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This paper investigates numerically the bubble-type vortex breakdown apparition in the case of closed rotating flows of a viscous, axisymmetric, and incompressible fluid. First, a truncated conical/cylindrical cavity of spherical end disks is used to simulate and analyze the vortex structure under rigid surface conditions. The geometric effects of the enclosure are also studied. Vortex breakdown is demonstrated beyond the lower disk rotation rate threshold by introducing the no-slip condition imposed on the upper wall. The objective is to explore ways of controlling the evolution of this physical event by modifying the confinement conditions upstream of the vortex rupture. Particular attention is also paid to the effective kinematic viscosity, thermal diffusivity and geometric control of recirculation zones on the axis of rotation (axial bubble type). The second geometry consists of a spherical annulus formed by two concentric hemispheres in differential rotation under plat-free surface conditions. The results show that rotation of the inner hemisphere induces a vortex bubble on the polar axis. In contrast, the outer hemisphere rotation induces a toroidal vortex on the equator. [ABSTRACT FROM AUTHOR]