A quick study looking at the Strouhal number for a medium-length cylinder – above is an animation of Q isosurfaces, coloured by vertical velocity. I ran some 2d preliminary models, followed by a 3d model with a structured mesh that I then refined. The Reynolds number was 51,355, which according to data from Achenbach (1968) is in a transitional range for the coefficient of drag:
My results gave = 0.73, which is higher than for a long cylinder the above chart indicates – likely due to the three-dimensionality of the flow around the ends.
A plot of vs time clearly shows the oscillations of the Karman vortex sheet, at a frequency of about 37 Hz. This gives a Strouhal number of about 0.12, which is not far off experimental values of 0.18-0.50.
Also visible in the plot is that after about 0.4s, the oscillations become unstable and appear to ‘beat’. The RMS value does remain pretty constant at around 0.4, but I’m curious whether this is due to end effects or maybe just the integration schemes used!