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Kilin A. A., Artemova E. M., Solodyankin D. A.
Dynamics of two point vortices inside a rectangular region
European Journal of Mechanics - B/Fluids, 2026, vol. 119, 204544, 14 pp.
Abstract
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In this paper we consider the motion of two point vortices in an ideal incompressible fluid confined in a rectangular region. We construct a mathematical model describing the motion of point vortices in a rectangular region from the equations of vortex motion on a finite flat cylinder. We show invariant manifolds (centrally symmetric and reflection-symmetric) existing in the system under some restrictions on vortex strengths. The cases of a vortex pair and vortices of the same strength are examined in detail. We show that even in these cases the system under consideration is nonintegrable.
| Keywords: |
ideal fluid, point vortex, invariant manifold, chaos, Poincaré map |
| Citation: |
Kilin A. A., Artemova E. M., Solodyankin D. A., Dynamics of two point vortices inside a rectangular region, European Journal of Mechanics - B/Fluids, 2026, vol. 119, 204544, 14 pp. |
| DOI: |
10.1016/j.euromechflu.2026.204544 |
| Full text: |
pdf
(3.78 Mb)
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