The sensitivity of the vortex filament method to different reconnection models

We present a detailed analysis on the effect of using different algorithms to model the reconnection of vortices in quantum turbulence, using the thin-filament approach. We examine differences between four main algorithms for the case of turbulence driven by a counterflow. In calculating the velocity field we use both the local induction approximation (LIA) and the full Biot-Savart integral. We show that results of Biot-Savart simulations are not sensitive to the particular reconnection method used, but LIA results are.Comment: 9 pages, 9 figure

Tree method for quantum vortex dynamics

We present a numerical method to compute the evolution of vortex filaments in superfluid helium. The method is based on a tree algorithm which considerably speeds up the calculation of Biot-Savart integrals. We show that the computational cost scales as Nlog{(N) rather than N squared, where $N$ is the number of discretization points. We test the method and its properties for a variety of vortex configurations, ranging from simple vortex rings to a counterflow vortex tangle, and compare results against the Local Induction Approximation and the exact Biot-Savart law.Comment: 12 pages, 10 figure

Transition to turbulence for a quartz tuning fork in superfluid He-4

We have studied the resonance of a commercial quartz tuning fork immersed in superfluid He-4, at temperatures between 5 mK and 1 K, and at pressures between zero and 25 bar. The force-velocity curves for the tuning fork show a linear damping force at low velocities. On increasing velocity we see a transition corresponding to the appearance of extra drag due to quantized vortex lines in the superfluid. We loosely call this extra contribution "turbulent drag". The turbulent drag force, obtained after subtracting a linear damping force, is independent of pressure and temperature below 1 K, and is easily fitted by an empirical formula. The transition from linear damping (laminar flow) occurs at a well-defined critical velocity that has the same value for the pressures and temperatures that we have measured. Later experiments using the same fork in a new cell revealed different behaviour, with the velocity stepping discontinuously at the transition, somewhat similar to previous observations on vibrating wire resonators and oscillating spheres. We compare and contrast the observed behaviour of the superfluid drag and inertial forces with that measured for vibrating wires

Hysteresis, switching and anomalous behaviour of a quartz tuning fork in superfluid 4He

We have been studying the behaviour of commercial quartz tuning forks immersed in superfluid 4He and driven at resonance. For one of the forks we have observed hysteresis and switching between linear and non-linear damping regimes at temperatures below 10 mK. We associate linear damping with pure potential flow around the prongs of the fork, and non-linear damping with the production of vortex lines in a turbulent regime. At appropriate prong velocities, we have observed metastability of both the linear and the turbulent flow states, and a region of intermittency where the flow switched back and forth between each state. For the same fork, we have also observed anomalous behaviour in the linear regime, with large excursions in both damping, resonant frequency, and the tip velocity as a function of driving force

Response of a mechanical oscillator in solid 4He

We present the first measurements of the response of a mechanical oscillator in solid 4He. We use a lithium niobate tuning fork operating in its fundamental resonance mode at a frequency of around 30 kHz. Measurements in solid 4He were performed close to the melting pressure. The tuning fork resonance shows substantial frequency shifts on cooling from around 1.5 K to below 10 mK. The response shows an abrupt change at the bcc-hcp transition. At low temperatures, below around 100 mK, the resonance splits into several overlapping resonances

The damping of a quartz tuning fork in superfluid He-3-B at low temperatures

We have measured the damping on a quartz tuning fork in the B-phase of superfluid He-3 at low temperatures, below 0.3T (c). We present extensive measurements of the velocity dependence and temperature dependence of the damping force. At the lowest temperatures the damping is dominated by intrinsic dissipation at low velocities. Above some critical velocity an extra temperature independent damping mechanism quickly dominates. At higher temperatures there is additional damping from thermal quasiparticle excitations. The thermal damping mechanism is found to be the same as that for a vibrating wire resonator; Andreev scattering of thermal quasiparticles from the superfluid back-flow leads to a very large damping force. At low velocities the thermal damping force varies linearly with velocity, but tends towards a constant at higher velocities. The thermal damping fits very well to a simple model developed for vibrating wire resonators. This is somewhat surprising, since the quasiparticle trajectories through the superfluid flow around the fork prongs are more complicated due to the relatively high frequency of motion. We also discuss the damping mechanism above the critical velocity and compare the behaviour with other vibrating structures in superfluid He-3-B and in superfluid He-4 at low temperatures. In superfluid He-4 the high velocity response is usually dominated by vortex production (quantum turbulence), however in superfluid He-3 the response may either be dominated by pair-breaking or by vortex production. In both cases the critical velocity in superfluid He-3-B is much smaller and the high velocity drag coefficient is much larger, compared to equivalent measurements in superfluid He-4