The mean flow speed dependence on vortex streets on flowing soap films

It is implied that a stable vortex street shall have its aspect ratio (ratio between the transverse to longitudinal spacing between vortices) close to 0.28, predicted by Th. von Karman by using the point vortex mdoel. In the point vortex model, it is assumed that the fluid is inviscid and incompressible, however, such an ideal fluid is scarse in reality. In experimental studies using flowing soap film, we constantly observe vortex streets with aspect ratio greater than 0.28, and we found that if it increases as the mean flow speed of the channel decreases. We suspect this effect is due to the retardation effect, based on facts that the vorticity field and the thickness field is strongly correlated in flowing soap film channel and that the thickness variation propagates at the elastic wave speed. We present our experimental result covering the Mach-like number, Ma, from 0.2 to 0.8 and compare data with crudely modeled theoretical curve that the ratio scales with 1/(1+Ma). The theory is roughly consistent with the experiments.