Numerical generation of a vortex ring cascade in quantum turbulence

Professor Robert M. Kerr

Department of Mathematics, University of Warwick

A symmetric anti-parallel quantum pair of vortices is simulated using the three-dimensional Gross-Pitaevski equations. The initial development demonstrates vortex dynamics of stretching, curvature and torsion consistent with a filament calculation and simulations of the classical, ideal Euler equations. How a vacuum mediates reconnection between the pair is illustrated.  Out of the reconnection, 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. Analysis is in progress to determine the flow of energies in spectral scale and physical space.