Abstract

For the axi-symmetric incompressible Euler equations, we prove linear in time filamentation near Hill’s vortex: there exists an arbitrary small outward perturbation growing linearly for all times. This is based on combining the recent nonlinear orbital stability obtained by the first author with a dynamical bootstrapping scheme for particle trajectories. These results rigorously confirm numerical simulations by Pozrikidis in 1986.

中文翻译：

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希尔涡旋附近的细丝化

摘要

对于轴对称不可压缩欧拉方程，我们证明了希尔涡附近的线性时间细丝化：存在一个任意小的向外扰动，在所有时间都线性增长。这是基于将第一作者最近获得的非线性轨道稳定性与粒子轨迹的动态自举方案相结合。这些结果严格证实了 Pozrikidis 在 1986 年所做的数值模拟。