Velocity fields of helium II carrying a heat current

Abstract

The velocity fields of heliumn have been studied in a short, wide tunnel in which a heat current can be made to flow. A fine quartz fibre suspended from the tunnel roof and carrying a small weight at its lower end is used as a probe. The random motion of the fibre measures the intensity of turbulence in the normal fluid, while its response to short heat pulses, either alone or superimposed on a heat current, is related to the superfluid circulation about the fibre. From the size, direction and rate of change of this circulation the state of vorticity of the superfluid can be deduced. At 1*3 °K three flow regimes are found. In low or zero heat currents the normal-fluid flow is laminar; observed circulations are of the order of one quantum and persist for many seconds. It is believed that they are created by the measurement process (the heat pulse) itself, so that in this régime the superfluid is essentially undisturbed. In the second regime, which occurs above an onset heat current determined by the geometry, the observed circulations are smaller and more variable. It is argued that this results from superfluid vorticity associated with secondary flow. In the third regime random motion of the fibre occurs. It is shown that this motion cannot be due to superfluid turbulence alone: the normal fluid must be turbulent, and probably the superfluid also. The régime occurs when a modified Reynolds number, based on the normal-fluid viscosity and mean velocity, the mean tunnel diameter and the total density of the helium, exceeds a critical value of about 1350. The onset of the third regime is the analogue for heliumn of the classical transition from laminar to turbulent flow. The behaviour at higher temperatures is similar but less clear cut. It is concluded that, while the behaviour of the measured circulations about the fibre is consistent with the quantization of superfluid circulation, the critical velocities observed in heat currents in wide channels are directly related not to the creation of quantized vortex lines, but to the quasi-classical effects, secondary flow and turbulence.