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arXiv · 0712.4048

Unstable periodic orbits in a chaotic meandering jet flow

M. Yu. Uleysky·M. V. Budyansky·S. V. Prants
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Abstract

We study the origin and bifurcations of typical classes of unstable periodic orbits in a jet flow that was introduced before as a kinematic model of chaotic advection, transport and mixing of passive scalars in meandering oceanic and atmospheric currents. A method to detect and locate the unstable periodic orbits and classify them by the origin and bifurcations is developed. We consider in detail period-1 and period-4 orbits playing an important role in chaotic advection. We introduce five classes of period-4 orbits: western and eastern ballistic ones, whose origin is associated with ballistic resonances of the fourth order, rotational ones, associated with rotational resonances of the second and fourth orders, and rotational-ballistic ones associated with a rotational-ballistic resonance. It is a new kind of nonlinear resonances that may occur in chaotic flow with jets and/or circulation cells. Varying the perturbation amplitude, we track out the origin and bifurcations of the orbits for each class.

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M. Yu. Uleysky, M. V. Budyansky, S. V. Prants. 2007-12-25. Unstable periodic orbits in a chaotic meandering jet flow. https://doi.org/10.1088/1751-8113%2F41%2F21%2F215102

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