Adnan Balci

This numerical study explains the eddy formation and disappearance in a slow steady axisymmetric air–water flow in a vertical truncated conical container, driven by the rotating top disk. Numerous topological metamorphoses occur as the water height, H _w , and the bottom-sidewall angle, α , vary. It is found that the sidewall convergence (divergence) from the top to the bottom stimulates (suppresses) the development of vortex breakdown (VB) in both water and air. At α = 60°, the flow topology changes eighteen times as H _w varies. The changes are due to (a) competing effects of AMF (the air meridional flow) and swirl, which drive meridional motions of opposite directions in water, and (b) feedback of water flow on AMF. For small H _w , the AMF effect dominates. As H _w increases, the swirl effect dominates and causes VB. The water flow feedback produces and modifies air eddies. The results are of fundamental interest and can be relevant for aerial bioreactors.

A vortex close to a no-slip wall gives rise to the creation of new vorticity at the wall. This vorticity may organize itself into vortices that erupt from the separated boundary layer. We study how the eruption process in terms of the streamline topology is initiated and varies in dependence of the Reynolds number Re. We show that vortex structures are created in the boundary layer for Re around 600, but that these disappear again without eruption unless Re > 1000. The eruption process is topologically unaltered for Re up to 5000. Using bifurcation theory, we obtain a topological phase space for the eruption process, which can account for all observed changes in the Reynolds number range we consider. The bifurcation diagram complements previously analyzes such that the classification of topological bifurcations of flows close to no-slip walls with up to three parameters is now complete.