We present evidence of Kelvin excitations in space-time resolved spectra of
numerical simulations of quantum turbulence. Kelvin waves are transverse and
circularly polarized waves that propagate along quantized vortices, for which
the restitutive force is the tension of the vortex line, and which play an
important role in theories of superfluid turbulence. We use the
Gross-Pitaevskii equation to model quantum flows, letting an initial array of
well-organized vortices develop into a turbulent bundle of intertwined vortex
filaments. By achieving high spatial and temporal resolution we are able to
calculate space-time resolved mass density and kinetic energy spectra. Evidence
of Kelvin and sound waves is clear in both spectra. Identification of the waves
allows us to extract the spatial spectrum of Kelvin waves, clarifying their
role in the transfer of energ
