A concurrent computational and experimental study will be conducted which focuses on explaining the physics of vortex breakdown through observing the kinematics of vortex lines of the flow, as well as their topology in bundles which constitute the vortex core. To establish the importance of vortex tilting and stretching in vortex breakdown, axisymmetric swirling flows as well as those with elliptic cross sections will be studied. To support the theory a novel experimental device is proposed which consists of a large Plexiglass sphere containing a smaller sphere and oil filling the large gap. The inner sphere is suspended and spun magnetically. The device allows for nonaxisymmetric spinning of the inner sphere and is fully nonintrusive: neither the hardware nor the visualization method (based on laser velocimetry) intrude into the flow. Vortex breakdown has proven to be a problem of fundamental interest with applications to areas as diverse as air-traffic safety, flame holding in swirl combustors as well as supersonic combustors, and laminar-flo w control. A vast body of literature has been devoted to the study of this phenomenon; however there is still no consensus as to its underlying physics.