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.