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Commercial quartz oscillators of the tuning-fork type with a resonant frequency of ∼ 32 kHz have been investigated in helium liquids. The oscillators are found to have at best Q values in the range 10 5 -10 6 , when measured in vacuum below 1.5 K. However, the variability is large and for very low temperature operation the sensor has to be preselected. We explore their properties in the regime of linear viscous hydrodynamic response in normal and superfluid 3 He and 4 He, by comparing measurements to the hydrodynamic model of the sensor.

Hydrodynamic flow in classical and quantum fluids can be either laminar or turbulent. Vorticity in turbulent flow is often modelled with vortex filaments. While this represents an idealization in classical fluids, vortices are topologically stable quantized objects in superfluids. Superfluid turbulence is therefore thought to be important for the understanding of turbulence more generally. The fermionic 3He superfluids are attractive systems to study because their characteristics vary widely over the experimentally accessible temperature regime. Here we report nuclear magnetic resonance measurements and numerical simulations indicating the existence of sharp transition to turbulence in the B phase of superfluid 3He. Above 0.60T(c) (where T(c) is the transition temperature for superfluidity) the hydrodynamics are regular, while below this temperature we see turbulent behaviour. The transition is insensitive to the fluid velocity, in striking contrast to current textbook knowledge of turbulence. Rather, it is controlled by an intrinsic parameter of the superfluid: the mutual friction between the normal and superfluid components of the flow, which causes damping of the vortex motion.

The first realization of instabilities in the shear flow between two superfluids is examined. The interface separating the A and B phases of superfluid 3 He is magnetically stabilized. With uniform rotation we create a state with discontinuous tangential velocities at the interface, supported by the difference in quantized vorticity in the two phases. This state remains stable and nondissipative to high relative velocities, but finally undergoes an instability when an interfacial mode is excited and some vortices cross the phase boundary. The measured properties of the instability are consistent with a modified Kelvin-Helmholtz theory.Instabilities in the shear flow between two layers of fluids [1] belong to a class of interfacial hydrodynamics which is attributed to many natural phenomena. Examples are wave generation by wind blowing over water [2], the flapping of a sail or flag in the wind [3,4], and even flow in granular beds [5]. In the hydrodynamics of inviscid and incompressible fluids the transition from calm to wavy interfaces is known as the Kelvin-Helmholtz (KH) instability [6,2]. Since Lord Kelvin's treatise in 1871, difficulties have plagued its description in ordinary fluids, which are viscous and dissipative. They also display a shear-flow instability, but its correspondence with that in the ideal limit is not straightforward. The tangential velocity discontinuity in the shear-flow instability is created by a vortex sheet. In a viscous fluid a planar vortex sheet is not a stable equilibrium state and not a solution of the hydrodynamic equations [7].Superfluids provide a close variation of the ideal inviscid limit considered by Lord Kelvin and thus an environment where the KH theory can be tested. The initial state is a non-dissipative vortex sheet -the interface between two superfluids brought into a state of relative shear flow. So far the only experimentally accessible case where this can be studied in stationary conditions, is the interface between 3 He-A and 3 He-B [8], where the order parameter changes symmetry and magnitude, but is continuous on the scale of the superfluid coherence length ξ ∼ 10 nm. We discuss an experiment, where the two phases slide with respect to each other in a rotating cryostat:3 He-A performs solid-body-like rotation while 3 He-B is in the vortex-free state and thus stationary in the laboratory frame. While increasing the rotation velocity Ω, we record the events when the AB phase boundary becomes unstable -when some circulation from the A-phase crosses the AB interface and vortex lines are introduced into the initially vortex-free B phase. On increasing the rotation further, the instability occurs repeatedly. Such a succession of instability events can be understood as a spin-up of 3 He-B by rotating 3 He-A. Our experimental setup is shown in Fig. 1. The AB boundary is forced against a magnetic barrier in a smooth-walled quartz container, by cooling the sample below T AB at constant pressure in a rotating refrigerator. The number of vortices in both phases is indepe...

