From unsteady to quasi-steady dynamics in the streamwise-oscillating cylinder wake

TL;DR

This study investigates the wake dynamics of a streamwise-oscillating cylinder at low forcing frequencies using Particle Image Velocimetry and Koopman Mode Decomposition, revealing a transition from unsteady to quasi-steady behavior.

Contribution

It introduces a scaling transformation that relates forced wake dynamics to unforced ones, providing new insights into flow modulation and frequency spreading.

Findings

Flow modulation by forcing frequencies alters wake amplitude and frequency.

Koopman modes exhibit frequency spreading under forcing.

A transformation links forced and unforced wake dynamics.

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 Koopman Mode Decomposition 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, $Re_0 = 900$. 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. Koopman analysis reveals a frequency spreading of Koopman modes. A scaling parameter and associated transformation are developed to relate the unsteady, or forced, dynamics of a system to that of a quasi-steady, or unforced, system. For the streamwise-oscillating cylinder, it is shown that this transformation leads to a Koopman Mode Decomposition similar to that of the unforced system.