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We study the statistical properties of the Kelvin waves propagating alongquantized superfluid vortices driven by the Gross-Pitaevskii equation. Noartificial forcing or dissipation is added. Vortex positions are accuratelytracked. This procedure directly allows us to obtain the Kevin-wavesoccupation-number spectrum. Numerical data obtained from long time integrationand ensemble-average over initial conditions supports the spectrum proposed in[L'vov and Nazarenko, JETP Lett 91, 428 (2010)]. Kelvin wave modes in theinertial range are found to be Gaussian as expected by weak-turbulencepredictions. Finally the dissipative range of the Kelvin-wave spectrum isstudied. Strong non-Gaussian fluctuations are observed in this range.

Kelvin-wave cascade and dissipation in low-temperature superfluids vortices