Unstable periodic orbits in a chaotic meandering jet flow

Details Unstable periodic orbits in a chaotic meandering jet flow Unstable periodic orbits in a chaotic meandering jet flow

2007-12-25

arxiv.org/abs/0712.4048v1

Journal of Physics A. 2008. V.41. Art 215102

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

10.1088/1751-8113/41/21/215102

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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