Heteroclinic orbits and chaotic dynamics in planar fluid flows. (English) Zbl 0656.76025

An extension of the planar Smale-Birkhoff homoclinic theorem to the case of a heteroclinic saddle connection containing a finite number of fixed points is presented. This extension is used to find chaotic dynamics present in certain time-periodic perturbations of planar fluid models. Specifically, the Kelvin-Stuart cat’s eye flow is studied, a model for a vortex pattern found in shear layers. A flow on the two-torus with Hamiltonian \(H_ 0=(2\pi)^{-1}\sin (2\pi x_ 1)\cos (2\pi x_ 2)\) is studied, as well as the evolution equations for an elliptical vortex in a three-dimensional strain flow.


76B47 Vortex flows for incompressible inviscid fluids
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
70K99 Nonlinear dynamics in mechanics
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
54H20 Topological dynamics (MSC2010)
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