The repeated filamentation of vorticity interfaces

Arbitrarily shallow, localised disturbances to the boundary of a uniform circular vortex are found to steepen to the point of ejecting a thin filament into the surrounding irrotational fluid after a time inversely proportional to the initial wave steepness squared. Subsequent to the formation of the first filament, a second filament is produced in the much shorter time inversely proportional to the vorticity within the vortex. This process appears to repeat itself endlessly, and the vortex boundary rapidly grows in complexity.