Point vortex interactions
Abstract
The dynamics of point vortices with a view towards the onset of chaos in these systems were studied. It was conjectured that for a given geometry and external flow, a chaotic threshold N* exists such that NN* Quasiperiodic Motion NN* Chaotic Motion where N is the number of vortices. The conjecture (and the determination of N*) for a few special cases is proven. The existence of Horseshoes in the Poincare map of the perturbed system via Melnikov function technique are shown. Such a chaotic threshold suggests the nonintegrability of the two dimensional Euler Equations, in which the vortex equations are imbedded. It is shown that a vortex moving in a bounded, simply connected region of the plane has precisely one equilibrium point that is elliptic and Liapunov stable. The problem of two vortices inside a circle is solved exactly and the role of Morse theory in estimating special solutions is illustrated.
- Publication:
-
Ph.D. Thesis
- Pub Date:
- December 1985
- Bibcode:
- 1985PhDT........53S
- Keywords:
-
- Euler Equations Of Motion;
- Liapunov Functions;
- Morse Potential;
- Poincare Spheres;
- Vortex Generators;
- Vorticity;
- Cavitation Flow;
- Differential Equations;
- Kinetic Theory;
- Velocity Measurement;
- Fluid Mechanics and Heat Transfer