Internal Tide Generation Using Green Function Analysis: To WKB or Not to WKB?

An established analytical technique for modeling internal tide generation by barotropic flow over bottom topography in the ocean is the Green function–based approach. To date, however, for realistic ocean studies this method has relied on the WKB approximation. In this paper, the complete Green func...

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Main Authors: Mathur, Manikandan, Carter, Glenn S., Peacock, Thomas
Other Authors: Massachusetts Institute of Technology. Department of Mechanical Engineering
Format: Article
Language:en_US
Published: American Meteorological Society 2017
Online Access:http://hdl.handle.net/1721.1/107747
https://orcid.org/0000-0002-7639-0194
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author Mathur, Manikandan
Carter, Glenn S.
Peacock, Thomas
author2 Massachusetts Institute of Technology. Department of Mechanical Engineering
author_facet Massachusetts Institute of Technology. Department of Mechanical Engineering
Mathur, Manikandan
Carter, Glenn S.
Peacock, Thomas
author_sort Mathur, Manikandan
collection MIT
description An established analytical technique for modeling internal tide generation by barotropic flow over bottom topography in the ocean is the Green function–based approach. To date, however, for realistic ocean studies this method has relied on the WKB approximation. In this paper, the complete Green function method, without the WKB approximation, is developed and tested, and in the process, the accuracy of the WKB approximation for realistic ridge geometries and ocean stratifications is considered. For isolated Gaussian topography, the complete Green function approach is shown to be accurate via close agreement with the results of numerical simulations for a wide range of height ratios and criticality; in contrast, the WKB approach is found to be inaccurate for small height ratios in the subcritical regime and all tall topography that impinges on the pycnocline. Two ocean systems are studied, the Kaena and Wyville Thomson Ridges, for which there is again excellent agreement between the complete Green function approach and numerical simulations, and the WKB approximate solutions have substantial errors. This study concludes that the complete Green function approach, which is typically only modestly more computationally expensive than the WKB approach, should be the go-to analytical method to model internal tide generation for realistic ocean ridge scenarios.
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spelling mit-1721.1/1077472022-10-02T03:09:09Z Internal Tide Generation Using Green Function Analysis: To WKB or Not to WKB? Mathur, Manikandan Carter, Glenn S. Peacock, Thomas Massachusetts Institute of Technology. Department of Mechanical Engineering Peacock, Thomas An established analytical technique for modeling internal tide generation by barotropic flow over bottom topography in the ocean is the Green function–based approach. To date, however, for realistic ocean studies this method has relied on the WKB approximation. In this paper, the complete Green function method, without the WKB approximation, is developed and tested, and in the process, the accuracy of the WKB approximation for realistic ridge geometries and ocean stratifications is considered. For isolated Gaussian topography, the complete Green function approach is shown to be accurate via close agreement with the results of numerical simulations for a wide range of height ratios and criticality; in contrast, the WKB approach is found to be inaccurate for small height ratios in the subcritical regime and all tall topography that impinges on the pycnocline. Two ocean systems are studied, the Kaena and Wyville Thomson Ridges, for which there is again excellent agreement between the complete Green function approach and numerical simulations, and the WKB approximate solutions have substantial errors. This study concludes that the complete Green function approach, which is typically only modestly more computationally expensive than the WKB approach, should be the go-to analytical method to model internal tide generation for realistic ocean ridge scenarios. National Science Foundation (U.S.) (Grants OCE 0645529 and OCE1129757) 2017-03-28T14:45:16Z 2017-03-28T14:45:16Z 2016-06 2015-08 Article http://purl.org/eprint/type/JournalArticle 0022-3670 1520-0485 http://hdl.handle.net/1721.1/107747 Mathur, Manikandan, Glenn S. Carter, and Thomas Peacock. “Internal Tide Generation Using Green Function Analysis: To WKB or Not to WKB?” Journal of Physical Oceanography 46.7 (2016): 2157–2168. © 2016 American Meteorological Society https://orcid.org/0000-0002-7639-0194 en_US http://dx.doi.org/10.1175/jpo-d-15-0145.1 Journal of Physical Oceanography Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Meteorological Society American Meteorological Society
spellingShingle Mathur, Manikandan
Carter, Glenn S.
Peacock, Thomas
Internal Tide Generation Using Green Function Analysis: To WKB or Not to WKB?
title Internal Tide Generation Using Green Function Analysis: To WKB or Not to WKB?
title_full Internal Tide Generation Using Green Function Analysis: To WKB or Not to WKB?
title_fullStr Internal Tide Generation Using Green Function Analysis: To WKB or Not to WKB?
title_full_unstemmed Internal Tide Generation Using Green Function Analysis: To WKB or Not to WKB?
title_short Internal Tide Generation Using Green Function Analysis: To WKB or Not to WKB?
title_sort internal tide generation using green function analysis to wkb or not to wkb
url http://hdl.handle.net/1721.1/107747
https://orcid.org/0000-0002-7639-0194
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