This paper reports computational simulations of the Navier–Stokes equations for confined axisymmetric rotating flows induced by rotating the endwalls instantaneously at a different rate to the sidewall. The transient behavior of the recirculation zones in the meridional plane is investigated during the temporal evolution. The changes in the topological structure of the meridional-plane streamline pattern are significant and the temporal evolution from one pattern to another reveals similarities between spin-up and spin-down at the early stages but subsequently differs. As the onset bubble for the first recirculating period always sets out from a certain axial station, a recirculation factor, Rf, is suggested to predict the onset time and location for the first period of recirculation. Accordingly, a stagnation point is observed numerically from a central axial station for low Reynolds numbers around 70–80. The effect of changing the rotation of the sidewall is also discussed, but no substantial influence is observed on the characteristics of the recirculation zones if there is no appearance of the Taylor–Görtler vortices in the sidewall boundary layer.