论文标题
Kirchhoff的椭圆形涡旋的线性和非线性不稳定性
Linear and non-linear instabilities of Kirchhoff's Elliptical Vortices
论文作者
论文摘要
我们研究了二维不可压缩的欧拉流体中均匀的椭圆形涡旋的稳定性。事实证明，对于小偏心率，涡流放松到核心挂结构，该结构与中央核心保持椭圆形的刚性旋转。对于较大的偏心率，涡流分成两个准圆形涡流，它们围绕质量中心旋转。独立于纵横比，稳态显示低密度光环。我们提出了一个理论，该理论从定性地解释了两个国家之间的过渡。将所有理论结果与基于涡旋中的涡旋算法的广泛分子动力学模拟进行比较。
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.
