Tidally generated internal-wave attractors between double ridges
A study is presented of the generation of internal tides by barotropic tidal flow over topography in the shape of a double ridge. An iterative map is constructed to expedite the search for the closed ray paths that form wave attractors in this geometry. The map connects the positions along a ray pat...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | en_US |
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Cambridge University Press
2013
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| Online Access: | http://hdl.handle.net/1721.1/79126 https://orcid.org/0000-0002-7639-0194 |
| _version_ | 1826193432328011776 |
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| author | Echeverri, Paula Yokossi, Tite Peacock, Thomas Balmforth, Neil J. |
| author2 | Massachusetts Institute of Technology. Department of Economics |
| author_facet | Massachusetts Institute of Technology. Department of Economics Echeverri, Paula Yokossi, Tite Peacock, Thomas Balmforth, Neil J. |
| author_sort | Echeverri, Paula |
| collection | MIT |
| description | A study is presented of the generation of internal tides by barotropic tidal flow over topography in the shape of a double ridge. An iterative map is constructed to expedite the search for the closed ray paths that form wave attractors in this geometry. The map connects the positions along a ray path of consecutive reflections from the surface, which is double-valued owing to the presence of both left- and right-going waves, but which can be made into a genuine one-dimensional map using a checkerboarding algorithm. Calculations are then presented for the steady-state scattering of internal tides from the barotropic tide above the double ridges. The calculations exploit a Green function technique that distributes sources along the topography to generate the scattering, and discretizes in space to calculate the source density via a standard matrix inversion. When attractors are present, the numerical procedure appears to fail, displaying no convergence with the number of grid points used in the spatial discretizations, indicating a failure of the Green function solution. With the addition of dissipation into the problem, these difficulties are avoided, leading to convergent numerical solutions. The paper concludes with a comparison between theory and a laboratory experiment. |
| first_indexed | 2024-09-23T09:39:09Z |
| format | Article |
| id | mit-1721.1/79126 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T09:39:09Z |
| publishDate | 2013 |
| publisher | Cambridge University Press |
| record_format | dspace |
| spelling | mit-1721.1/791262022-09-30T15:57:30Z Tidally generated internal-wave attractors between double ridges Echeverri, Paula Yokossi, Tite Peacock, Thomas Balmforth, Neil J. Massachusetts Institute of Technology. Department of Economics Massachusetts Institute of Technology. Department of Mechanical Engineering Echeverri, Paula Yokossi, Tite Peacock, Thomas A study is presented of the generation of internal tides by barotropic tidal flow over topography in the shape of a double ridge. An iterative map is constructed to expedite the search for the closed ray paths that form wave attractors in this geometry. The map connects the positions along a ray path of consecutive reflections from the surface, which is double-valued owing to the presence of both left- and right-going waves, but which can be made into a genuine one-dimensional map using a checkerboarding algorithm. Calculations are then presented for the steady-state scattering of internal tides from the barotropic tide above the double ridges. The calculations exploit a Green function technique that distributes sources along the topography to generate the scattering, and discretizes in space to calculate the source density via a standard matrix inversion. When attractors are present, the numerical procedure appears to fail, displaying no convergence with the number of grid points used in the spatial discretizations, indicating a failure of the Green function solution. With the addition of dissipation into the problem, these difficulties are avoided, leading to convergent numerical solutions. The paper concludes with a comparison between theory and a laboratory experiment. United States. Office of Naval Research (Grant N00014-09-0282) 2013-06-17T15:27:58Z 2013-06-17T15:27:58Z 2011-01 2010-09 Article http://purl.org/eprint/type/JournalArticle 0022-1120 1469-7645 http://hdl.handle.net/1721.1/79126 ECHEVERRI, P., T. YOKOSSI, N. J. BALMFORTH, and T. PEACOCK. Tidally Generated Internal-wave Attractors Between Double Ridges. Journal of Fluid Mechanics 669 (February 11, 2011): 354-374. Copyright © Cambridge University Press 2011 https://orcid.org/0000-0002-7639-0194 en_US http://dx.doi.org/10.1017/S0022112010005069 Journal of Fluid Mechanics 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 Cambridge University Press MIT web domain |
| spellingShingle | Echeverri, Paula Yokossi, Tite Peacock, Thomas Balmforth, Neil J. Tidally generated internal-wave attractors between double ridges |
| title | Tidally generated internal-wave attractors between double ridges |
| title_full | Tidally generated internal-wave attractors between double ridges |
| title_fullStr | Tidally generated internal-wave attractors between double ridges |
| title_full_unstemmed | Tidally generated internal-wave attractors between double ridges |
| title_short | Tidally generated internal-wave attractors between double ridges |
| title_sort | tidally generated internal wave attractors between double ridges |
| url | http://hdl.handle.net/1721.1/79126 https://orcid.org/0000-0002-7639-0194 |
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