Application of the ideas and techniques of classical fluid mechanics to some problems in physical oceanography
This review makes a case for describing many of the flows observed in our oceans, simply based on the Euler equation, with (piecewise) constant density and with suitable boundary conditions. The analyses start from the Euler and mass conservation equations, expressed in a rotating, spherical coordin...
Published in: | Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |
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crroyalsociety:10.1098/rsta.2017.0092 2024-06-02T07:57:30+00:00 Application of the ideas and techniques of classical fluid mechanics to some problems in physical oceanography Johnson, R. S. 2017 http://dx.doi.org/10.1098/rsta.2017.0092 https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2017.0092 https://royalsocietypublishing.org/doi/full-xml/10.1098/rsta.2017.0092 en eng The Royal Society https://royalsociety.org/journals/ethics-policies/data-sharing-mining/ Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences volume 376, issue 2111, page 20170092 ISSN 1364-503X 1471-2962 journal-article 2017 crroyalsociety https://doi.org/10.1098/rsta.2017.0092 2024-05-07T14:16:41Z This review makes a case for describing many of the flows observed in our oceans, simply based on the Euler equation, with (piecewise) constant density and with suitable boundary conditions. The analyses start from the Euler and mass conservation equations, expressed in a rotating, spherical coordinate system (but the f -plane and β -plane approximations are also mentioned); five examples are discussed. For three of them, a suitable non-dimensionalization is introduced, and a single small parameter is identified in each case. These three examples lead straightforwardly and directly to new results for: waves on the Pacific Equatorial Undercurrent (EUC) with a thermocline (in the f -plane); a nonlinear, three-dimensional model for EUC-type flows (in the β -plane); and a detailed model for large gyres. The other two examples are exact solutions of the complete system: a flow which corresponds to the underlying structure of the Pacific EUC; and a flow based on the necessary requirement to use a non-conservative body force, which produces the type of flow observed in the Antarctic Circumpolar Current. (All these examples have been discussed in detail in the references cited.) This review concludes with a few comments on how these solutions can be extended and expanded. This article is part of the theme issue ‘Nonlinear water waves’. Article in Journal/Newspaper Antarc* Antarctic The Royal Society Antarctic Pacific The Antarctic Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376 2111 20170092 |
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This review makes a case for describing many of the flows observed in our oceans, simply based on the Euler equation, with (piecewise) constant density and with suitable boundary conditions. The analyses start from the Euler and mass conservation equations, expressed in a rotating, spherical coordinate system (but the f -plane and β -plane approximations are also mentioned); five examples are discussed. For three of them, a suitable non-dimensionalization is introduced, and a single small parameter is identified in each case. These three examples lead straightforwardly and directly to new results for: waves on the Pacific Equatorial Undercurrent (EUC) with a thermocline (in the f -plane); a nonlinear, three-dimensional model for EUC-type flows (in the β -plane); and a detailed model for large gyres. The other two examples are exact solutions of the complete system: a flow which corresponds to the underlying structure of the Pacific EUC; and a flow based on the necessary requirement to use a non-conservative body force, which produces the type of flow observed in the Antarctic Circumpolar Current. (All these examples have been discussed in detail in the references cited.) This review concludes with a few comments on how these solutions can be extended and expanded. This article is part of the theme issue ‘Nonlinear water waves’. |
format |
Article in Journal/Newspaper |
author |
Johnson, R. S. |
spellingShingle |
Johnson, R. S. Application of the ideas and techniques of classical fluid mechanics to some problems in physical oceanography |
author_facet |
Johnson, R. S. |
author_sort |
Johnson, R. S. |
title |
Application of the ideas and techniques of classical fluid mechanics to some problems in physical oceanography |
title_short |
Application of the ideas and techniques of classical fluid mechanics to some problems in physical oceanography |
title_full |
Application of the ideas and techniques of classical fluid mechanics to some problems in physical oceanography |
title_fullStr |
Application of the ideas and techniques of classical fluid mechanics to some problems in physical oceanography |
title_full_unstemmed |
Application of the ideas and techniques of classical fluid mechanics to some problems in physical oceanography |
title_sort |
application of the ideas and techniques of classical fluid mechanics to some problems in physical oceanography |
publisher |
The Royal Society |
publishDate |
2017 |
url |
http://dx.doi.org/10.1098/rsta.2017.0092 https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2017.0092 https://royalsocietypublishing.org/doi/full-xml/10.1098/rsta.2017.0092 |
geographic |
Antarctic Pacific The Antarctic |
geographic_facet |
Antarctic Pacific The Antarctic |
genre |
Antarc* Antarctic |
genre_facet |
Antarc* Antarctic |
op_source |
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences volume 376, issue 2111, page 20170092 ISSN 1364-503X 1471-2962 |
op_rights |
https://royalsociety.org/journals/ethics-policies/data-sharing-mining/ |
op_doi |
https://doi.org/10.1098/rsta.2017.0092 |
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Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |
container_volume |
376 |
container_issue |
2111 |
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20170092 |
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