Vortex Breakdown After Six Decades: A Structural Explanation of Persistent Theoretical Fragmentation

Vortex breakdown has been studied for more than six decades across aerodynamics, combustion, and rotating flows, yet no generally accepted theoretical explanation has emerged despite extensive experimental and numerical advances. This paper argues that the persistence of theoretical fragmentation is structural rather than mechanistic, arising from an implicit assumption that the admissible flow state space persists across breakdown. By treating admissibility and state-space persistence as explicit analytical objects, vortex breakdown is reinterpreted as a regime transition in which the admissible state space itself changes or loses continuity, even when energy remains bounded and organized flow structures persist. The framework introduces distance to admissibility and geometry-attached time to clarify why numerical continuation and smooth measurements may coexist with regime invalidity, and positions vortex breakdown as a canonical example of regime geometry with implications beyond fluid mechanics.