As one fundamental flow structure, the vortex ring behind an impulsively starting disc can vividly characterize the vortex structure around the flapping flight and the drag-based paddling propulsions. In this paper, an elaborate experiment is performed to investigate the formation of the vortex rings (termed as DVR) by using digital particle image velocimetry (DPIV), as well as by investigating the ridges of finite-time Lyapunov exponent (FTLE) and the elliptic Lagrangian coherent structures (LCSs). Experimental results demonstrate that the circulation growth of DVRs satisfies the Logistic law and can be well predicted by a scaling model based on the shear-layer feeding velocity. Applying the criterion originated from the Kelvin-Benjamin variational principle, the formation number of DVRs when DVRs pinch off is found to stay within the range of $F^{\ast }=3.35~4.1$. Then, the pinch-off process of the DVRs is re-examined based on a Lagrangian analysis, and the dynamic signals are detected to coincide with the onset of DVRs pinch-off. Once DVRs pinch off, a trailing pressure maximum appears in the edge of disc and a closed boundary forms to define the region of DVRs based on the FTLE ridges, fluid detrainment by the dynamic lobes is observed, and a saturation phase of the circulation evolution is clearly observed in terms of the elliptic LCSs. Furthermore, the scaling laws, i.e., circulation growth and formation number, of DVR formation suggest a confined formation mode to understand the formation of wake vortices behind a moving body for reference.

作为一种基本的流动结构，脉冲启动盘后面的涡环可以生动地表征扑翼飞行和基于阻力的桨式推进周围的涡流结构。在本文中，通过使用数字粒子图像测速仪 (DPIV) 以及通过研究有限时间李雅普诺夫指数 (FTLE) 的脊和椭圆拉格朗日相干结构 (LCS)。实验结果表明，DVR 的循环增长满足 Logistic 定律，并且可以通过基于剪切层进料速度的缩放模型很好地预测。应用源自 Kelvin-Benjamin 变分原理的判据，发现 DVR 夹断时 DVR 的形成数保持在$F^{＊}=3.35~4.1$. 然后，基于拉格朗日分析重新检查 DVR 的夹断过程，并检测到与 DVR 夹断的开始一致的动态信号。一旦 DVRs 夹断，在盘边缘出现最大尾压，并形成闭合边界以定义基于 FTLE 脊的 DVRs 区域，观察到动态瓣的流体排阻，并且循环演化的饱和阶段是在椭圆 LCS 方面可以清楚地观察到。此外，DVR编队的尺度规律，即环流增长和编队数量，提出了一种限制编队模式，以了解运动物体后面尾涡的形成，以供参考。