高阶球形涡的一般性质及三阶球形涡的混沌现象<sup>*</sup>

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高阶球形涡的一般性质及三阶球形涡的混沌现象^*

基金项目: *国家基础研究项目《非线性科学》基金

摘要: 讨论了n阶球形涡的一般性质,找到了一族分布在同心球面上的周期轨道的代数表达式,讨论了不动点的分布和流动的对称性.对叠加的三阶球形涡进行了数值计算,结果表明：在Poincaré截面上,伴随着岛形规则区,出现了不同程度的浑沌(Lagrange湍流)区,观察到了并分析了规则区和浑沌区随特征参数的变化而出现的一些有趣的现象.
- Beltrami流动 /
- 球形涡 /
- 一般性质 /
- Poincaré截面 /
- 混沌轨道 /
- 规则岛数值计算
Abstract: The general properties of the spherical vortices(SV)of n-th order are discussedin this paper Numerical calculations are carried out in the case of n=3.We find outsome interesting phenomena concerning the chaotic regions and ordered islands on the Poincaré sections.Interpretations of these phenomena are also given.
- Beltrami flow /
- spherical vortex /
- general properties /
- Poincaré section /
- chaotic trajectory /
- ordered island

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