Articles | Volume 24, issue 1
Nonlin. Processes Geophys., 24, 1–8, 2017

Special issue: Current perspectives in modelling, monitoring, and predicting...

Nonlin. Processes Geophys., 24, 1–8, 2017

Research article 12 Jan 2017

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 Konstantin V. Koshel and Eugene A. Ryzhov
  • 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.

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.