Torsion Bursting vs. Vortex Bursting.

When a jet fighter attains a high angle of attack, a visual tube of condensation often appears at the leading edge discontinuity between the wing and the shrake. The narrow tube is in apparent rotational motion, and is commonly called a "Vortex". At somewhat higher angles of attack, the tube bursts into a bubble of re-entrant flow, causing loss of aircraft stability and a great deal of stress on the pilot.

An exact solution to the Navier-Stokes equations was found by the Cartan technique, a solution that emulates the sudden growth of a re-entrant bubble, as the mean flow speed is increased [Kiehn 1991a]. Topologically, the surface of null topological torsion, A^dA=0, changes from a connected set to a disconnected set at the time of the burst. Remarkably, the vorticity of the fluid (dA) is the same before and after the generation of the burst.
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