A study of the drag on the prongs of a number of quartz forks vibrating in the superfluid phase of ${}^4\text{H}\text{e}$ is reported, and particular attention is paid to the transitions from laminar to turbulent flow over a wide range of temperature. Behavior in the normal phase is consistent with that for a classical fluid, as has already been reported [Phys. Rev. E 75, 025302 (2007)]. Behavior in the superfluid phase is compared to that of other structures vibrating in superfluid ${}^4\text{H}\text{e}$, and similarities and differences are noted. We focus on the observed behavior of the drag coefficient as a function of velocity, and the problems posed by this behavior are explored. There is evidence for a sharp critical velocity at which significant turbulence starts to be generated in the superfluid component. At high velocities the drag coefficient tends to that observed in a classical fluid, suggesting that the two fluids, strongly coupled by mutual friction, are then behaving like a single classical viscous fluid. Behavior in the intermediate region seems to vary from one case to another. Evidence is presented that in the case of some structures the transition to single-fluid behavior takes place rather abruptly at a velocity that is only slightly greater than the sharp superfluid critical velocity, but that in other structures the transition is more gradual. Observed values of both the superfluid critical velocity and the effective viscosity of the fully coupled fluids are presented and discussed. It is suggested that the critical superfluid velocity is always closely similar to that at which the coupled fluids would be expected to undergo a classical transition between a flow that is strictly laminar and one that displays the first instability, and a possible reason is discussed.

• Received 28 October 2008

DOI:https://doi.org/10.1103/PhysRevB.79.054522