Motion of three vortices
Motion of three vortices
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DOI：
10.1063/1.862605
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发表时间：
1979-03
影响因子：
4.6
通讯作者：
H. Aref
中科院分区：
文献类型：
--
作者：
H. Aref
本文对任意强度的三点涡的运动作了定性分析。这简化和扩展了诺维科夫最近关于三个相同涡旋运动的工作。使用相图技术，运动的可能制度进行分类，根据三个涡强度的算术，几何和谐波平均值的符号。对于涡旋强度（κ1，κ2，κ3）取（+κ，+κ，−κ）的特殊情况，该图可以解释为中性对被单个涡旋散射。定量的细节是这种情况下。如果三个涡强度的调和平均值为零，则对于某些初始条件，三角形涡可以在有限时间内坍缩到一个点。
A qualitative analysis of the motion of three point vortices with arbitrary strengths is given. This simplifies and extends recent work by Novikov on the motion of three identical vortices. Using a phase diagram technique, the possible regimes of motion are classified according to the signs of the arithmetic, geometric, and harmonic means of the three vortex strengths. For the special case where the vortex strengths (κ1,κ2,κ3) take the values (+κ,+κ,−κ), the diagram has an interpretation in terms of the scattering of a neutral pair by a single vortex. Quantitative details are presented for this case. If the harmonic mean of the three vortex strengths is zero, the triangle of vortices can collapse to a point in a finite time for certain initial conditions.