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Mathematical Modeling of Vortex Interaction Using a Three-Layer Quasigeostrophic Model. Part 1: Point-Vortex Approach
Article

Mathematical Modeling of Vortex Interaction Using a Three-Layer Quasigeostrophic Model. Part 2: Finite-Core-Vortex Approach and Oceanographic Application

1
Water Problems Institute, Russian Academy of Science, 3 Gubkina Str., 119333 Moscow, Russia
2
Shirshov Institute of Oceanology, Russian Academy of Science, 36 Nahimovskiy Prosperkt, 117997 Moscow, Russia
3
Laboratoire d’Océanographie Physique et Spatiale, IUEM/UBO, Rue Dumont D’Urville, 29280 Plouzané, France
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(8), 1267; https://doi.org/10.3390/math8081267
Received: 2 July 2020 / Revised: 16 July 2020 / Accepted: 27 July 2020 / Published: 2 August 2020
(This article belongs to the Special Issue Vortex Dynamics: Theory and Application to Geophysical Flows)
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. View Full-Text
Keywords: quasi-geostrophic model; vortex interaction; intrathermocline lens; point vortex; finite-core vortices quasi-geostrophic model; vortex interaction; intrathermocline lens; point vortex; finite-core vortices
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MDPI and ACS Style

Sokolovskiy, M.A.; Carton, X.J.; Filyushkin, B.N. Mathematical Modeling of Vortex Interaction Using a Three-Layer Quasigeostrophic Model. Part 2: Finite-Core-Vortex Approach and Oceanographic Application. Mathematics 2020, 8, 1267. https://doi.org/10.3390/math8081267

AMA Style

Sokolovskiy MA, Carton XJ, Filyushkin BN. Mathematical Modeling of Vortex Interaction Using a Three-Layer Quasigeostrophic Model. Part 2: Finite-Core-Vortex Approach and Oceanographic Application. Mathematics. 2020; 8(8):1267. https://doi.org/10.3390/math8081267

Chicago/Turabian Style

Sokolovskiy, Mikhail A., Xavier J. Carton, and Boris N. Filyushkin 2020. "Mathematical Modeling of Vortex Interaction Using a Three-Layer Quasigeostrophic Model. Part 2: Finite-Core-Vortex Approach and Oceanographic Application" Mathematics 8, no. 8: 1267. https://doi.org/10.3390/math8081267

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