Swirling, turbulent vortex rings formed from a chain reaction of reconnection events

Long, straight, anti-parallel vortex tubes, with balanced profiles and a local perturbation, are simulated using the Navier-Stokes equations and evolve into a chain of spiral vortex rings with the characteristics of three-dimensional turbulence. This includes evidence of a cascade of energy to high wavenumbers, the formation of a k(-5/3) inertial subrange and a new hierarchy of rescaled vorticity moments where, against expectations, the lower-order moments bound the higher-order moments. This order holds for all times even as the individual moments fluctuate significantly and could explain the observation that ratios converge faster than the individual moments in very high Reynolds number forced turbulence simulations. The transformation of the original pair of vortices into turbulent swirling vortex rings is outlined by describing first the twists and turns of the first two reconnection steps in detail, next how these create the first set of vortex rings, and finally the formation of the additional reconnections and stretched, swirling rings that lead to turbulence. The k-5/3 spectrum is interpreted in terms of a model of stretched, spiral vortices similar to those seen in these simulations. (C) 2013 AIP Publishing LLC.