  The development and decay of a turbulent vortex tangle driven by the
Gross-Pitaevskii equation is studied. Using a recently-developed accurate and
robust tracking algorithm, all quantised vortices are extracted from the
fields. The Vinen's decay law for the total vortex length with a coefficient
that is in quantitative agreement with the values measured in Helium II is
observed. The topology of the tangle is then studied showing that linked rings
may appear during the decay. The tracking also allows for determining the
statistics of small-scales quantities of vortex lines, exhibiting large
fluctuations of curvature and torsion. Finally, the temporal evolution of the
Kelvin wave spectrum is obtained providing evidence of the development of a
weak-wave turbulence cascade.
