Dept. Math, Hokkaido Univ. EPrints Server

Motion of a vortex sheet on a sphere with pole vortices

Preprint Series # 614
Sakajo, Takashi Motion of a vortex sheet on a sphere with pole vortices. (22 November 2003);

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We cons i der the motion of a vortex sheet on the surface of a unit sphere in the presence of point vortices xed on north and south poles.Analytic and numerical research revealed that a vortex sheet in two-dimensional space has the following three properties.First,the vortex sheet is linearly unstable due to Kelvin-Helmholtz instability.Second,the curvature of the vortex sheet diverges in nite time.Last,the vortex sheet evolves into a rolling-up doubly branched spiral,when the equation of motion is regularized by the vortex method.The purpose of this article is to investigate how the curvature of the sphere and the presence of the pole vortices a

Item Type:Preprint
Subjects:76-xx FLUID MECHANICS
ID Code:19