| This work outlines a numerical investigation of the dynamics of a high Reynolds number axisymmetric vortex flow in a pipe with high levels of swirl. A global picture of bifurcations in the flow is revealed by mapping the branches of equilibrium fixed points, their stability behavior and possible transitions to vortex breakdown or other secondary branches. These branches characterize a domain of local attractiveness where the flow tends to align itself along a low dimensional subspace. In order to study the local stability characteristics of the branches, we developed numerical schemes for Linear Stability Analysis both through direct simulations and through System Identification. We further study the nonlinear dynamics of the flow along this attractive domain and model the transients with low order models. A central role in the investigation is played by low and least order, mean-field Galerkin models of the local dynamics near bifurcation branches. Indeed, as this is a first case study of mean field Galerkin models in a flow configuration with multiple coexisting attractors, the technical and conceptual aspects of these models and of their identification, are of independent interest. The unveiled picture is that of an inertial manifold that is well approximated with only few dominant coherent structures, or modes that are well characterized by temporal and spatial frequencies, and that continuously deform with changes in the operating conditions. |
