Local parametric instability near elliptic points in vortex flows under shear deformation
Abstract
The dynamics of two point vortices embedded in an oscillatory external flow consisted of shear and rotational components is addressed. The region associated with steadystate elliptic points of the vortex motion is established to experience local parametric instability. The instability forces the point vortices with initial positions corresponding to the steadystate elliptic points to move in spirallike divergent trajectories. This divergent motion continues until the nonlinear effects suppress their motion near the region associated with the steadystate separatrices. The local parametric instability is then demonstrated not to contribute considerably to enhancing the size of the chaotic motion regions. Instead, the size of the chaotic motion region mostly depends on overlaps of the nonlinear resonances emerging in the perturbed system.
 Authors:
 Pacific Oceanological Institute, FEB RAS, 43, Baltiyskaya Street, Vladivostok 690041 (Russian Federation)
 (Russian Federation)
 Publication Date:
 OSTI Identifier:
 22596478
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 26; Journal Issue: 8; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICAL METHODS AND COMPUTING; CHAOS THEORY; NONLINEAR PROBLEMS; PARAMETRIC INSTABILITIES; STEADYSTATE CONDITIONS; TRAJECTORIES; VORTEX FLOW; VORTICES
Citation Formats
Koshel, Konstantin V., Email: kvkoshel@poi.dvo.ru, Institute of Applied Mathematics, FEB RAS, 7, Radio Street, Vladivostok 690022, Far Eastern Federal University, 8, Sukhanova Street, Vladivostok 690950, and Ryzhov, Eugene A., Email: ryzhovea@gmail.com. Local parametric instability near elliptic points in vortex flows under shear deformation. United States: N. p., 2016.
Web. doi:10.1063/1.4961123.
Koshel, Konstantin V., Email: kvkoshel@poi.dvo.ru, Institute of Applied Mathematics, FEB RAS, 7, Radio Street, Vladivostok 690022, Far Eastern Federal University, 8, Sukhanova Street, Vladivostok 690950, & Ryzhov, Eugene A., Email: ryzhovea@gmail.com. Local parametric instability near elliptic points in vortex flows under shear deformation. United States. doi:10.1063/1.4961123.
Koshel, Konstantin V., Email: kvkoshel@poi.dvo.ru, Institute of Applied Mathematics, FEB RAS, 7, Radio Street, Vladivostok 690022, Far Eastern Federal University, 8, Sukhanova Street, Vladivostok 690950, and Ryzhov, Eugene A., Email: ryzhovea@gmail.com. 2016.
"Local parametric instability near elliptic points in vortex flows under shear deformation". United States.
doi:10.1063/1.4961123.
@article{osti_22596478,
title = {Local parametric instability near elliptic points in vortex flows under shear deformation},
author = {Koshel, Konstantin V., Email: kvkoshel@poi.dvo.ru and Institute of Applied Mathematics, FEB RAS, 7, Radio Street, Vladivostok 690022 and Far Eastern Federal University, 8, Sukhanova Street, Vladivostok 690950 and Ryzhov, Eugene A., Email: ryzhovea@gmail.com},
abstractNote = {The dynamics of two point vortices embedded in an oscillatory external flow consisted of shear and rotational components is addressed. The region associated with steadystate elliptic points of the vortex motion is established to experience local parametric instability. The instability forces the point vortices with initial positions corresponding to the steadystate elliptic points to move in spirallike divergent trajectories. This divergent motion continues until the nonlinear effects suppress their motion near the region associated with the steadystate separatrices. The local parametric instability is then demonstrated not to contribute considerably to enhancing the size of the chaotic motion regions. Instead, the size of the chaotic motion region mostly depends on overlaps of the nonlinear resonances emerging in the perturbed system.},
doi = {10.1063/1.4961123},
journal = {Chaos (Woodbury, N. Y.)},
number = 8,
volume = 26,
place = {United States},
year = 2016,
month = 8
}

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