A partly open vertical disk-cylinder system, with an annular top lid, is used to model numerically the characteristics of axisymmetric swirling flows with stagnation and associated flows reversal; commonly referred to as vortex breakdown. The flows are driven by the bottom disk uniform rotation and controlled by the competition between the no-slip and stress-free surface conditions applied at the top. Depending on the radial extent of the free surface, distinct regions of toroidal, corner and on-axis vortex type flows were identified and mapped into a state diagram then discussed. In addition, the impact of the cavity aspect ratio on the onset conditions of stagnation and breakdown was highlighted. Moreover, the study explored the influence of a diffusion driven meridian circulation, induced by the sidewall differential rotation, which is revealed to constitute an effective non intrusive kinematic means of flow control.