Mathematical Modeling of Vortex Interaction Using a Three-Layer Quasigeostrophic Model. Part 2: Finite-Core-Vortex Approach and Oceanographic Application
The three-layer version of the contour dynamics/surgery method is used to study the interaction mechanisms of a large-scale surface vortex with a smaller vortex/vortices of the middle layer (prototypes of intrathermocline vortices in the ocean) belonging to the middle layer of a three-layer rotating...
Published in: | Mathematics |
---|---|
Main Authors: | , , |
Format: | Article in Journal/Newspaper |
Language: | English |
Published: |
MDPI AG
2020
|
Subjects: | |
Online Access: | https://doi.org/10.3390/math8081267 https://doaj.org/article/18a08323840945f0984de251303e5a49 |
id |
ftdoajarticles:oai:doaj.org/article:18a08323840945f0984de251303e5a49 |
---|---|
record_format |
openpolar |
spelling |
ftdoajarticles:oai:doaj.org/article:18a08323840945f0984de251303e5a49 2023-05-15T17:35:24+02:00 Mathematical Modeling of Vortex Interaction Using a Three-Layer Quasigeostrophic Model. Part 2: Finite-Core-Vortex Approach and Oceanographic Application Mikhail A. Sokolovskiy Xavier J. Carton Boris N. Filyushkin 2020-08-01T00:00:00Z https://doi.org/10.3390/math8081267 https://doaj.org/article/18a08323840945f0984de251303e5a49 EN eng MDPI AG https://www.mdpi.com/2227-7390/8/8/1267 https://doaj.org/toc/2227-7390 doi:10.3390/math8081267 2227-7390 https://doaj.org/article/18a08323840945f0984de251303e5a49 Mathematics, Vol 8, Iss 1267, p 1267 (2020) quasi-geostrophic model vortex interaction intrathermocline lens point vortex finite-core vortices Mathematics QA1-939 article 2020 ftdoajarticles https://doi.org/10.3390/math8081267 2022-12-31T05:52:52Z The three-layer version of the contour dynamics/surgery method is used to study the interaction mechanisms of a large-scale surface vortex with a smaller vortex/vortices of the middle layer (prototypes of intrathermocline vortices in the ocean) belonging to the middle layer of a three-layer rotating fluid. The lower layer is assumed to be dynamically passive. The piecewise constant vertical density distribution approximates the average long-term profile for the North Atlantic, where intrathermocline eddies are observed most often at depths of 300–1600 m. Numerical experiments were carried out with different initial configurations of vortices, to evaluate several effects. Firstly, the stability of the vortex compound was evaluated. Most often, it remains compact, but when unstable, it can break as vertically coupled vortex dipoles (called hetons). Secondly, we studied the interaction between a vertically tilted cyclone and lenses. Then, the lenses first undergo anticlockwise rotation determined by the surface cyclone. The lenses can induce alignment or coupling with cyclonic vorticity above them. Only very weak lenses are destroyed by the shear stress exerted by the surface cyclone. Thirdly, under the influence of lens dipoles, the surface cyclone can be torn apart. In particular, the shedding of rapidly moving vortex pairs at the surface reflects the presence of lens dipoles below. More slowly moving small eddies can also be torn away from the main surface cyclone. In this case, they do not appear to be coupled with middle layer vortices. They are the result of large shear-induced deformation. Common and differing features of the vortex interaction, modeled in the framework of the theory of point and finite-core vortices, are noted. Article in Journal/Newspaper North Atlantic Directory of Open Access Journals: DOAJ Articles Mathematics 8 8 1267 |
institution |
Open Polar |
collection |
Directory of Open Access Journals: DOAJ Articles |
op_collection_id |
ftdoajarticles |
language |
English |
topic |
quasi-geostrophic model vortex interaction intrathermocline lens point vortex finite-core vortices Mathematics QA1-939 |
spellingShingle |
