The applications of freely falling bodies in steady water or air have been widely observed in nature, from the dispersing of a tree seed to the re-entry of a space shuttle. Disparate objects exhibit particular falling styles which have been studied for a long time. However, the mechanism behind this extensive phenomenon has not been clearly understood. In this paper, we investigate experimentally the dynamics of an annular disk falling freely in water in steady state. Three distinct falling motions namely, lengthways vibration motion (LV), hula-hoop motion (HH) and helical motion (HM), are examined, and Proper Orthogonal Decomposition (POD) is used to extract the coherent structures behind the falling disks. The forces and torques governing the falling motion of annular disks are determined by analyzing the recorded kinematics. The results show a rapid eigenvalue convergence where the first three modes account for the highest percentage of the total energy. Depending on the falling motions, the corresponding POD modes show different characteristics. The second and third POD mode identify the perturbations in the region downstream of the disks. The shedding pattern featured by the periodic vortex loops is extracted for the LV motion and the forces frequency generated by the vortex loops is analyzed. By comparing the flow fields in different POD modes of HH and HM motions, it is clear that the vortices break down into smaller structures due to the violent twists at the turning point of the trajectory in HH motion, while the vorticity field of HM motion shows a relatively stronger continuity in the first three POD modes. It is found that the vortical torques, i.e. the hydrodynamic torque due to wake vortices, acting on the disks of HH motion have sharp peaks compared to HM motion. This work illuminates the reason for the disparity between HH and HM motion by decomposing the flow field into distinct POD modes.

从分散树木种子到重新进入航天飞机，自然界已经广泛观察到自由落体在稳定水或空气中的应用。不同的物体表现出特殊的下落样式，这已经被研究了很长时间。但是，尚未广泛了解这种广泛现象背后的机制。在本文中，我们通过实验研究了环形盘在稳态下自由下落的动力学。考察了三种不同的下降运动，即纵向振动运动（LV），呼啦圈运动（HH）和螺旋运动（HM），并使用适当的正交分解（POD）提取了下降盘后面的相干结构。通过分析记录的运动学来确定控制环形盘下落运动的力和转矩。结果表明，特征值快速收敛，其中前三种模式占总能量的最高百分比。根据下降运动，相应的POD模式显示不同的特性。第二和第三POD模式标识磁盘下游区域中的扰动。为LV运动提取周期性涡旋循环的脱落模式，并对涡旋循环产生的力频率进行分析。通过比较HH和HM运动在不同POD模式下的流场，很明显，由于HH运动的轨迹转折点处的剧烈扭曲，涡流分解成较小的结构，而HM运动的涡流场显示前三个POD模式具有相对较强的连续性。发现旋涡转矩，即 与HM运动相比，作用在HH运动圆盘上的由尾流涡流引起的流体动力转矩具有尖锐的峰值。这项工作通过将流场分解为不同的POD模式，阐明了HH和HM运动之间存在差异的原因。