Vortex Interactions Subjected to Deformation Flows: A Review

Type Article
Date 2019-01
Language English
Author(s) Koshel Konstantin V.1, Ryzhov Eugene A.2, Carton Xavier3
Affiliation(s) 1 : RAS, FEB, VI Ilichev Pacific Oceanol Inst, 43,Baltiyskaya St, Vladivostok 690041, Russia.
2 : Imperial Coll London, Dept Math, London SW7 2AZ, England.
3 : IUEM UBO, Lab Oceanog Phys & Spatiale, Rue Dumont Urville, F-29280 Plouzane, France.
Source Fluids (2311-5521) (Mdpi), 2019-01 , Vol. 4 , N. 1 , P. 14 (48p.)
DOI 10.3390/fluids4010014
WOS© Times Cited 7
Note This article belongs to the Collection Geophysical Fluid Dynamics
Keyword(s) shear flow, deformation flow, point vortex, elliptic vortex, chaotic dynamics, parametric instability, stability islands

Deformation flows are the flows incorporating shear, strain and rotational components. These flows are ubiquitous in the geophysical flows, such as the ocean and atmosphere. They appear near almost any salience, such as isolated coherent structures (vortices and jets) and various fixed obstacles (submerged obstacles and continental boundaries). Fluid structures subject to such deformation flows may exhibit drastic changes in motion. In this review paper, we focus on the motion of a small number of coherent vortices embedded in deformation flows. Problems involving isolated one and two vortices are addressed. When considering a single-vortex problem, the main focus is on the evolution of the vortex boundary and its influence on the passive scalar motion. Two vortex problems are addressed with the use of point vortex models, and the resulting stirring patterns of neighbouring scalars are studied by a combination of numerical and analytical methods from the dynamical system theory. Many dynamical effects are reviewed with emphasis on the emergence of chaotic motion of the vortex phase trajectories and the scalars in their immediate vicinity.

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