Wall-separation and vortex-breakdown zones in a solid-body rotation flow in a rotating pipe

The axisymmetric dynamics of perturbations on a solid-body rotation flow with a uniform axial velocity in a rotating, finite-length circular pipe is studied via global analysis methods and numerical simulations. We first describe the bifurcation diagram of steady-state solutions of the flow problem as a function of the swirl ratio $\omega$. We prove that the base columnar flow is a unique steady-state solution when $\omega$ is below a critical level, $\omega_1$. This state is asymptotically stable and a global attractor of the flow dynamics. However, when $\omega>\omega_1$, we reveal, in addition to the base columnar flow, the co-existence of states that describe swirling flows around either centerline stagnant breakdown zones or wall pseudo-stagnant zones. The base columnar flow is a min-max point of the energy functional that governs the problem while the swirling flows with wall-separation and breakdown zones are global and local minimizer states and attractors of the flow dynamics. We also find additional min-max states that are transient attractors of the flow dynamics. The wall-separation states have same chance to appear as that of the breakdown states and there is no hysteresis loop between these states.