Explicit and exact solutions concerning the Antarctic Circumpolar Current with variable density in spherical coordinates
We use spherical coordinates to devise a new exact solution to the governing equations of geophysical fluid dynamics for an inviscid and incompressible fluid with a general density distribution and subjected to forcing terms. The latter are of paramount importance for the modeling of realistic flows...
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craippubl:10.1063/1.5120627 2024-05-12T07:56:34+00:00 Explicit and exact solutions concerning the Antarctic Circumpolar Current with variable density in spherical coordinates Martin, Calin Iulian Quirchmayr, Ronald Austrian Science Fund 2019 http://dx.doi.org/10.1063/1.5120627 https://pubs.aip.org/aip/jmp/article-pdf/doi/10.1063/1.5120627/15773099/101505_1_online.pdf en eng AIP Publishing Journal of Mathematical Physics volume 60, issue 10 ISSN 0022-2488 1089-7658 Mathematical Physics Statistical and Nonlinear Physics journal-article 2019 craippubl https://doi.org/10.1063/1.5120627 2024-04-18T06:45:04Z We use spherical coordinates to devise a new exact solution to the governing equations of geophysical fluid dynamics for an inviscid and incompressible fluid with a general density distribution and subjected to forcing terms. The latter are of paramount importance for the modeling of realistic flows, that is, flows that are observed in some averaged sense in the ocean. Owing to the employment of spherical coordinates we do not need to resort to approximations (e.g., of f- and β-plane type) that simplify the geometry in the governing equations. Our explicit solution represents a steady purely azimuthal stratified flow with a free surface that—thanks to the inclusion of forcing terms and the consideration of the Earth’s geometry via spherical coordinates—makes it suitable for describing the Antarctic Circumpolar Current and enables an in-depth analysis of the structure of this flow. In line with the latter aspect, we employ functional analytical techniques to prove that the free surface distortion is defined in a unique and implicit way by means of the pressure applied at the free surface. We conclude our discussion by setting out relations between the monotonicity of the surface pressure and the monotonicity of the surface distortion that concur with the physical expectations. Article in Journal/Newspaper Antarc* Antarctic AIP Publishing Antarctic The Antarctic Journal of Mathematical Physics 60 10 101505 |
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AIP Publishing |
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English |
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Mathematical Physics Statistical and Nonlinear Physics |
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Mathematical Physics Statistical and Nonlinear Physics Martin, Calin Iulian Quirchmayr, Ronald Explicit and exact solutions concerning the Antarctic Circumpolar Current with variable density in spherical coordinates |
topic_facet |
Mathematical Physics Statistical and Nonlinear Physics |
description |
We use spherical coordinates to devise a new exact solution to the governing equations of geophysical fluid dynamics for an inviscid and incompressible fluid with a general density distribution and subjected to forcing terms. The latter are of paramount importance for the modeling of realistic flows, that is, flows that are observed in some averaged sense in the ocean. Owing to the employment of spherical coordinates we do not need to resort to approximations (e.g., of f- and β-plane type) that simplify the geometry in the governing equations. Our explicit solution represents a steady purely azimuthal stratified flow with a free surface that—thanks to the inclusion of forcing terms and the consideration of the Earth’s geometry via spherical coordinates—makes it suitable for describing the Antarctic Circumpolar Current and enables an in-depth analysis of the structure of this flow. In line with the latter aspect, we employ functional analytical techniques to prove that the free surface distortion is defined in a unique and implicit way by means of the pressure applied at the free surface. We conclude our discussion by setting out relations between the monotonicity of the surface pressure and the monotonicity of the surface distortion that concur with the physical expectations. |
author2 |
Austrian Science Fund |
format |
Article in Journal/Newspaper |
author |
Martin, Calin Iulian Quirchmayr, Ronald |
author_facet |
Martin, Calin Iulian Quirchmayr, Ronald |
author_sort |
Martin, Calin Iulian |
title |
Explicit and exact solutions concerning the Antarctic Circumpolar Current with variable density in spherical coordinates |
title_short |
Explicit and exact solutions concerning the Antarctic Circumpolar Current with variable density in spherical coordinates |
title_full |
Explicit and exact solutions concerning the Antarctic Circumpolar Current with variable density in spherical coordinates |
title_fullStr |
Explicit and exact solutions concerning the Antarctic Circumpolar Current with variable density in spherical coordinates |
title_full_unstemmed |
Explicit and exact solutions concerning the Antarctic Circumpolar Current with variable density in spherical coordinates |
title_sort |
explicit and exact solutions concerning the antarctic circumpolar current with variable density in spherical coordinates |
publisher |
AIP Publishing |
publishDate |
2019 |
url |
http://dx.doi.org/10.1063/1.5120627 https://pubs.aip.org/aip/jmp/article-pdf/doi/10.1063/1.5120627/15773099/101505_1_online.pdf |
geographic |
Antarctic The Antarctic |
geographic_facet |
Antarctic The Antarctic |
genre |
Antarc* Antarctic |
genre_facet |
Antarc* Antarctic |
op_source |
Journal of Mathematical Physics volume 60, issue 10 ISSN 0022-2488 1089-7658 |
op_doi |
https://doi.org/10.1063/1.5120627 |
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Journal of Mathematical Physics |
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60 |
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10 |
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101505 |
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1798836712007270400 |