Velocity spectra of superfluid turbulence

We study numerically statistics of superfluid turbulence. We generate a quantized superfiuid vortex tangle driven by a realistic model of normal-fluid turbulence whose energy spectrum obeys Kolmogorov's classical k-5/3 law, where k is the wave number. We find that the resulting superfluid velocity spectrum has approximately a k-1 -dependence for wave numbers of the order of 1/δ and larger, where δ is the average intervortex spacing. This result is similar to what happens in a pure superflow. We also find that the spectrum of the total velocity field follows the classical k-5/3 law, even at temperatures low enough that the normal-fluid mass is only 5% of the total helium mass. We discuss our assumptions and results in view of recent experiments.