Fast Stretching of Paired Vortex Filaments in Axisymmetric and General Geometry

Colloquium:

Speaker: Andrew Gilbert (Exeter)

Abstract: (With Steve Childress, New York University).

Coherent vortices are a component of many high Reynolds number flows including turbulence. A fundamental question is how quickly vortex stretching can occur, linked to the thorny question of whether Euler or Navier--Stokes flows can become singular in a finite time, or whether these remain well-behaved indefinitely. I will first discuss work with Steve Childress on vortex stretching in axisymmetric geometry --- collision of two vortex rings --- where stretching is accelerated giving a power law growth. Then, I will outline work on extending these calculations to a vortex dipole pair with arbitrary centre line. In simplified models similarity solutions can be obtained that become singular in a finite time, but these neglect axial flow, which complicates any analysis and may suppress this behaviour.