Kelvin-Wave Cascades in Turbulent Superfluid 4He at Very Low Temperatures

There has been much interest recently in the mechanism by which superfluid (quantum) turbulence can decay in liquid 4He at very low temperatures, where mutual friction has a negligible effect. As in classical turbulence, energy must probably flow from larger to smaller length scales, and it has been suggested that on the smallest scales the relevant motion is a Kelvin wave on a quantized vortex with wave number greater than the inverse vortex spacing. By considering the behaviour of a simple model it is shown by computer simulations how energy can flow to shorter length scales (higher wave numbers) in a system of Kelvin waves, and how this process can lead to a remarkably simple Kelvin-wave energy spectrum. A discussion is included of the relevance of this model to the decay of superfluid grid turbulence at a very low temperature.