H.Aref, V.V.Meleshko, A.A.Guba, A.A.Gourjii Uniformly-rotating configurations of point vortices |
Applied hydromechanics, Vol. 9 (81) ¹ 2-3, (2007) |
| A problem on construction of configurations and analysis of stability of stationary rotation of a system N of identical point vortices on a plane is considered. A brief review on existing in literature methods to search the uniformly-rotating vortex structures is carried out. A new method to construct the symmetric and asymmetric configurations of point vortices with equal intensity based on numeral solution of a system of nonlinear algebraic equalizations is proposed. The analysis of achieved solutions allowed to form an extended catalogue of uniformly-rotated structures containing N (where 2 ? N ? 10) point vortices. The catalogue has 13 symmetric and 25 asymmetrical vortex configurations. The comparative analysis of trajectories of point vortex system without initial perturbations and with initial perturbations shows that symmetric configurations contain both steady and unsteady structures. On the other hand, all asymmetrical vortex configurations are unsteady. |
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KEY WORDS: *** |
| TEXT LANGUAGE: Russian |