The flow around a cylinder oscillating in the streamwise direction with a frequency, $f_f$, much lower than the shedding frequency, $f_s$, has been relatively less studied than the case when these frequencies have the same order of magnitude or the transverse oscillation configuration. In this study, particle image velocimetry and the dynamic mode decomposition (DMD) are used to investigate the streamwise-oscillating cylinder wake for forcing frequencies $f_f/f_s\sim 0.04$–0.2 and mean Reynolds number, ${\mathrm{Re}}_0=900$. The amplitude of oscillation is such that the instantaneous Reynolds number remains above the critical value for vortex shedding at all times. Characterization of the wake reveals a range of phenomena associated with the interaction of the two frequencies, including modulation of both the amplitude and frequency of the wake structure by the forcing. DMD reveals a frequency spreading of dynamic modes. A scaling parameter and associated transformation are developed to relate the unsteady, or forced, dynamics of a system to that of an unforced system. For the streamwise-oscillating cylinder, it is shown that this transformation leads to a dynamic mode decomposition similar to that of the unforced system.

中文翻译：

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流向振荡圆柱尾流中的非定常动力学迫使频率低于锁定

圆柱体周围的流动以一定频率沿流向振荡， $F_F$，远低于脱落频率， $F_{秒}$, 与这些频率具有相同数量级或横向振荡配置的情况相比，研究相对较少。在这项研究中，粒子图像测速法和动态模式分解 (DMD) 用于研究流向振荡的圆柱尾流的强迫频率$F_F/F_{秒}～0.04$–0.2 和平均雷诺数， ${\mathrm{关于}}_0=900$. 振荡的幅度使得瞬时雷诺数始终保持在涡旋脱落的临界值之上。尾迹的表征揭示了与两个频率相互作用相关的一系列现象，包括强迫对尾迹结构的幅度和频率的调制。DMD 揭示了动态模式的频率扩展。缩放参数和相关变换被开发以将系统的非稳态或受迫动力学与非受迫系统的动力学联系起来。对于流向振荡圆柱体，表明这种转换导致类似于非受力系统的动态模式分解。