Regular and chaotic motion of uniform elliptical vortices in external linear time dependent velocity fields

Citation

Ide, Kayo (1990) Regular and chaotic motion of uniform elliptical vortices in external linear time dependent velocity fields. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/sc2s-3749. https://resolver.caltech.edu/CaltechETD:etd-04132004-092941

Abstract

The motion of a uniform vorticity of an elliptical shape (UEV) induced by an external linear flow field and a self induced effect in a two dimensional incompressible inviscid flow is investigated. The fluid particle motion around the UEV is also investigated. The techniques from dynamical systems are intensively used. In particular, we develop some modified versions of the Melnikov techniques which show how the perturbations influence the dynamics and allow us to predict the perturbed dynamics by knowing the unperturbed dynamics.

The UEV motions in steady external linear flow fields are regular, however there are quite a few possibilities for types of motion depending on the UEV initial configuration and the external linear flow field parameters. When time periodic perturbation is imposed, the UEV motion drastically changes and various new types of motion become possible. This includes transition dynamics (i.e., the UEV changes its type of motion), chaotic motion, irregular oscillation and rotation, and quasiperiodic motion. The Melnikov techniques tell that the excess kinetic energy play significant roles in determining the UEV dynamics. A periodic motion of the UEV in a steady external linear flow field results in the generation of chaotic fluid particle mixing regions around the UEV where the fluid particles from distinct flow regions are chaotically transported. Our study emphasizes on the finite core size effect of the UEV in comparison to flow fields induced by a point vortex in unsteady external linear flow fields. We show that the size of the UEV core and the UEV initial configuration are important factors in determining the size of the mixing region.

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