Two-dimensional Floquet stability analysis of the flow produced by an oscillating circular cylinder in quiescent fluid

We study the two-dimensional symmetry breaking transitions in the time-periodic flow generated in quiescent fluid by a rigid cylinder with simple harmonic rectilinear translation in a direction normal to its axis. The base flow possesses two symmetries: a spatio-temporal symmetry and a spatial reflection symmetry about the axis of oscillation. Two distinct regimes of marginal stability are identified through two-dimensional Floquet analysis. These correspond to (I) a pair of real Floquet multipliers simultaneously crossing the unit circle at mu = +1 and (II) a pair of complex-conjugate multipliers crossing the unit circle, mu = e(+/-itheta) (a Neimark-Sacker bifurcation). In both transitions the spatial reflection symmetry of the base flow is broken, but for type I transitions, the spatio-temporal symmetry of the base flow is retained. (C) 2003 Elsevier SAS. All rights reserved.