Singularity formation of vortex sheet on a sphere
Abstract:
The motion of a vortex sheet on a sphere is numerically investigated. Kaneda's equation which is the closed Lagrangian equation of three dimensional vortex sheet is used to obtain the governing equation of the vortex sheet. Vortex blob method with Krasny's Fourier filtering is applied to compute the equation. We study the singularity formation and long time evolution of the vortex sheet. Since the total vorticity on a sphere must vanishes because of Stokes' theorem, we assume that there is a vortex sheet with strength one on a sphere where minus one vorticity is distributed uniformly.
Discussion:
Singularity that the curvature of the sheet becomes infinity emerges in finite time.This is the same as the result of planar vortex sheet. After the formation of singularity the vortex sheet begins to roll-up and forms spirals. This is preliminary study to understand the singularity formation of vortex sheet which is not in a plane.
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