F211 一定渦度をもつ中心渦領域とその周りの渦領域の平衡形

概要

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It is widely known that the system composed of a central point vortex and ambient point vortices of equal strength located on a circle around this vortex with an equal spacing rotates around the central vortex at a constant angular velocity with keeping the configuration. In this paper, we examine similar steady configurations of vortex regions of finite size and of uniform vorticity. The shapes of a central vortex region and a few ambient vortex regions constituting this steady configuration are numerically calculated. When all of these vortex regions are sufficiently far from other vortex regions, their shapes are nearly circular. Moreover, even if the distances between these vortices are small, the central vortex has a nearly circular shape when the number N of ambient vortices is large enough However, if N is small and the central vortex is large enough, the shape of this vortex is associated with the highest curvature at the points closest to the ambient vortices. Finally, we compare the angular velocity Ω of the rotation of the steady configuration with the angular velocity Ω_p of the corresponding system composed of point vortices. We find that Ω is close to Ω_p when the area of vortex region is small enough, and that Ω is always larger than Ω_p.
日本流体力学会の論文
2002-07-23