Vortex Ring Reconnections

We investigate numerically the Navier-Stokes dynamics of reconnecting vortex rings at small $Re$ number. We find that reconnections are dissipative due to the smoothing of vorticity gradients at reconnection kinks and to the formation of secondary structures of stretched anti-parallel vorticity which transfer kinetic energy to small scales where it is subsequently dissipated efficiently. In addition, the relaxation of the reconnection kinks excites Kelvin waves which due to strong damping are of low wavenumber and affect directly only large scale properties of the flow.