Fully Developed Hydrodynamic Turbulence from a Chain Reaction of Reconnection Events

From a new anti-parallel initial condition using long vortices, three-dimensional incompressible turbulence forms after two re- connection steps and the formation of at least one set of vortex rings, similar to how anti-parallel quantum vortices evolve [10]. The long domain allows multiple reconnections, which enhance vortex stretching rates and the generation of small-scale vortex structures within the vortex rings. For the Navier-Stokes vortices, further new features are a profile less likely to shed vortex sheets and an improved mapping of the direction of the vorticity onto the three-dimensional mesh. The vortices evolve via the following steps: First, until the first reconnection, dynamics largely consistent with how vortices attract in the Euler equations. Second, vortex reconnection where the symmetry planes meet. Third, a series of vortex rings, with the stretching at each following set of reconnections leading to the new reconnections and rings. Roughly half of the circulation reconnects into two “bridges”, leaving two distinct “threads”, as he extra stretching transforms the threads into spirals wrapped around the bridges. It is argued that these spirals are the source of the observed k−5/3 energy spectra and other statistics commonly associated with high Reynolds number turbulence.