Unsteady swirling flow in an enclosed cylinder with reflectional symmetry

A numerical investigation of the multiple stable solutions found in confined swirling flows is presented. The flows consist of fluid in a completely filled cylinder driven by the constant corotation of the two end walls. When reflectional symmetry at the cylinder half-plane is imposed, the flow corresponds to that in a cylinder of half the height driven by the bottom end wall, with the top surface being flat and stress-free. Comparisons with available experiments in this case are made and the observed toroidal recirculation zones attached to the free surface are described in terms of secondary motions induced by the bending of vortex lines. Calculations are also presented where the reflectional symmetry is not imposed and the possibility of the flow breaking this symmetry is discussed.