论文标题
在山上的流体和等离子体的球形涡旋上，其概括和稳定性
On the Hill's Spherical Vortex in Fluid and Plasma, its Generalization, and Stability
论文作者
论文摘要
1894年M.J.M.希尔（Hill）发表了一篇文章，描述了一个球形涡流中的固定液体。使用圆柱坐标并假设方位角速度分量为零，Hill找到了一个简单的解决方案，描述了这种流动。 A. A. Bobnev于1987年提出了类似的现代问题，并于1987年由R. Kaiser和D. Lortz于1995年提出，他们应用了该设置来对球照明进行建模。我们使用Bragg-Hawthorne方程式对Hill的球形涡流提出了更简单的推导。特别是，通过使用移动的参考框架，Euler方程将平衡流量减少到等同于静态平衡MHD方程的平衡流量。得出了带有非零方位角组件的Hill球形涡流的新广义版。通过查看球形坐标中的毕业生 - shafranov方程的分离解决方案来计算静态平衡MHD方程的物理解决方案。最后，通过执行描述的轴对称扰动来检查Hill球形涡流的稳定性。结果表明，相对于某些类型的小扰动，山的球形涡流是线性不稳定的。
In 1894 M.J.M. Hill published an article describing a spherical vortex moving through a stationary fluid. Using cylindrical coordinates and assuming the azimuthal velocity component zero, Hill found a simple solution that described this flow. A similar modern problem in the MHD framework was put forth in 1987 by A. A. Bobnev and in 1995 by R. Kaiser and D. Lortz who applied the setup to model a ball lighting. We present a much simpler derivation of Hill's spherical vortex using the Bragg-Hawthorne equation. In particular, by using the moving frame of reference, the Euler equations reduce to equilibrium flow which are equivalent to the static equilibrium MHD equations up to relabelling. A new generalized version of Hill's spherical vortex with a nonzero azimuthal component is derived. A physical solution to the static equilibrium MHD equations is computed by looking at a separated solution to the Grad-Shafranov equation in spherical coordinates. Finally, the stability of Hill's spherical vortex is examined by performing an axisymmetric perturbation described; it is shown that the Hill's spherical vortex is linearly unstable with respect to certain kinds of small perturbations.
