Rob Blaauwgeers

An intrinsic velocity-independent criterion for superfluid turbulence

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 0.60Tc (where Tc 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.Hydrodynamic flow in both classical and quantum fluids can be either laminar or turbulent. To describe the latter, vortices in turbulent flow are modelled with stable vortex filaments. While this is an idealization in classical fluids, vortices are real topologically stable quantized objects in superfluids. Thus superfluid turbulence is thought to hold the key to new understanding on turbulence in general. The fermion superfluid 3He offers further possibilities owing to a large variation in its hydrodynamic characteristics over the experimentally accessible temperatures. While studying the hydrodynamics of the B phase of superfluid 3He, we discovered a sharp transition at 0.60Tc between two regimes, with regular behaviour at high-temperatures and turbulence at low-temperatures. Unlike in classical fluids, this transition is insensitive to velocity and occurs at a temperature where the dissipative vortex damping drops below a critical limit. This discovery resolves the conflict between existing high- and low-temperature measurements in 3He-B: At high temperatures in rotating flow a vortex loop injected into superflow has been observed to expand monotonically to a single rectilinear vortex line, while at very low temperatures a tangled network of quantized vortex lines can be generated in a quiescent bath with a vibrating wire. The solution of this conflict reveals a new intrinsic criterion for the existence of superfluid turbulence.

Shear Flow and Kelvin-Helmholtz Instability in Superfluids

The first realization of instabilities in the shear flow between two superfluids is examined. The interface separating the A and B phases of superfluid 3He 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 the classic Kelvin-Helmholtz theory when modified for two-fluid hydrodynamics.

Double-quantum vortex in superfluid 3He-A

Linear defects are generic in continuous media. In quantum systems they appear as topological line defects which are associated with a circulating persistent current. In relativistic quantum field theories they are known as cosmic strings, in superconductors as quantized flux lines, and in superfluids and low-density Bose–Einstein condensates as quantized vortex lines. A conventional quantized vortex line consists of a central core around which the phase of the order parameter winds by 2πn, while within the core the order parameter vanishes or is depleted from the bulk value. Usually vortices are singly quantized (that is, have n = 1). But it has been theoretically predicted that, in superfluid 3He-A, vortex lines are possible that have n = 2 and continuous structure, so that the orientation of the multi-component order parameter changes smoothly throughout the vortex while the amplitude remains constant. Here we report direct proof, based on high-resolution nuclear magnetic resonance measurements, that the most common vortex line in 3He-A has n = 2. One vortex line after another is observed to form in a regular periodic process, similar to a phase-slip in the Josephson effect.

Structure of the surface vortex sheet between two rotating 3He superfluids

We study a two-phase sample of superfluid 3He where vorticity exists in one phase (3He-A) but cannot penetrate across the interfacial boundary to a second coherent phase (3He-B). We calculate the bending of the vorticity into a surface vortex sheet on the interface and solve the internal structure of this new type of vortex sheet. The compression of the vorticity from three to two dimensions enforces a structure which is made up of 1 / 2-quantum units, independently of the structure of the source vorticity in the bulk. These results are consistent with our NMR measurements.

Transitions from vortex lines to sheets: interplay of topology and dynamics in an anisotropic superfluid.

In isotropic macroscopic quantum systems vortex lines can be formed while in anisotropic systems also vortex sheets are possible. Based on measurements of superfluid 3He-A, we present the principles which select between these two competing forms of quantized vorticity: sheets displace lines if the frequency of the external field exceeds a critical limit. The resulting topologically stable state consists of multiple vortex sheets and has much faster dynamics than the state with vortex lines.

NMR Line Shape of Rotating 3He-B at Large Counterflow Velocity

We have investigated the NMR line shapes of superfluid 3He-B in a rotating cylinder. In the vortex-free state at sufficiently large angular velocity of rotation, Ω≳1 rad/s, the main feature of the absorption spectrum is a large frequency-shifted peak above the Larmor frequency. The shape of this counterflow peak is both measured and calculated as a function of external magnetic field strength, angular velocity, temperature, and number of vortex lines. The NMR spectrum is derived from the calculated order-parameter texture. Reasonable agreement with the measured line shape is obtained by including line-broadening effects due to the external field inhomogeneity and Leggett–Takagi relaxation.

Onset of Turbulence in Superfluid 3He‐B and its Dependence on Vortex Injection in Applied Flow

Vortex dynamics in 3He‐B is divided by the temperature dependent damping into a high‐temperature regime, where the number of vortices is conserved, and a low‐temperature regime, where rapid vortex multiplication takes place in a turbulent burst. We investigate experimentally the hydrodynamic transition between these two regimes by injecting seed vortex loops into vortex‐free rotating flow. The onset temperature of turbulence is dominated by the roughly exponential temperature dependence of vortex friction, but its exact value is found to depend on the injection method.

Instability of AB interfaces of different shapes in rotating 3He

Abstract In our experiments on rotating superfluid 3 He the interface between the A and B phases is stabilized in a magnetic field. With decreasing current in the barrier magnet, the shape of the interface changes from almost flat and perpendicular to the sample axis to a ring of A phase which coats the outer sample boundary, with B phase in the center. The influence of the shape of the interface on the critical velocity of its shear-flow instability is investigated.

Superfluid He in Rotation: Single-Vortex Resolution and Requirements on Rotation

The present generation of rotating refrigerators, which are used for the study of quantized vorticity in helium superfluids, are often capable of cooling to mK temperatures and rotate up to ∼ 1 rev/s. To achieve single-vortex resolution at all rotation velocities, smooth and stable rotation is required. This calls for low and stable rotational friction, sufficient axial alignment and lateral balancing of weights, to promote mechanical stability and precession-free rotation. We comment on general design principles, discuss the rotation noise spectrum of our installation, and describe interference problems from the rotation in low-noise measurement.

Magnetically driven cold valve for He4

We have designed a low temperature valve for liquid helium, which uses a magnetic field gradient and a permanent magnet to close. For closing, it presses a small ruby ball onto a Torlon seat. We present a small valve that is easy to build and easily controlled via two wires. It has a fast response, reliable, and has the advantage that there is no dead volume change on closing and no additional helium line is required to operate.