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...
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MDPI AG
2020-08-01
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| Series: | Mathematics |
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| 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 |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-10T18:00:42Z |
| format | Article |
| id | doaj.art-18a08323840945f0984de251303e5a49 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T18:00:42Z |
| publishDate | 2020-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-18a08323840945f0984de251303e5a492023-11-20T08:50:12ZengMDPI AGMathematics2227-73902020-08-0188126710.3390/math8081267Mathematical Modeling of Vortex Interaction Using a Three-Layer Quasigeostrophic Model. Part 2: Finite-Core-Vortex Approach and Oceanographic ApplicationMikhail A. Sokolovskiy0Xavier J. Carton1Boris N. Filyushkin2Water Problems Institute, Russian Academy of Science, 3 Gubkina Str., 119333 Moscow, RussiaLaboratoire d’Océanographie Physique et Spatiale, IUEM/UBO, Rue Dumont D’Urville, 29280 Plouzané, FranceShirshov Institute of Oceanology, Russian Academy of Science, 36 Nahimovskiy Prosperkt, 117997 Moscow, RussiaThe 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.https://www.mdpi.com/2227-7390/8/8/1267quasi-geostrophic modelvortex interactionintrathermocline lenspoint vortexfinite-core vortices |
| spellingShingle | 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 Mathematics quasi-geostrophic model vortex interaction intrathermocline lens point vortex finite-core vortices |
| title | 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_short | 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 |
| topic | quasi-geostrophic model vortex interaction intrathermocline lens point vortex finite-core vortices |
| url | https://www.mdpi.com/2227-7390/8/8/1267 |
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