Kinematics and Dynamics of Sphere Wake Transition

The wake of a sphere undergoes a number of symmetry-breaking transitions as it changes from laminar to turbulent. This paper concentrates on the "rst two transitions. At Re"212 a regular transition occurs, when the wake develops a spectacular two-tailed structure consisting of two trailing streamwise vortices. During the second transition at Re"272 the #ow undergoes a Hopf bifurcation. In this case there is a complex interaction between the trailing vortices leading to the periodic shedding of vortex loops. Both these transitions are shown to be supercritical (or nonhysteretic). Landau models are constructed for both transitions and the coe$cients determined. The visual impression of an apparently sudden bifurcation to the two-tailed wake is shown to be due to the focal nature of the trailing vortices, which draws dye into the cores, even if their net circulation is small. A precursor to the second transition to the periodic wake is strong kinking of the trailing vortices about 1 diameter downstream from the back of the sphere. The vorticity structure of the two-tailed wake prior to transition is also quanti"ed which may prove useful for development of models of the transition process. ( 2001 Academic Press