Instability of vortex pair leapfrogging
Instability of vortex pair leapfrogging
复制标题
涡对越级不稳定
DOI：
10.1063/1.4774333
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发表时间：
2013
影响因子：
4.6
通讯作者：
H. Aref
中科院分区：
文献类型：
--
作者：
L. Tophøj;H. Aref
跳跃是四涡问题的一种周期解，其中两个正、负点涡都是以同轴涡对的形式排列在同一绝对环流中。同轴运动的集合可以用比率0σ2来参数化，其中σ=2−1是银比率。自1877年格罗布利的论文和1894年洛夫的一篇著名论文以来，这项动议就已经充分分析了细节。作者声明：Echeson[Echeson][涡旋跳跃的不稳定性》，欧洲。J.Phys.[10.1088/0143-0807/21/3/310通过数值实验确定，对于σ2<；α<；0.382，跳跃是线性不稳定的，但对于较大的α，跳跃明显是稳定的。在这里，我们推导出控制跳跃运动的微小摄动的线性方程组。我们证明了对称破缺微扰本质上是由一个具有时间周期系数的二维线性系统控制的，并进行了Floquet分析。我们找到了凌日...
Leapfrogging is a periodic solution of the four-vortex problem with two positive and two negative point vortices all of the same absolute circulation arranged as co-axial vortex pairs. The set of co-axial motions can be parameterized by the ratio 0 σ2, where σ=2−1 is the silver ratio. The motion is known in full analytical detail since the 1877 thesis of Grobli and a well known 1894 paper by Love. Acheson [“Instability of vortex leapfrogging,” Eur. J. Phys. 21, 269–273 (2000)]10.1088/0143-0807/21/3/310 determined by numerical experiments that leapfrogging is linearly unstable for σ2 < α < 0.382, but apparently stable for larger α. Here we derive a linear system of equations governing small perturbations of the leapfrogging motion. We show that symmetry-breaking perturbations are essentially governed by a 2D linear system with time-periodic coefficients and perform a Floquet analysis. We find transi...