Classical character of turbulence in a quantum liquid

A theoretical discussion is presented of recent experiments in which it has been shown that turbulence in the superfluid phase of liquid ${}^4\mathrm{He}$ can be very similar in its characteristics to that in a conventional fluid; particular attention is focused on the work of Stalp, Skrbek, and Donnelly [Phys Rev. Lett. 82, 4831 (1999)]. It is argued that on length scales significantly greater than both the spacing between the quantized vortex lines in the turbulent superfluid component and the scale on which viscous dissipation occurs in the normal fluid, the two fluids are likely to be coupled together and to behave like a conventional fluid. On smaller length scales account must be taken of dissipation, due to viscosity in the normal fluid, frictional interaction between the vortex lines and the normal fluid, and the radiation of sound from the vortex lines; it is shown that the rate of dissipation is likely to be given by an expression that is similar to that in a conventional fluid but with some important differences. Emphasis is placed on the need for experiments at a very low temperature in which the complicating effects of the normal fluid are either absent or easily taken into account, and the paper includes some theoretical discussion of the decay of superfluid turbulence in the absence of normal fluid and when the normal fluid density is very low. This last discussion is inspired by the ideas of Svistunov [Phys. Rev. B 52, 3647 (1995)].