Quantum turbulence: pure superflow through channels

We are studying experimentally the turbulent state of bellows-driven ⁴He superfluid flows in channels. Turbulence in a superfluid takes the form of a tangle of atomically-thin vortex lines with quantized velocity circulation, which arise as a consequence of the Bose-Einstein condensation of the superfluid [1]. In one project [2-4] we have studied the dependence of the total length of vortex lines, L, with mean flow velocity, v, in conditions of steady-state turbulence. The flow is provided by a home-build low temperature bellows forcing superfluid helium into a vertical channel (see Fig. 1). The channel has superleak plugs at both ends to allow flow of the zero-viscosity superfluid component only. We estimate L by observing the attenuation of second-sound (a temperature wave existing in superfluid helium) resonating across the channel width (see Fig. 2).

We observed that L^1/2 = γ(T)(v - v_c) (see Fig. 3) where γ(T) is a temperature dependent prefactor, and v_c is a nearly temperature independent critical velocity for the onset of turbulence, of order 0.2 cm/s. These results, both formally and quantitatively are understood within the framework of the theory of thermal counterflow [1], the thermally activated relative motion of normal component (viscous, with entropy) and superfluid component (no viscosity, no entropy) of superfluid helium. We deduced that our net flow of the superfluid component can be thought of as thermal counterflow in the frame of reference of the normal component.

Fig.1

Fig.2

Fig.3

References:
[1] W. F. Vinen, J. J. Niemela, J. Low Temp. Phys. 128 (2002) 167.
[2] S. Babuin, M. Stammeier, E. Varga, M. Rotter, L. Skrbek, Quantum turbulence of bellows-driven ⁴He superflow: Steady state, Phys. Rev. B 86 (2012) 134515 .
[3]S. Babuin, E. Varga, L. Skrbek, E. Leveque, P.E. Roche, Effective viscosity in quantum turbulence: A steady-state approach, Europhys. Lett. 106 (2014) 24006 .
[4]S. Babuin, E. Varga, L. Skrbek The Decay of Forced Turbulent Coflow of He II Past a Grid, J. Low. Temp. Phys. 175 (2014) 324 .