Vorticity matching in superfluid helium

Recent experiments have rekindled interest in high Reynolds number flows using superfluid helium. In a continuing series of experiments, the flow of helium II through various devices (smooth pipes, corrugated pipes, valves, venturies, turbine flowmeters, and coanda flowmeters for example) was investigated. In all cases, the measured values (typically, mass flow rates and pressure drops) were found to be well described by classical relations for high Reynolds flows. This is unexpected since helium II consists of two interpenetrating fluids; one fluid with nonzero viscosity (the normal fluid) and one with zero viscosity (the superfluid). Only the normal fluid component should directly obey classical relations. Since the experiments listed above only measure the external behavior of the flow (i.e., pressure drops over devices), there is a great deal of room for interpretation of their results. One possible interpretation is that in turbulent flows the normal fluid and the superfluid velocity fields are somehow 'locked' together, presumably by the mutual friction force between the superfluid vortex filaments and the normal fluid. We refer to this locking together of the two fluids as 'vorticity matching.'