  By solving numerically the governing Gross-Pitaevskii equation, we study the
dynamics of Kelvin waves on a superfluid vortex. After determining the
dispersion relation, we monitor the turbulent decay of Kelvin waves with energy
initially concentrated at large length scales. At intermediate length scales,
we find that the decay is consistent with scaling predictions of theoretical
models. Finally we report the unexpected presence of large-length scale phonons
in the system.
