Unsteady dynamics in the streamwise-oscillating cylinder wake for forcing frequencies below lock-on

Abstract

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 ∼0.04–0.2 and mean Reynolds number, Re₀ = 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.

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