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Saturation of the Internal Tide over the Inner Continental Shelf. Part II: Parameterization

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  • 1 a College of Earth, Ocean, and Atmospheric Sciences, Oregon State University, Corvallis, Oregon
  • | 2 b Institute of Coastal Research, Helmholtz-Zentrum Hereon, Geesthacht, Germany
  • | 3 c Ocean Sciences Division, U.S. Naval Research Laboratory, Stennis Space Center, Mississippi
  • | 4 d Department of Oceanography, Naval Postgraduate School, Monterey Bay, California
  • | 5 e Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California
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Abstract

Here, we develop a framework for understanding the observations presented in Part I. In this framework, the internal tide saturates as it shoals as a result of amplitude limitation with decreasing water depth H. From this framework evolves estimates of averaged energetics of the internal tide; specifically, energy ⟨APE⟩, energy flux ⟨FE⟩, and energy flux divergence ∂xFE⟩. Since we observe that dissipation ⟨D⟩ ≈ ∂xFE⟩, we also interpret our estimate of ∂xFE⟩ as ⟨D⟩. These estimates represent a parameterization of the energy in the internal tide as it saturates over the inner continental shelf. The parameterization depends solely on depth-mean stratification and bathymetry. A summary result is that the cross-shelf depth dependencies of ⟨APE⟩, ⟨FE⟩, and ∂xFE⟩ are analogous to those for shoaling surface gravity waves in the surf zone, suggesting that the inner shelf is the surf zone for the internal tide. A test of our simple parameterization against a range of datasets suggests that it is broadly applicable.

Significance Statement

Observational results from Part I suggest a new approach to understanding the complicated breakdown of the internal tide over continental shelves. By defocusing on the details in favor of focusing on the integral energy of the internal tide, we develop a new framework analogous to breaking surface waves on beaches. This framework leads to a simple parameterization that depends solely on the surface-to-seafloor temperature difference and the bathymetry of the continental shelf. A test of this parameterization against a range of datasets shows broad applicability. At the same time, it provides a means of determining the net mixing of continental shelf waters and suggests that the inner continental shelf is the surf zone for the internal tide.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Johannes Becherer, johannes.becherer@hereon.de

This article has a companion article which can be found at http://journals.ametsoc.org/doi/abs/10.1175/JPO-D-20-0264.1.

Abstract

Here, we develop a framework for understanding the observations presented in Part I. In this framework, the internal tide saturates as it shoals as a result of amplitude limitation with decreasing water depth H. From this framework evolves estimates of averaged energetics of the internal tide; specifically, energy ⟨APE⟩, energy flux ⟨FE⟩, and energy flux divergence ∂xFE⟩. Since we observe that dissipation ⟨D⟩ ≈ ∂xFE⟩, we also interpret our estimate of ∂xFE⟩ as ⟨D⟩. These estimates represent a parameterization of the energy in the internal tide as it saturates over the inner continental shelf. The parameterization depends solely on depth-mean stratification and bathymetry. A summary result is that the cross-shelf depth dependencies of ⟨APE⟩, ⟨FE⟩, and ∂xFE⟩ are analogous to those for shoaling surface gravity waves in the surf zone, suggesting that the inner shelf is the surf zone for the internal tide. A test of our simple parameterization against a range of datasets suggests that it is broadly applicable.

Significance Statement

Observational results from Part I suggest a new approach to understanding the complicated breakdown of the internal tide over continental shelves. By defocusing on the details in favor of focusing on the integral energy of the internal tide, we develop a new framework analogous to breaking surface waves on beaches. This framework leads to a simple parameterization that depends solely on the surface-to-seafloor temperature difference and the bathymetry of the continental shelf. A test of this parameterization against a range of datasets shows broad applicability. At the same time, it provides a means of determining the net mixing of continental shelf waters and suggests that the inner continental shelf is the surf zone for the internal tide.

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Corresponding author: Johannes Becherer, johannes.becherer@hereon.de

This article has a companion article which can be found at http://journals.ametsoc.org/doi/abs/10.1175/JPO-D-20-0264.1.

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