A modified vortex filament method is used to simulate the evolution of the transient formation of vortex breakdown. The method supports previous studies, illustrating that vortex breakdown. The method supports previous studies, illustrating that vortex breakdown is initiated by a negative vorticity gradient which triggers an inviscid self-induction feedback mechanism and when subsequently subjected to viscous effects, results in steady state vortex breakdown. The results of the method are first validated experimentally with numerous past dye flow visualization and particle image velocimetry investigations, and then used to qualitatively investigate the self-induction flow mechanisms during the formative stages of stages of transient breakdown. As a complement to the qualitative investigation, a quantitative analysis is performed, which yields a local and dynamical relationship relating the azimuthal vorticity gradient at a particular location to the curvature of the instantaneous streamline, projected onto the meridional plane, at the same location. This relationship further shows that once radial expansion commences in the region of negative azimuthal vorticity, it continues to expand such that the meridional streamline becomes more curved with time, supporting that the negative vorticity gradient not only initiates the radial expansion, but also, feeds its subsequent growth. On the contrary, in the region of a positive gradient, the streamline continues to flatten fostering radial contraction of the vortex tube, which provides a closure to expansion. In attempt to suppress breakdown in two preliminary control simulations, this positive azimuthal vorticity gradient is then introduced to the vortex flow just prior to breakdown. Results from these control simulations illustrated a temporal and spatial delay in breakdown as well as exhibiting flow behavior associated with complete elimination of breakdown.