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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union

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Nonlin. Processes Geophys., 24, 1-8, 2017
http://www.nonlin-processes-geophys.net/24/1/2017/
doi:10.5194/npg-24-1-2017
© Author(s) 2017. This work is distributed
under the Creative Commons Attribution 3.0 License.
Research article
12 Jan 2017
Parametric resonance in the dynamics of an elliptic vortex in a periodically strained environment
Konstantin V. Koshel1,2,3 and Eugene A. Ryzhov1 1V.I.Il'ichev Pacific Oceanological Institute, FEB RAS, 43, Baltiyskaya Street, Vladivostok, 690041, Russia
2Far Eastern Federal University, 8, Sukhanova Street, Vladivostok, 690950, Russia
3Institute of Applied Mathematics, FEB RAS, 7, Radio Street, Vladivostok, 690022, Russia
Abstract. The model of an elliptic vortex evolving in a periodically strained background flow is studied in order to establish the possible unbounded regimes. Depending on the parameters of the exterior flow, there are three classical regimes of the elliptic vortex motion under constant linear deformation: (i) rotation, (ii) nutation, and (iii) infinite elongation. The phase portrait for the vortex dynamics features critical points which correspond to the stationary vortex not changing its form and orientation. We demonstrate that, given superimposed periodic oscillations to the exterior deformation, the phase space region corresponding to the elliptic critical point experiences parametric instability leading to locally unbounded dynamics of the vortex. This dynamics manifests itself as the vortex nutates along the strain axis while continuously elongating. This motion continues until nonlinear effects intervene near the region associated with the steady-state separatrix. Next, we show that, for specific values of the perturbation parameters, the parametric instability is effectively suppressed by nonlinearity in the primal parametric instability zone. The secondary zone of the parametric instability, on the contrary, produces an effective growth of the vortex's aspect ratio.

Citation: Koshel, K. V. and Ryzhov, E. A.: Parametric resonance in the dynamics of an elliptic vortex in a periodically strained environment, Nonlin. Processes Geophys., 24, 1-8, doi:10.5194/npg-24-1-2017, 2017.
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Short summary
The paper deals with the dynamics of an isolated vortex that evolves in a time-dependent strain environment. We establish parameters leading to parametric instability of stationary steady-state configuration using a combination of analytical and numerical techniques. Our findings may contribute to a deeper understanding of the coherent vortex dynamics in the ocean.
The paper deals with the dynamics of an isolated vortex that evolves in a time-dependent strain...
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