The three-dimensional structure of confined swirling flows with vortex breakdown

Abstract

In a recent experimental study, Spohn, Mory & Hopfinger (1998) investigated in detail the flow in a closed cylindrical container with a rotating bottom for Reynolds numbers in the steady and unsteady regimes. Their visualization photographs revealed that the stationary vortex breakdown bubbles, which form along the container axis within a range of governing parameters, are open, with inflow and outflow, and asymmetric at their downstream end. For Reynolds numbers within the unsteady regime, visualizations of the limiting streamlines on the cylindrical wall showed that the Stewartson layer separates asymmetrically along stationary spiral convergence lines that form below the top cover. We study numerically the container flow, by solving the unsteady, three-dimensional Navier–Stokes equations, in order to clarify the origin and elucidate the underlying physics of these complex, three-dimensional flow features. The stationary vortex breakdown bubbles we simulate exhibit all the asymmetries observed in the laboratory. By analysing the Lagrangian characteristics of the calculated flow fields, we explain the origin of these asymmetries, clarify the experimentally documented filling and emptying mechanisms, and show that the flow in the interior of stationary vortex breakdown bubbles exhibits chaotic particle paths. We also show that the spiral separation lines observed by Spohn et al. (1998) inside the Stewartson layer at high Reynolds numbers are due to the growth of pairs of counter-rotating, spiral vortices and the interaction of these vortices with the stationary-cover boundary layer.