The wake of a transversely oscillating circular cylinder in a flowing soap film at low Reynolds number

Abstract

An inclined gravity-driven soap film channel was used to study the wake patterns formed behind a transversely oscillating cylinder at $Re=235\pm 14$. The natural frequency of vortex shedding from a stationary cylinder, $f_{\text{St}}$, was used to identify the oscillation frequencies of interest. The (dimensionless) frequency, $f^{\ast }=f/f_{\text{St}}$, and amplitude, $A^{\ast }=A/D$, of the cylinder's motion was varied over a large portion of the fundamental synchronization region (i.e., for $f^{\ast }\approx 1$), and a `map' of wake patterns was constructed in $(f^{\ast },A^{\ast })$ space. Lock-on between the frequency of the cylinder's motion and the dominant frequency of the resulting vortex wake was observed for a large range of this parameter space, predominantly manifested as synchronized `2S' and `2P' wake modes. Synchronized `P+S', `2T', and `transitional' wakes were also found in smaller regions of parameter space. Unsynchronized `coalescing' and `perturbed von~\karman' wakes were observed as the oscillation frequency became sufficiently different from $f_{\text_{St}}$. The wake patterns and vortex formation processes found in this study, particularly for the 2P mode wakes, are more similar to those observed by \cite{Williamson1988} in three-dimensional experiments than those found by \cite{Leontini2006} in two-dimensional simulations, despite the physical constraint from the soap film that prevents three-dimensional effects in the wake.

Updated with revised version after peer review. 'Accepted Manuscript'