Exact solutions for geophysical flows with discontinuous variable density and forcing terms in spherical coordinates
We present here exact solutions to the equations of geophysical fluid dynamics that depict inviscid flows moving in the azimuthal direction on a circular path, around the globe, and which admit a velocity profile below the surface and along it. These features render this model suitable for the descr...
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fttudelft:oai:tudelft.nl:uuid:9d51bacb-ec0e-4095-aebe-212e5b9c3191 2024-02-11T09:57:29+01:00 Exact solutions for geophysical flows with discontinuous variable density and forcing terms in spherical coordinates Chu, Jifeng (author) Iulian Martin, Calin (author) Marynets, K. (author) 2023 http://resolver.tudelft.nl/uuid:9d51bacb-ec0e-4095-aebe-212e5b9c3191 https://doi.org/10.1080/00036811.2023.2207589 en eng http://www.scopus.com/inward/record.url?scp=85158126121&partnerID=8YFLogxK Applicable Analysis--0003-6811--57cafb8a-9def-4c2c-af00-5d7341993636 http://resolver.tudelft.nl/uuid:9d51bacb-ec0e-4095-aebe-212e5b9c3191 https://doi.org/10.1080/00036811.2023.2207589 © 2023 Jifeng Chu, Calin Iulian Martin, K. Marynets Coriolis force discontinuous stratification Exact solutions in spherical coordinates forcing terms the Antarctic Circumpolar Current journal article 2023 fttudelft https://doi.org/10.1080/00036811.2023.2207589 2024-01-24T23:34:32Z We present here exact solutions to the equations of geophysical fluid dynamics that depict inviscid flows moving in the azimuthal direction on a circular path, around the globe, and which admit a velocity profile below the surface and along it. These features render this model suitable for the description of the Antarctic circumpolar current (ACC). The governing equations we work with–taken to be the Euler equations written in spherical coordinates–also incorporate forcing terms which are generally regarded as means that ensure the general balance of the ACC. Our approach allows for a variable density (depending on the depth and latitude) of discontinuous type which divides the water domain into two layers. Thus, the discontinuity gives rise to an interface. The velocity in both layers and the pressure in the lower layer are determined explicitly, while the pressure in the upper layer depends on the free surface and the interface. Functional analytical techniques render (uniquely) the surface and interface-defining functions in an implicit way. We conclude our discussion by deriving relations between the monotonicity of the surface pressure and the monotonicity of the surface distortion that concur with the physical expectations. A regularity result concerning the interface is also derived. Mathematical Physics Article in Journal/Newspaper Antarc* Antarctic Delft University of Technology: Institutional Repository Antarctic The Antarctic Applicable Analysis 1 14 |
institution |
Open Polar |
collection |
Delft University of Technology: Institutional Repository |
op_collection_id |
fttudelft |
language |
English |
topic |
Coriolis force discontinuous stratification Exact solutions in spherical coordinates forcing terms the Antarctic Circumpolar Current |
spellingShingle |
Coriolis force discontinuous stratification Exact solutions in spherical coordinates forcing terms the Antarctic Circumpolar Current Chu, Jifeng (author) Iulian Martin, Calin (author) Marynets, K. (author) Exact solutions for geophysical flows with discontinuous variable density and forcing terms in spherical coordinates |
topic_facet |
Coriolis force discontinuous stratification Exact solutions in spherical coordinates forcing terms the Antarctic Circumpolar Current |
description |
We present here exact solutions to the equations of geophysical fluid dynamics that depict inviscid flows moving in the azimuthal direction on a circular path, around the globe, and which admit a velocity profile below the surface and along it. These features render this model suitable for the description of the Antarctic circumpolar current (ACC). The governing equations we work with–taken to be the Euler equations written in spherical coordinates–also incorporate forcing terms which are generally regarded as means that ensure the general balance of the ACC. Our approach allows for a variable density (depending on the depth and latitude) of discontinuous type which divides the water domain into two layers. Thus, the discontinuity gives rise to an interface. The velocity in both layers and the pressure in the lower layer are determined explicitly, while the pressure in the upper layer depends on the free surface and the interface. Functional analytical techniques render (uniquely) the surface and interface-defining functions in an implicit way. We conclude our discussion by deriving relations between the monotonicity of the surface pressure and the monotonicity of the surface distortion that concur with the physical expectations. A regularity result concerning the interface is also derived. Mathematical Physics |
format |
Article in Journal/Newspaper |
author |
Chu, Jifeng (author) Iulian Martin, Calin (author) Marynets, K. (author) |
author_facet |
Chu, Jifeng (author) Iulian Martin, Calin (author) Marynets, K. (author) |
author_sort |
Chu, Jifeng (author) |
title |
Exact solutions for geophysical flows with discontinuous variable density and forcing terms in spherical coordinates |
title_short |
Exact solutions for geophysical flows with discontinuous variable density and forcing terms in spherical coordinates |
title_full |
Exact solutions for geophysical flows with discontinuous variable density and forcing terms in spherical coordinates |
title_fullStr |
Exact solutions for geophysical flows with discontinuous variable density and forcing terms in spherical coordinates |
title_full_unstemmed |
Exact solutions for geophysical flows with discontinuous variable density and forcing terms in spherical coordinates |
title_sort |
exact solutions for geophysical flows with discontinuous variable density and forcing terms in spherical coordinates |
publishDate |
2023 |
url |
http://resolver.tudelft.nl/uuid:9d51bacb-ec0e-4095-aebe-212e5b9c3191 https://doi.org/10.1080/00036811.2023.2207589 |
geographic |
Antarctic The Antarctic |
geographic_facet |
Antarctic The Antarctic |
genre |
Antarc* Antarctic |
genre_facet |
Antarc* Antarctic |
op_relation |
http://www.scopus.com/inward/record.url?scp=85158126121&partnerID=8YFLogxK Applicable Analysis--0003-6811--57cafb8a-9def-4c2c-af00-5d7341993636 http://resolver.tudelft.nl/uuid:9d51bacb-ec0e-4095-aebe-212e5b9c3191 https://doi.org/10.1080/00036811.2023.2207589 |
op_rights |
© 2023 Jifeng Chu, Calin Iulian Martin, K. Marynets |
op_doi |
https://doi.org/10.1080/00036811.2023.2207589 |
container_title |
Applicable Analysis |
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1 |
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14 |
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1790609778921177088 |