Kelvin Waves Cascade in Superfluid Turbulence

We study numerically the interaction of four initial superfluid vortex rings in the absence of any dissipation or friction. We find evidence for a cascade of Kelvin waves generated by individual vortex reconnection events which transfers energy to higher and higher wave numbers $k$. After the vortex reconnections occur, the energy spectrum scales as $k^{-1\mathrm{}}$ and the curvature spectrum becomes flat. These effects highlight the importance of Kelvin waves and reconnections in the transfer of energy within a turbulent vortex tangle.