Chaotic capture of vortices by a moving body. I. The single point vortex case

Chaos
James B. Kadtke, E A Novikov

Abstract

The study of the dynamical properties of vortex systems is an important and topical research area, and is becoming of ever increasing usefulness to a variety of physical applications. In this paper, we present a study of a model of a rotational singularity which obeys a logarithmic potential interacting with a bluff body in a uniform inviscid laminar flow, e.g., a line vortex interacting with a cylinder in three dimensions or a point vortex with a circular boundary in two dimensions. We show that this system is Hamiltonian and simple enough to be solved analytically for the stagnation points and separatrices of the flow, and a bifurcation diagram for the relevant parameters and classification of the various types of motion is given. We also show that, by introducing a periodic perturbation to the body, chaotic motion of the vortex can be readily generated, and we present analytic criteria for the generation of chaos using the Poincare-Melnikov-Arnold method. This leads to an important dynamical effect for the model, i.e., that the possibility exists for the vortex to be chaotically captured around the body for periods of time which are extremely sensitive to initial conditions. The basic mechanism for this capture is due to the...Continue Reading

References

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Citations

Jan 5, 2011·Chaos·Serdar Tulu, Oguz Yilmaz
Oct 1, 1993·Chaos·Edward Ott, Tamas Tel
Dec 1, 1994·Chaos·Harry H. LuithardtGianni Pedrizzetti
Jun 5, 2003·Chaos·Tamas TelJames Kadtke
Dec 1, 1995·Chaos·Gustavo StolovitzkyLawrence Sirovich
Oct 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·A E Novikov, E A Novikov
Jul 22, 2020·Physical Review. E·C Reichhardt, C J O Reichhardt

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