We investigate the stability of a uniform elliptical vortex in a two-dimensional incompressible Euler fluid. It's demonstrated that for small eccentricities, the vortex relaxes to a core-halo structure that undergoes rigid rotation with the central core remaining elliptical. For large eccentricities, the vortex splits into two quasi-circular vortices that revolve around the center of mass. Independent of the aspect ratio, the steady-state displays a low-density halo. We present a theory that qualitatively explains the transition between the two states. All theoretical results are compared with extensive molecular dynamics simulations based on the vortex-in-cell algorithm.

中文翻译：

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基尔霍夫椭圆涡的线性和非线性不稳定性

我们研究了二维不可压缩欧拉流体中均匀椭圆涡旋的稳定性。已经证明，对于小偏心率，涡旋松弛为核心晕结构，该结构经历刚性旋转，中央核心保持椭圆形。对于大的离心率，涡流分裂成两个围绕质心旋转的准圆形涡流。与纵横比无关，稳态显示低密度光晕。我们提出了一个定性解释两种状态之间转换的理论。所有理论结果都与基于 vortex-in-cell 算法的广泛分子动力学模拟进行了比较。