Vortex formation length in the two-dimensional wake of a circular cylinder

Vortex formation length (VFL) has been used over the past 75 years as a characteristic length scale for defining the spatial extent of initial wake development behind a bluff body. Early considerations of VFL were informed by estimates of the vorticity field, but in practice the historical definitions are based on features of the time-averaged velocity or pressure fields, with each giving a single characteristic length at a fixed value of Reynolds number. We investigate the use of Proper Orthogonal Decomposition (POD) to extract information about vortex formation from the time-dependent flow, with a focus here on low Reynolds numbers (50<Re<200) so that the flow can be reasonably modeled as 2D. We compare results based on the velocity and pressure fields with those from the vorticity field as quantified by the lambda-2 criterion. We use the leading modes from the POD analysis to define upper and lower bounds on the VFL as a function of Reynolds number. Identifying a range, rather than a single value, for the VFL at a particular value of Reynolds number is consistent, both physically and quantitatively, with the hysteresis observed in the critical spacing of two in-line tandem cylinders.