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A survey of the stability criteria of Thomson’s vortex polygons outside a circular domain. (English) Zbl 1348.76041

Summary: The model of point vortices located outside a circular domain is considered. The review of stability and instability conditions of a system of identical point vortices located uniformly on a circle is given. Theoretical results are confirmed by numerical calculations.

MSC:

76B47 Vortex flows for incompressible inviscid fluids
34D20 Stability of solutions to ordinary differential equations
70K30 Nonlinear resonances for nonlinear problems in mechanics
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