Eddy Acceleration and Decay Driven by Internal Tides

Callum J. Shakespeare aResearch School of Earth Sciences, The Australian National University, Canberra, Australian Capital Territory, Australia
bARC Centre of Excellence for Climate Extremes, The Australian National University, Canberra, Australia

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Abstract

Recent observations and numerical simulations have demonstrated the potential for significant interactions between mesoscale eddies and smaller-scale tidally generated internal waves—also known as internal tides. Here, we develop a simple theoretical model that predicts the one-way upscale transfer of energy from internal tides to mesoscale eddies through a critical level mechanism. We find that—in the presence of a critical level—the internal tide energy flux into an eddy is partitioned according to the wave frequency Ω and local inertial frequency f: a fraction of 1 − f/Ω is transferred to the eddy kinetic energy, while the remainder is viscously dissipated or supports mixing. These predictions are validated by comparison with a suite of numerical simulations. The simulations further show that the wave-driven energization of the eddies also accelerates the onset of hydrodynamical instabilities and the breakdown of the eddies, thereby increasing eddy kinetic energy, but reducing eddy lifetimes. Our estimates suggest that in regions of the ocean with both significant eddy fields and internal tides—such as parts of the Gulf Stream and Antarctic Circumpolar Current—the critical level effect could drive a ∼10% month−1 increase in the kinetic energy of a typical eddy. Our results provide a basis for parameterizing internal tide–eddy interactions in global ocean models where they are currently unrepresented.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Callum J. Shakespeare, callum.shakespeare@anu.edu.au

Abstract

Recent observations and numerical simulations have demonstrated the potential for significant interactions between mesoscale eddies and smaller-scale tidally generated internal waves—also known as internal tides. Here, we develop a simple theoretical model that predicts the one-way upscale transfer of energy from internal tides to mesoscale eddies through a critical level mechanism. We find that—in the presence of a critical level—the internal tide energy flux into an eddy is partitioned according to the wave frequency Ω and local inertial frequency f: a fraction of 1 − f/Ω is transferred to the eddy kinetic energy, while the remainder is viscously dissipated or supports mixing. These predictions are validated by comparison with a suite of numerical simulations. The simulations further show that the wave-driven energization of the eddies also accelerates the onset of hydrodynamical instabilities and the breakdown of the eddies, thereby increasing eddy kinetic energy, but reducing eddy lifetimes. Our estimates suggest that in regions of the ocean with both significant eddy fields and internal tides—such as parts of the Gulf Stream and Antarctic Circumpolar Current—the critical level effect could drive a ∼10% month−1 increase in the kinetic energy of a typical eddy. Our results provide a basis for parameterizing internal tide–eddy interactions in global ocean models where they are currently unrepresented.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Callum J. Shakespeare, callum.shakespeare@anu.edu.au
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