A-235 一定渦度をもつ中心渦領域とその周りの渦領域からなる平衡形の安定性

概要

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It is widely known that the system composed of a central point vortex of circulation Г_0 and equally spaced N satellite point vortices of circulation Гlocated on a circle of radius γ around the central vortex rotates around the central vortex. In this paper, we calculate similar steady configurations of vortex regions of finite size and of uniform vorticity for N=5,and examine their stability under the assumption that the area of a central vortex of circulation Г_0 is the same as the area of one of satellite vortices of circulation Г. The circulation ratio Г^*_0=Г_0/Г is chosen within the range of -0.5 ≤ Г^*_0 ≤ 4,where the corresponding system composed of point vortices is stable. When the area S of each vortex is small enough, the shapes of all the vortices are nearly circular irrespective of the value of Г^*_0. However, if S is large enough, we often observe a large deformation of the vortex shape from a circle. We also find from the stability analysis that, for -0.5 ≤ Г^*_0 ≤ 4,the system always becomes unstable when S exceeds a threshold value S_u, and that the value of S_u is the largest when Г^*_0 is close to 0.
日本流体力学会の論文
2003-07-28