论文标题
一对同轴圆形涡流丝的正面碰撞
Head-On Collision of a Pair of Coaxial Circular Vortex Filament
论文作者
论文摘要
我们考虑两个同轴涡流环的正面碰撞，描述为在局部感应近似下的两个圆形涡流丝的运动。我们证明了在碰撞的作者提出的非线性偏微分方程系统中存在解决方案。我们还为直面碰撞的细丝的初始配置和参数提供了必要的条件。我们的结果表明，存在一个临界值$γ_{\ ast}> 1 $，比率为循环的绝对价值的比例$γ$，因此，当$γ\ in [1，γ_ {\ ast}] $中时，两个接近的环将collide collide collide collide collide，以及$γ\ in $γ\ in $ cirt counters croirter croirters courters crimption crighters crighters crighters crighters crighters crighters crighters crighters，另一个，然后无限期地分开。
We consider the head-on collision of two coaxial vortex rings described as the motion of two circular vortex filaments under the localized induction approximation. We prove the existence of solutions to a system of nonlinear partial differential equations proposed by the author which exhibit head--on collision. We also give a necessary and sufficient condition for the initial configuration and parameters of the filaments for head-on collision to occur. Our results suggest that there exists a critical value $ γ_{\ast}>1 $ for the ratio $ γ$ of the absolute value of the circulations such that when $ γ\in [1,γ_{\ast}]$, two approaching rings will collide, and when $ γ\in (γ_{\ast},\infty) $, the ring with the larger circulation passes through the other and then separate indefinitely.
