Numerical generation of a vortex ring cascade in quantum turbulence

A symmetric anti-parallel quantum pair of vortices is simulated using the three-dimensional Gross-Pitaevski equations. The initial development before cores interact directly demonstrates the traditional vortex dynamics of stretching, curvature and torsion in a manner consistent with a filament calculation and simulations of the classical, ideal Euler equations. Once the cores begin to interact, reconnection develops in the vacuum that forms between the pair. Out of the reconnection region, vortex waves are emitted with properties similar to waves in the local induction approximation. These waves propagate down the initial vortex and deepen. When they deepen far enough, secondary reconnections occur and vortex rings form. Near this time, spectra have a $k^{-3}$ regime. As the vortex rings fully separate, the high wavenumber spectra grow until, at the final time simulated, spectra in two directions develop nearly -5/3 subranges. This occurs without the dissipation of energy. Preliminary analysis of the flow of energies in spectral scale and physical space is discussed.