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The energy transfer mechanism in zero temperature superfluid turbulence ofhelium-4 is still a widely debated topic. Currently, the main hypothesis isthat weakly nonlinear interacting Kelvin waves transfer energy to sufficientlysmall scales such that energy is dissipated as heat via phonon excitations.Theoretically, there are at least two proposed theories for Kelvin-waveinteractions. We perform the most comprehensive numerical simulation of weaklynonlinear interacting Kelvin-waves to date and show, using a specially designednumerical algorithm incorporating the full Biot-Savart equation, that ourresults are consistent with nonlocal six-wave Kelvin wave interactions asproposed by L'vov and Nazarenko.

The Kelvin-wave cascade in the vortex filament model