Unstable periodic orbits in a chaotic meandering jet flow
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.
Cite
@article{arxiv.0712.4048,
title = {Unstable periodic orbits in a chaotic meandering jet flow},
author = {M. Yu. Uleysky and M. V. Budyansky and S. V. Prants},
journal= {arXiv preprint arXiv:0712.4048},
year = {2012}
}