Dept. Math, Hokkaido Univ. EPrints Server

Transition of global dynamics of a polygonal vortex ring on a sphere with pole vortices

Preprint Series # 642
SAKAJO, Takashi Transition of global dynamics of a polygonal vortex ring on a sphere with pole vortices. (2004);

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Abstract

This paper deal with the motion of a polygonal ring of identical vortex points that are equally spaced at a line of latitude on a sphere with vortex points fixed at the both poles, which we call "N-ring". We give not only all the eigenvalues but also all the eigenvectors corresponding to them for the linearized steationary N-ring. Then, we also reduce the equations to those for a pair of two vortex points, when N is even. As a consequence of the mathematical and numerical studies of the reduced system, we obtain a transition of global periodic motions of the perturbed N-ring and the stability of these periodic motions.

Item Type:Preprint
Subjects:76-xx FLUID MECHANICS
ID Code:147