Vortex Synchronization Regions in Shedding From an Oscillating Cylinder

A classification of the vortex patterns in the wake of a normally oscillating cylinder was given by Williamson and Roshko who also studied when the various vortex patterns would occur. Using a symbolic code of letters and numbers that describes the combination of pairs and single vortices shed during each cycle of the forced oscillation of the cylinder, they gave a "map" of vortex-synchronization regions with the wavelength and amplitude of the oscillation as coordinates. In this study, we provide a theoretical basis for the experimental Williamson-Roshko map of vortex synchronization. We show that the region boundaries consist of two families of curves given by specific relations between the values of two nondimensional parameters defining the map. We construct a synthetic map that compares favorably with the experimental data. (C) 2005 American Institute of Physics.