quasi-geostrophic model vortex interaction intrathermocline lens point vortex finite-core vortices Mathematics QA1-939 Mikhail A. Sokolovskiy Xavier J. Carton Boris N. Filyushkin Mathematical Modeling of Vortex Interaction Using a Three-Layer Quasigeostrophic Model. Part 2: Finite-Core-Vortex Approach and Oceanographic Application |
topic_facet |
quasi-geostrophic model vortex interaction intrathermocline lens point vortex finite-core vortices Mathematics QA1-939 |
description |
The three-layer version of the contour dynamics/surgery method is used to study the interaction mechanisms of a large-scale surface vortex with a smaller vortex/vortices of the middle layer (prototypes of intrathermocline vortices in the ocean) belonging to the middle layer of a three-layer rotating fluid. The lower layer is assumed to be dynamically passive. The piecewise constant vertical density distribution approximates the average long-term profile for the North Atlantic, where intrathermocline eddies are observed most often at depths of 300–1600 m. Numerical experiments were carried out with different initial configurations of vortices, to evaluate several effects. Firstly, the stability of the vortex compound was evaluated. Most often, it remains compact, but when unstable, it can break as vertically coupled vortex dipoles (called hetons). Secondly, we studied the interaction between a vertically tilted cyclone and lenses. Then, the lenses first undergo anticlockwise rotation determined by the surface cyclone. The lenses can induce alignment or coupling with cyclonic vorticity above them. Only very weak lenses are destroyed by the shear stress exerted by the surface cyclone. Thirdly, under the influence of lens dipoles, the surface cyclone can be torn apart. In particular, the shedding of rapidly moving vortex pairs at the surface reflects the presence of lens dipoles below. More slowly moving small eddies can also be torn away from the main surface cyclone. In this case, they do not appear to be coupled with middle layer vortices. They are the result of large shear-induced deformation. Common and differing features of the vortex interaction, modeled in the framework of the theory of point and finite-core vortices, are noted. |
format |
Article in Journal/Newspaper |
author |
Mikhail A. Sokolovskiy Xavier J. Carton Boris N. Filyushkin |
author_facet |
Mikhail A. Sokolovskiy Xavier J. Carton Boris N. Filyushkin |
author_sort |
Mikhail A. Sokolovskiy |
title |
Mathematical Modeling of Vortex Interaction Using a Three-Layer Quasigeostrophic Model. Part 2: Finite-Core-Vortex Approach and Oceanographic Application |
title_short |
Mathematical Modeling of Vortex Interaction Using a Three-Layer Quasigeostrophic Model. Part 2: Finite-Core-Vortex Approach and Oceanographic Application |
title_full |
Mathematical Modeling of Vortex Interaction Using a Three-Layer Quasigeostrophic Model. Part 2: Finite-Core-Vortex Approach and Oceanographic Application |
title_fullStr |
Mathematical Modeling of Vortex Interaction Using a Three-Layer Quasigeostrophic Model. Part 2: Finite-Core-Vortex Approach and Oceanographic Application |
title_full_unstemmed |
Mathematical Modeling of Vortex Interaction Using a Three-Layer Quasigeostrophic Model. Part 2: Finite-Core-Vortex Approach and Oceanographic Application |
title_sort |
mathematical modeling of vortex interaction using a three-layer quasigeostrophic model. part 2: finite-core-vortex approach and oceanographic application |
publisher |
MDPI AG |
publishDate |
2020 |
url |
https://doi.org/10.3390/math8081267 https://doaj.org/article/18a08323840945f0984de251303e5a49 |
genre |
North Atlantic |
genre_facet |
North Atlantic |
op_source |
Mathematics, Vol 8, Iss 1267, p 1267 (2020) |
op_relation |
https://www.mdpi.com/2227-7390/8/8/1267 https://doaj.org/toc/2227-7390 doi:10.3390/math8081267 2227-7390 https://doaj.org/article/18a08323840945f0984de251303e5a49 |
op_doi |
https://doi.org/10.3390/math8081267 |
container_title |
Mathematics |
container_volume |
8 |
container_issue |
8 |
container_start_page |
1267 |
_version_ |
1766134555124695040 |