A cylindrical coordinates approach concerning internal waves for the Antarctic Circumpolar Current
In this paper, we devise a new exact and partially explicit solution to the governing equations of geophysical fluid dynamics for an inviscid and incompressible azimuth flow with a discontinuous density distribution and subjected to forcing terms in terms of cylindrical coordinates. The obtained sol...
Main Authors: | , |
---|---|
Format: | Article in Journal/Newspaper |
Language: | unknown |
Published: |
arXiv
2022
|
Subjects: | |
Online Access: | https://dx.doi.org/10.48550/arxiv.2202.09062 https://arxiv.org/abs/2202.09062 |
id |
ftdatacite:10.48550/arxiv.2202.09062 |
---|---|
record_format |
openpolar |
spelling |
ftdatacite:10.48550/arxiv.2202.09062 2023-05-15T14:01:28+02:00 A cylindrical coordinates approach concerning internal waves for the Antarctic Circumpolar Current Fan, Lili Shen, Shuge 2022 https://dx.doi.org/10.48550/arxiv.2202.09062 https://arxiv.org/abs/2202.09062 unknown arXiv arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Fluid Dynamics physics.flu-dyn Analysis of PDEs math.AP FOS Physical sciences FOS Mathematics Article CreativeWork article Preprint 2022 ftdatacite https://doi.org/10.48550/arxiv.2202.09062 2022-03-10T13:50:04Z In this paper, we devise a new exact and partially explicit solution to the governing equations of geophysical fluid dynamics for an inviscid and incompressible azimuth flow with a discontinuous density distribution and subjected to forcing terms in terms of cylindrical coordinates. The obtained solution represents a steady, purely azimuthal, stratified flow with an associated free surface and an interface that is suitable for describing the Antarctic Circumpolar Current. Resorting to a functional analysis, we demonstrate that the relationship between the imposed pressure at the free surface and the resulting surface deformation is well-defined and show that the continuity of the pressure along the interface generates an equation that describes implicitly the shape of the interface. Moreover, a particular example is considered to show that the interface can be determined explicitly. Finally, we derive an infinite regularity about the interface and obtain the expected monotonicity properties between the surface pressure and its distortion. Article in Journal/Newspaper Antarc* Antarctic DataCite Metadata Store (German National Library of Science and Technology) Antarctic The Antarctic |
institution |
Open Polar |
collection |
DataCite Metadata Store (German National Library of Science and Technology) |
op_collection_id |
ftdatacite |
language |
unknown |
topic |
Fluid Dynamics physics.flu-dyn Analysis of PDEs math.AP FOS Physical sciences FOS Mathematics |
spellingShingle |
Fluid Dynamics physics.flu-dyn Analysis of PDEs math.AP FOS Physical sciences FOS Mathematics Fan, Lili Shen, Shuge A cylindrical coordinates approach concerning internal waves for the Antarctic Circumpolar Current |
topic_facet |
Fluid Dynamics physics.flu-dyn Analysis of PDEs math.AP FOS Physical sciences FOS Mathematics |
description |
In this paper, we devise a new exact and partially explicit solution to the governing equations of geophysical fluid dynamics for an inviscid and incompressible azimuth flow with a discontinuous density distribution and subjected to forcing terms in terms of cylindrical coordinates. The obtained solution represents a steady, purely azimuthal, stratified flow with an associated free surface and an interface that is suitable for describing the Antarctic Circumpolar Current. Resorting to a functional analysis, we demonstrate that the relationship between the imposed pressure at the free surface and the resulting surface deformation is well-defined and show that the continuity of the pressure along the interface generates an equation that describes implicitly the shape of the interface. Moreover, a particular example is considered to show that the interface can be determined explicitly. Finally, we derive an infinite regularity about the interface and obtain the expected monotonicity properties between the surface pressure and its distortion. |
format |
Article in Journal/Newspaper |
author |
Fan, Lili Shen, Shuge |
author_facet |
Fan, Lili Shen, Shuge |
author_sort |
Fan, Lili |
title |
A cylindrical coordinates approach concerning internal waves for the Antarctic Circumpolar Current |
title_short |
A cylindrical coordinates approach concerning internal waves for the Antarctic Circumpolar Current |
title_full |
A cylindrical coordinates approach concerning internal waves for the Antarctic Circumpolar Current |
title_fullStr |
A cylindrical coordinates approach concerning internal waves for the Antarctic Circumpolar Current |
title_full_unstemmed |
A cylindrical coordinates approach concerning internal waves for the Antarctic Circumpolar Current |
title_sort |
cylindrical coordinates approach concerning internal waves for the antarctic circumpolar current |
publisher |
arXiv |
publishDate |
2022 |
url |
https://dx.doi.org/10.48550/arxiv.2202.09062 https://arxiv.org/abs/2202.09062 |
geographic |
Antarctic The Antarctic |
geographic_facet |
Antarctic The Antarctic |
genre |
Antarc* Antarctic |
genre_facet |
Antarc* Antarctic |
op_rights |
arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
op_doi |
https://doi.org/10.48550/arxiv.2202.09062 |
_version_ |
1766271298567143424 |