Numerical and Analytical Estimates of M2 Tidal Conversion at Steep Oceanic Ridges

Emanuele Di Lorenzo School of Earth and Atmospheric Sciences, Georgia Institute of Technology, Atlanta, Georgia

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William R. Young Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California

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Stefan Llewellyn Smith Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, California

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Abstract

Numerical calculations of the rate at which energy is converted from the external to internal tides at steep oceanic ridges are compared with estimates from analytic theories. The numerical calculations are performed using a hydrostatic primitive equation ocean model that uses a generalized s-coordinate system as the vertical coordinate. The model [Regional Ocean Modeling System (ROMS)] estimates of conversion compare well with inviscid and nondiffusive theory in the sub- and supercritical regimes and are insensitive to the strength of viscosity and diffusivity. In the supercritical regime, the nondissipative analytic solution is singular all along the internal tide beams. Because of dissipation the ROMS solutions are nonsingular, although the density gradients are strongly enhanced along the beams. The agreement between model and theory indicates that the prominent singularities in the inviscid solution do not compromise the estimates of tidal conversion and that the linearization used in deriving the analytical estimates is valid. As the model beams radiate from the generation site the density gradients are further reduced and up to 20% of the energy is lost by model dissipation (vertical viscosity and diffusion) within 200 km of the ridge. As a result of the analysis of the numerical calculations the authors also report on the sensitivity of tidal conversion to topographic misrepresentation errors. These errors are associated with inadequate resolution of the topographic features and with the smoothing required to run the ocean model. In regions of steep topographic slope (i.e., the Hawaiian Ridge) these errors, if not properly accounted for, may lead to an underestimate of the true conversion rate up to 50%.

Corresponding author address: Emanuele Di Lorenzo, School of Earth and Atmospheric Sciences, Georgia Institute of Technology, 311 Ferst Drive, Atlanta, GA 30332-0340. Email: edl@eas.gatech.edu

Abstract

Numerical calculations of the rate at which energy is converted from the external to internal tides at steep oceanic ridges are compared with estimates from analytic theories. The numerical calculations are performed using a hydrostatic primitive equation ocean model that uses a generalized s-coordinate system as the vertical coordinate. The model [Regional Ocean Modeling System (ROMS)] estimates of conversion compare well with inviscid and nondiffusive theory in the sub- and supercritical regimes and are insensitive to the strength of viscosity and diffusivity. In the supercritical regime, the nondissipative analytic solution is singular all along the internal tide beams. Because of dissipation the ROMS solutions are nonsingular, although the density gradients are strongly enhanced along the beams. The agreement between model and theory indicates that the prominent singularities in the inviscid solution do not compromise the estimates of tidal conversion and that the linearization used in deriving the analytical estimates is valid. As the model beams radiate from the generation site the density gradients are further reduced and up to 20% of the energy is lost by model dissipation (vertical viscosity and diffusion) within 200 km of the ridge. As a result of the analysis of the numerical calculations the authors also report on the sensitivity of tidal conversion to topographic misrepresentation errors. These errors are associated with inadequate resolution of the topographic features and with the smoothing required to run the ocean model. In regions of steep topographic slope (i.e., the Hawaiian Ridge) these errors, if not properly accounted for, may lead to an underestimate of the true conversion rate up to 50%.

Corresponding author address: Emanuele Di Lorenzo, School of Earth and Atmospheric Sciences, Georgia Institute of Technology, 311 Ferst Drive, Atlanta, GA 30332-0340. Email: edl@eas.gatech.edu

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