Velocity spectra of superfluid turbulence

¹ Mathematics Department, University of Newcastle - Newcastle NE1 7RU, UK
² Department of Aeronautics, Imperial College South Kensington, London SW7 2BY, UK

Received: 17 September 2001
Accepted: 7 January 2002

Abstract

We study numerically statistics of superfluid turbulence. We generate a quantized superfluid vortex tangle driven by a realistic model of normal-fluid turbulence whose energy spectrum obeys Kolmogorov's classical 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 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 law, even at temperatures low enough that the normal-fluid mass is only of the total helium mass. We discuss our assumptions and results in view of recent experiments.