Unstable periodic orbits in a chaotic meandering jet flow

TL;DR

This paper investigates the origin, bifurcations, and classification of unstable periodic orbits in a chaotic jet flow model, revealing new types of nonlinear resonances relevant to oceanic and atmospheric mixing.

Contribution

It develops a method to detect, locate, and classify unstable periodic orbits, including five new classes associated with different resonances in chaotic jet flows.

Findings

Identified five classes of period-4 orbits with distinct resonance origins

Tracked bifurcations of orbits as perturbation amplitude varies

Discovered new nonlinear resonance types in chaotic flow with jets

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.