论文标题
涡流运动
Spirographic motion in a vortex
论文作者
论文摘要
涡流流中粒子运动的研究主要集中在惯性或自属性的点状颗粒上。该近似值假设围绕粒子的速度场是线性的。我们认为在二维稳定涡旋中的惯性刚性哑铃。尽管该系统在分析上仍然可以处理，但粒子会经历周围速度场的非线性。通过利用流动的旋转对称性，我们将问题减少到二维动力学系统的问题，该系统的固定点和周期轨道可用于解释哑铃的运动。对于所有随着径向距离降低的流体角速度降低的涡旋，哑铃的质量中心遵循涡流中心周围的弹性轨迹。这是由于径向方向的周期性振荡以及中心周围的革命而产生的。轨迹的形状在很大程度上取决于哑铃的初始位置和方向，但是在质量上，无论涡流的形式如何，动力学在质量上都是相同的。如果流体角速度不是单调的，则振动图运动会因运输壁垒的存在而改变，其形状现在对涡流的细节敏感。
Studies of particle motion in vortical flows have mainly focused on point-like particles, either inertial or self-propelled. This approximation assumes that the velocity field that surrounds the particle is linear. We consider an inertialess rigid dumbbell in a two-dimensional steady vortex. While the system remains analytically tractable, the particle experiences the nonlinearity of the surrounding velocity field. By exploiting the rotational symmetry of the flow, we reduce the problem to that of a two-dimensional dynamical system, whose fixed points and periodic orbits can be used to explain the motion of the dumbbell. For all vortices in which the fluid angular velocity decreases with radial distance, the center of mass of the dumbbell follows a spirographic trajectory around the vortex center. This results from a periodic oscillation in the radial direction combined with revolution around the center. The shape of the trajectory depends strongly on the initial position and orientation of the dumbbell, but the dynamics is qualitatively the same irrespective of the form of the vortex. If the fluid angular velocity is not monotonic, the spirographic motion is altered by the existence of transport barriers, whose shape is now sensitive to the details of the vortex.
