Friday 22 Mar 2019: Fast stretching of paired vortex filaments in axisymmetric and general geometry
Andrew Gilbert - University of Exeter
Exchange Green 15:00-16:00
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.
This is joint work with Steve Childress, New York University and Paul Valiant, Brown University