We describe measurements of the decay of pure superfluid turbulence in superfluid 3 He-B, in the low temperature regime where the normal fluid density is negligible. We follow the decay of the turbulence generated by a vibrating grid as detected by vibrating wire resonators. Despite the absence of any classical normal fluid dissipation processes, the decay is consistent with turbulence having the classical Kolmogorov energy spectrum and is remarkably similar to that measured in superfluid 4 He at relatively high temperatures. Further, our results strongly suggest that the decay is governed by the superfluid circulation quantum rather than kinematic viscosity.PACS numbers: 67.57. Fg, 67.57.De, 67.57.Hi In this paper we present the first quantitative measurements of the decay of turbulence in a pure superfluid system. This is a subject of considerable interest since no conventional dissipation mechanisms are available.In a classical fluid, turbulence at high Reynolds numbers is characterized by a range of eddy sizes obeying the well-known Kolmogorov spectrum. On large length scales the motion is dissipationless, whereas on small scales viscosity comes into play. Decay of the turbulence proceeds as energy is transferred by non-linear interactions from the largest non-dissipative length scales d (typically the size of the turbulent region) to smaller length scales where the motion is dissipated by viscous forces. The dissipation per unit volume is given by ρνω 2 where ρ is the fluid density, ν the kinematic viscosity and ω 2 the mean square vorticity [1]. An interesting question, which has received much theoretical speculation [1], is what happens in a pure superfluid with no viscous interactions?Conceptually, turbulence in a superfluid is greatly simplified. Superfluids such as He-II and 3 He-B are described by macroscopic wavefunctions with a well defined phase φ. The superfluid velocity is determined by gradients of the phase, v S = ( /m)∇φ where m is the mass of the entities constituting the superfluid (the mass of a 4 He atom for He-II or twice the mass of a 3 He atom, 2m 3 , for the Cooper pairs in 3 He-B). Consequently, in contrast to classical fluids, superfluid motion is inherently irrotational and vorticity may only be created in the superfluid by the injection of vortex lines. A superfluid vortex is a line defect around which the phase changes by 2π (ignoring here more complex structures such as in 3 He-A). The superfluid order parameter is distorted within the relatively narrow core of the vortex where all the circulation is concentrated. The superfluid flows around the core with a velocity, at distance r, given by v S = /mr corresponding to a quantized circulation κ = h/m. Vortex lines are topological defects. They cannot terminate in free space, and therefore must either form loops or * Electronic Address: s.fisher@lancaster.ac.uk terminate on container walls. Turbulence in a superfluid takes the form of a tangle of vortex lines.Superfluid hydrodynamics is further simplified by the superfluid compon...

We describe the first direct observations of turbulence in superfluid 3He-B. The turbulence is generated by a vibrating-wire resonator driven at velocities exceeding the pair-breaking critical velocity. It is detected by the resulting decrease in the thermal damping on a neighboring "detector" vibrating-wire resonator. The superfluid flow field associated with the turbulence Andreev reflects thermal quasiparticle excitations, effectively screening the detector wire, resulting in a decrease in the thermal damping.

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Using an existing experiment we have demonstrated in a pilot study that superfluid -'He at 100 p, K can be used as a nuclear recoil detector sensitive to neutron and y interactions depositing energies down to a few hundred eV. The deposited energy is converted to He quasiparticles which are detected by their damping effect on a vibrating wire resonator in the liquid. The system can be calibrated independently but a convenient fixed point is provided by the exothermic reaction n + 2He = p + [H + 764 keV. Given the great potential for improvement we propose that the 3 3 system might make a sensitive weakly interacting massive particle detector. PACS numbers: 29.40.Ym, 67.57.Bc, 95.35.+d, 95.55.Vj A favored candidate for the missing mass in the Universe is a sea of weakly interacting massive particles (WIMPs). Several experiments are currently searching for nuclear recoils from collisions with such objects [1].

We have studied the resonance of a commercial quartz tuning fork immersed in superfluid 4 He, 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.