Absence of small-scale structure in homogeneous superfluid turbulence

By contrast with classical turbulence, which is driven by large-scale shear instabilities, superfluid turbulence is driven homogeneously by the mutual friction between the normal fluid and the superfluid. We suggest that this difference implies that there is no equivalent to a Kolmogorov energy cascade in turbulent superfluid flows. We then compare a recent numerical simulation of superfluid turbulence by Schwartz [Phys. Rev. B 31, 5782 (1985)] with a recent simulation of singular vortex stretching in classical fluids by Siggia and Pumir. This comparison suggests that the rigidity of the quantum-mechanical vortex core inhibits any generation of small-scale structure in the superfluid case. Superfluid turbulence is essentially a two-length-scale phenomenon, where the scales are the average intervortex distance and the vortex-core diameter