulations of tidal dissipation at the Kauai ridge but predicts less dissipation than estimated from observations of the full Hawaiian ridge, perhaps because of unparameterized wave–wave interactions.

Corresponding author address: J. Klymak, School of Earth and Ocean Sciences, and Department of Physics, University of Victoria, P.O. Box 3055 STN CSC, Victoria BC V8W 4A3, Canada. Email: jklymak@uvic.ca

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