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- W3015511473 abstract "Abstract Two-dimensional uniform vortices that rotate without deforming in an isochoric, inviscid fluid are investigated. They have polygonal symmetry and are usually considered of the same kind of the famous Kirchhoff elliptical one. By following this idea, their shapes and rotation speeds are calculated through a new integral approach. It is heuristically proved, by examining the co-rotating streamlines, that the similitude with the elliptical vortex is not complete, due to the appearance of external singularities in the Schwarz functions of the polygonal boundaries. Once the effects of these singularities have been accounted for, exactly steady vortices are obtained. In this way, for any number of “sides”, a continuous family of rotating, steady polygonal vortices is obtained, parametrized in the ratio between minimum and maximum radial coordinates of the boundary. Solutions exist above a critical value of this ratio, at which the boundary ceases to be differentiable." @default.
- W3015511473 created "2020-04-17" @default.
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- W3015511473 date "2020-09-01" @default.
- W3015511473 modified "2023-09-23" @default.
- W3015511473 title "Remarks on equilibria of two-dimensional uniform vortices with polygonal symmetry" @default.
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- W3015511473 doi "https://doi.org/10.1016/j.euromechflu.2020.03.006" @default.
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