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 first two transitions. At Re = 212 a regular transition occurs, when the wake de velops a spectacular two-tailed structure consisting of two trailing stream wise vortices. During the second transition at Re = 272 the flow 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 t hese transitions are shown to be supercritical (or nonhysteretic). Landau m odels are constructed for both transitions and the coefficients determined. The visual impression of an apparently sudden bifurcation to the two-taile d wake is shown to be due to the focal nature of the trailing vortices, whi ch draws dye into the cores, even if their net circulation is small. 14 pre cursor to the second transition to the periodic wake is strong kinking of t he trailing vortices about 1 diameter downstream from the back of the spher e. The vorticity structure of the two-tailed wake prior to transition is al so quantified which may prove useful for development of models of the trans ition process. (C) 2001 Academic Press.