Quantum turbulence at finite temperature: The two-fluids cascade

¹  Institut Néel, CNRS/UJF - BP166, F-38042 Grenoble Cedex 9, France, EU
²  School of Mathematics and Statistics, Newcastle University - Newcastle upon Tyne NE1 7RU, UK, EU
³  Laboratoire de Physique, ENS Lyon, CNRS/Université de Lyon - F-69364 Lyon, France, EU

Received: 14 May 2009
Accepted: 25 August 2009

Abstract

To model isotropic homogeneous quantum turbulence in superfluid helium, we have performed Direct Numerical Simulations (DNS) of two fluids (the normal fluid and the superfluid) coupled by mutual friction. We have found evidence of strong locking of superfluid and normal fluid along the turbulent cascade, from the large scale structures where only one fluid is forced down to the vorticity structures at small scales. We have determined the residual slip velocity between the two fluids, and, for each fluid, the relative balance of inertial, viscous and friction forces along the scales. Our calculations show that the classical relation between energy injection and dissipation scale is not valid in quantum turbulence, but we have been able to derive a temperature-dependent superfluid analogous relation. Finally, we discuss our DNS results in terms of the current understanding of quantum turbulence, including the value of the effective kinematic viscosity.