To explain the observed decay of superfluid turbulence at very low
temperature, it has been proposed that a cascade of Kelvin waves (analogous to
the classical Kolmogorov cascade) transfers kinetic energy to length scales
which are small enough that sound can be radiated away. We report results of
numerical simulations of the interaction of quantized vortex filaments. We
observe the development of the Kelvin-waves cascade, and compute the statistics
of the curvature, the amplitude spectrum (which we compare with competing
theories) and the fractal dimension.Comment: 32 pages, 22 figure
