Symmetry breaking of two-dimensional time-periodic wakes
H. M. BLACKBURN a1, F. MARQUES a2andJ. M. LOPEZ a3 a1 CSIRO Manufacturing and Infrastructure Technology, PO Box 56, Highett, Vic. 3190, Australia a2 Departament de Física Aplicada, Universitat Politècnica de Catalunya, 08034, Barcelona, Spain a3 Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287, USA
A number of two-dimensional time-periodic flows, for example the Kármán street wake of a symmetrical bluff body such as a circular cylinder, possess a spatio-temporal symmetry: a combination of evolution by half a period in time and a spatial reflection leaves the flow invariant. Floquet analyses for the stability of these flows to three-dimensional perturbations have in the past been based on the Poincaré map, without attempting to exploit the spatio-temporal symmetry. Here, Floquet analysis based on the half-period-flip map provides a comprehensive interpretation of the symmetry-breaking bifurcations.