On the controversy regarding the effect of flow shear on the Strouhal number of cylinder vortex shedding

High lift devices generate asymmetric wakes that impact the aerodynamic and aeroacoustic performance of airplanes. Asymmetric wakes are also produced by a shear flow around a cylinder if the shear direction is perpendicular to the cylinder axis. Most of the work devoted to asymmetric wakes focuses on the latter scenario. In the literature there is no consensus about whether the shear reduces or increases the Strouhal number of the vortex shedding. The current work is concerned with this apparent controversy. The work presents a linear stability analysis of the asymmetric wake profiles, which shows that the dominant Strouhal number decreases with the asymmetry. The results are validated by direct numerical simulations. The literature shows that the shear affects the cylinder drag. These results are normalized by cylinder diameter and free-stream velocity, whereas it is recognized that wake scalings are more appropriate to describe the flow. Such a wake scaling is not available in the literature data; the drag is used here to re-scale the experimental data proportionally to the wake width, collapsing virtually all the data available. The re-scaled data shows that the shear decreases the dominant Strouhal number in qualitative agreement with the analysis.