Generation of ring vortices in axisymmetric spin‐down: A numerical investigation

In this paper the sequence of finite‐amplitude events that occurs prior to the onset of Taylor–Görtler (TG) vortices in axisymmetric spin‐down to rest is described. It is conjectured that the TG vortices are induced by these events, which include internal waves that propagate along the axis of rotation and transient vortex breakdown. The cascade of events is led by an internal ‘‘solitary wave’’ from each end wall. These waves are induced by the end‐wall (Bödewadt) boundary layers with concomitant Ekman ‘‘blowing.’’ The passage of the solitary wave causes a transient vortex breakdown followed by a train of internal waves. The combined effect of these phenomena induces disturbances in the sidewall boundary layer that grow and lead to the formation of TG vortices. The TG vortices that originate adjacent to the midplane of the cylinder in the sidewall (Rayleigh) boundary layer dominate the flow field at an intermediate time interval following the onset of spin‐down. Favorable comparisons with computationally determined onset times and subsequent evolution of TG vortices reported in the literature support the prediction that naturally occurring finite‐amplitude phenomena induce these vortices.