Velocity spectra of superfluid turbulence
Mathematics Department, University of Newcastle -
Newcastle NE1 7RU, UK
2 Department of Aeronautics, Imperial College South Kensington, London SW7 2BY, UK
Accepted: 7 January 2002
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.
PACS: 67.40.Vs – Vortices and turbulence / 47.37.+q – Hydrodynamics aspects of superfluidity
© EDP Sciences, 2002