The N-Vortex Problem on a Symmetric Ellipsoid: A Perturbation Approach

Details The N-Vortex Problem on a Symmetric Ellipsoid: A Perturbation Approach The N-Vortex Problem on a Symmetric Ellipsoid: A Perturbation Approach

2007-10-22

arxiv.org/abs/0710.4004v1

Mathematics

Dynamical Systems

14 pages, 1 figure

Scientific paper

10.1063/1.2863515

We consider the N-vortex problem on a ellipsoid of revolution. Applying standard techniques of classical perturbation theory we construct a sequence of conformal transformations from the ellipsoid into the complex plane. Using these transformations the equations of motion for the N-vortex problem on the ellipsoid are written as a formal series on the eccentricity of the ellipsoid's generating ellipse. First order equations are obtained explicitly. We show numerically that the truncated first order system for the three-vortices system on the symmetric ellipsoid is non-integrable.

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