Similarity Solution of Two-Dimensional Point Vortices
Similarity Solution of Two-Dimensional Point Vortices
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二维点涡的相似解
DOI：
10.1143/jpsj.56.2024
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发表时间：
1987
影响因子：
1.7
通讯作者：
Y. Kimura
中科院分区：
文献类型：
--
作者：
Y. Kimura
本文提出了无界区域内二维点涡的相似解理论。为了得到解，假设所有涡位置的解的时间依赖性是相同的。结果表明，系统根据涡的初始位置，要么刚性旋转，要么崩溃。然后对三涡系进行了数值计算。结果表明，刚性转动对应于正三角形解或直线解，且无论三个涡的强度如何，正三角形解总是存在的，而直线解是通过求解某个三次方程得到的。
Theory of the similarity solution of two-dimensional point vortices in an unbounded region is presented. To get the solution, the time dependence of the solution for all vortex positions are assumed to be the same. It is shown that the system either rotates rigidly or collapses according to the initial position of vortices. Then numerical calculations are made especially for the system of three vortices. It is found that the rigid rotation corresponds to the regular triangle solution or the straight line solution, and that irrespective of the strengths of three vortices, the regular triangle solution always exists while the straight line solution is obtained by solving a certain cubic equation.