Transition to quantum turbulence in a Bose-Einstein condensate through the bending-wave instability of a single-vortex ring

We investigate the dynamics of an unstable vortex ring in a pancake-shaped Bose-Einsten condensate by solving the Gross-Pitaevskii equation numerically. It is found that a quasisteady turbulent state with long relaxation time can be achieved through the disruption of a perturbed vortex ring in the condensate owing to the bending-wave instability. We verify that this quantum turbulent state is characterized by Kolmogorov energy spcetrum.