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The stability of the steady rotation of a system of three equidistant vortices outside a circle. (English. Russian original) Zbl 1272.76116

J. Appl. Math. Mech. 75, No. 2, 227-234 (2011); translation from Prikl. Mat. Mekh. 75, No. 2, 327-337 (2011).
Summary: A complete non-linear analysis of the stability of the steady rotation of three point vortices, placed in a plane at the vertices of a regular triangle outside a circular domain is carried out using the results of the Kolmogorov-Arnold-Moser theory. All the resonances of up to fourth order inclusive encountered here are listed and studied. The investigations of Havelock who solved this problem in a linear formulation are thereby completed.

MSC:

76E06 Convection in hydrodynamic stability
76B47 Vortex flows for incompressible inviscid fluids
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References:

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