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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com


Hyperbolicity in the Ocean

Discontinuity, Nonlinearity, and Complexity 4(3) (2016) 257--270 | DOI:10.5890/DNC.2016.09.004

S.V. Prants$^{1}$, M.V. Budyansky$^{1}$, M.Yu. Uleysky$^{1}$, J. Zhang$^{2}$

$^{1}$ Laboratory of Nonlinear Dynamical Systems, Pacific Oceanological Institute of the Russian Academy of Sciences, 43 Baltiiskaya st., 690041 Vladivostok, Russia

$^{2}$ School of Energy and Power Engineering, Xi-an Jiaotong University, 710049, P.R. China

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Abstract

Some manifestations of hyperbolicity in the ocean, the important concept in dynamical systems theory, are discussed. It is shown how to identify hyperbolic points, hyperbolic trajectories and their stable and unstable manifolds solving advection equations for passive scalars in a satellite-derived AVISO velocity field and computing finite-time Lyapunov exponents by the singular-value decomposition method. To validate our simulation we use available tracks of oceanic drifters following near surface currents in some areas in the Northwestern Pacific Ocean. The tracks illustrate how drifters “feel” the presence of hyperbolic points, hyperbolic trajectories and stable and unstable manifolds and change abruptly their trajectories when approaching a hyperbolicity region.

Acknowledgments

This work was supported by the Russian Foundation for Basic Research (project no. 13–01–12404ofim) and by the Program “Dalniy Vostok” of the Far-Eastern Branch of the Russian Academy of Sciences (project nos. 15-I-1-003 o, 15-I-1-047 o, and 15-I-4-041).

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