A New Approach for the Bifurcation Analysis of the Oscillating Cylinder Wake

Abstract

For the wake of an oscillating cylinder, distinct vortex patterns have been observed. It has been conjectured that the transitions between these patterns are representative of dynamical bifurcations. By focusing on the Poincar e plot of these periodic wakes, model reductive methods for stability analysis make it possible to rigorously characterize bifurcations of the unsteady dynamics. In particular, for the driven cylinder at Re = 100, two bifurcations are observed as amplitude is modulated. (1) The symmetry-breaking transition (2S - P +S wake transitions) is found to be representative of a supercritical pitchfork bifurcation, and (2), the loss of organized periodicity in the wake (2S - disordered wake transition)is marked by a torus bifurcation, which introduces quasiperiodicity. The relative success of this analysis suggests that this approach can be used for further bifurcation analysis of wake vortex patterns.