Structure-based interpretation of the Strouhal-Reynolds number relationship

The wake in the flow past a circular cylinder has posed a long-standing challenge to scientists since the late 19th century. Many aspects of this seemingly simple phenomenon remain unexplained. Of particular interest is the relationship between the dimensionless vortex shedding frequency (the Strouhal number St) and the ratio of inertial to viscous forces in the fluid (the Reynolds number Re). We propose a new St-Re relation based on the observations of the structure of a vortex street in flowing soap films. The measurements suggest a simple two-parameter form St=1/(A+B/Re) that describes laminar vortex shedding remarkably well for bulk fluids as well as for two-dimensional flowing soap films.