Abstract
The dynamics of a pair of point vortices of opposite signs in a rectangular domain is investigated in the whole range of energies. This simplest nonintegrable system reflects important features of different vortex flows: Bénard convection, Görtler vortices, flow in a cavity etc. In contrast to an approximate "cloud-in-cell" method that has been used for many vortices, the exact equations of motion for an arbitrary system of point vortices in a rectangle are derived and applied to the particular case of a pair of vortices. Patterns of periodic, quasiperiodic, chaotic and billiards-type motions are revealed for generic cases and two limiting cases: two close vortices (near-dipole) and a vortex close to the boundary. New criteria of ergodicity are introduced, and it is found that some chaotic motions are close to, in some sense, ergodic ones.
Original language | English (US) |
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Pages (from-to) | 1835-1844 |
Number of pages | 10 |
Journal | International Journal of Engineering Science |
Volume | 32 |
Issue number | 11 |
DOIs | |
State | Published - Nov 1994 |
ASJC Scopus subject areas
- Materials Science(all)
- Engineering(all)
- Mechanics of Materials
- Mechanical Engineering