Rapid new developments have occurred in superfluid hydrodynamics since the discovery of a host of unusual phenomena which arise from the diverse structure and dynamics of quantized vortices in 3 He superfluids. These have been studied in rotating flow with NMR measurements which at best provide an accurate mapping of the different types of topological defects in the superfluid order parameter field. Four observations are reviewed here: (1) the interplay of different vortex structures at the first-order interface between the two major superfluid 3 He phases, 3 He-A and 3 He-B; (2) the shear flow instability of this phase boundary, which is now known as the superfluid Kelvin-Helmholtz instability; (3) the hydrodynamic transition from turbulent to regular vortex dynamics as a function of increasing dissipation in vortex motion; and (4) the peculiar propagation of vortex lines in a long rotating column which even in the turbulent regime occurs in the form of a helically twisted vortex state behind a well-developed vortex front. The consequences and implications of these observations are discussed, as inferred from measurements, numerical calculations and analytical work.

We present experimental, numerical, and theoretical studies of a vortex front propagating into a region of vortex-free flow of rotating superfluid 3He-B. We show that the nature of the front changes from laminar through quasiclassical turbulent to quantum turbulent with decreasing temperature. Our experiment provides the first direct measurement of the dissipation rate in turbulent vortex dynamics of 3He-B and demonstrates that the dissipation becomes mutual-friction independent with decreasing temperature, and it is strongly suppressed when the Kelvin-wave cascade on vortex lines is predicted to be involved in the turbulent energy transfer to smaller length scales.

We present experimental proof that in rotating 3 He-Z? the vortex-core transition temperature 7V separates axisymmetric vortices above TV from vortices with spontaneously broken axial symmetry below TV. The nonaxisymmetry is observed in the presence of coherent spin precession as a new soft Goldstone mode, manifested as oscillations and spiral twisting of the core anisotropy axis. These are driven by the precessing spin via spin-orbit coupling and lead to magnetic relaxation from viscous losses, which depend on vortex pinning.PACS numbers: 67.50.FiThe quantized vortices of superfluid He-Z? were discovered in 1981: An abrupt change in NMR frequency shifts at a critical phase-transition line Ty(p) in the temperature-(T-) pressure (p) plane was interpreted to represent a change in the structure of the vortex core. l Theoretical investigations 2,3 in the Ginzburg-Landau regime close to T c revealed two types of vortices with the same number of circulation quanta but with different internal symmetries of their cores. At high pressure the most stable vortex is the axisymmetric V\ vortex 2 with broken parity and with 3 He-A superfluid inside a core with a diameter of several coherence lengths £o~13 nm. At low pressure the rotational symmetry is broken, resulting in the V2 vortex with a nonaxisymmetric double core, 3 which may be considered a bound state of two half-quantum vortices (see insets in Fig. 1). This is now regarded as being consistent with existing experimental information. 4 Here we present the first direct experimental evidence that the phase transition, indeed, separates an axisymmetric V\ vortex at high temperatures from an asymmetric V2 vortex at low temperatures. The results were obtained by making use of the homogeneously precessing magnetic domain 5 (HPD), an NMR mode of 3 He-Z? which has proven to be more sensitive to the core structure than conventional NMR. In the HPD mode all spins within the resonance domain precess uniformly at a tipping angle of roughly 104°. Several relaxation mechanisms contribute to losses in this mode; however, here we are only concerned with the absorption caused by vortices. 6 This additional absorption Py is proportional to the total length of vortices within the precessing domain and increases discontinuously by a factor of 3 at Tyip) during cooling. 7 It also turns out that the HPD absorption of a vortex array with a constant number Ny of V2 vortices depends on whether or not the rotation velocity ft is maintained constant: If ft changes with time then an increase APf in the absorption level Pvi is observed. We explain this unique feature in terms of the dipolar coupling between the homogeneously precessing total spin magnetization and the orbital inhomogeneity in the vortex-core region. The HPD absorption from V2 vortices is dominated by a soft Goldstone mode, associated with the viscous dynamics of the in-plane orbital anisotropy vector b of the asymmetric vortex core. The Goldstone mode is manifested by (i) rapid viscous oscillatory motion and by (ii) slow rotationa...

Parts, Ü.; Karimäki, J.; Koivuniemi, J.; Krusius, M.; Ruutu, V.; Thuneberg, E.; Volovik, Grigory Phase diagram of vortices in superfluid 3He-A