Microscopic dynamics of quantized vortices in turbulent superfluid in the T=0 limit

Turbulence is ubiquitous in nature and affects almost every aspect of our daily lives. Despite its overwhelming importance, turbulence is poorly understood, mainly because of the complexity of turbulent motion over a very wide range of length scales. Turbulence in superfluid helium, known as quantum turbulence, is special, because quantum mechanics restricts all vortices to have a single fixed value of circulation. Thus we are dealing with a dynamic tangle of vortex lines, all of the same strength. Turbulence, including its quantum variant, is an inherently non-equilibrium phenomenon: remove the driving force, and the turbulence decays.
Our goal is to confront the two remaining, mutually interconnected, challenges of quantum turbulence in the T=0 limit: (i) to observe and investigate the elementary processes occurring with individual vortex lines inside bulk tangles; (ii) explore the interaction, and its consequences, of vortex lines with solid boundaries.

(i) Below 0.5K damping of the motion of vortex lines effectively vanishes. While it is expected that vortex reconnection and deformation on a broad range of length scales are the main ingredients of their dynamics, no direct observations of these at low temperatures have been made so far. The programme will produce sequences of 2D and 3D images of vortex lines, their bundles and tangles - in different types of turbulent flow, visualized through fluorescence of either He2* excimers or dyed nanoparticles as tracers. Hence, we will obtain information on different aspects of quantum turbulence, and its distinction from classical turbulence. This new technique could revolutionize the study of quantum turbulence. As quantum turbulence mimics classical turbulence on large length scales, our direct visualization of the structure and dynamics of the region of concentrated vorticity might also make an important contribution to the understanding of intermittency in classical turbulence when coherent structures cause rare events of large amplitude.

(ii) The understanding of the dynamics of vortex tangles near solid walls is another outstanding fundamental question. The creation of quantum turbulence seems to be "seeded" by remanent vortices pre-existing in the superfluid. It was suggested that the evolution to fully-developed quantum turbulence as the amplitude of an oscillating structure increases may occur via a 2-stage process. First, shaking of the lines sloughs off a gas of small vortex rings, which reconnect to form a random tangle. This tangle itself behaves like a fluid of small viscosity undergoing laminar flow. Then at a higher velocity there is a second transition when the flow turns turbulent. We propose to test this picture experimentally.

All earlier experiments on the generation of quantum turbulence by oscillating structures have used objects with convex surfaces; the flow round them is classically unstable at a low velocity, so that the two supposed transitions are not clearly separated. In contrast, we propose experiments where the helium is inside a pill-box that oscillates about its axis, thus eliminating all flow over convex surfaces. The two transitions should then be well separated and identifiable as characteristic increases in damping. We will also illuminate the fundamental properties of the remanent vortices themselves, by investigating their pinning to microscopic protuberance. Recent measurements indicate that vortex pinning get weaker at low temperatures, perhaps through reconnections with lines of the mesh of remanent vortices. To test these results, we propose experiments in a spherical cell, a geometry in which pinned vortex loops are inherently unstable, as well as visualization of remanent vortices, both away from and near boundaries.

The investigations of quantum turbulence that we propose represent cutting-edge basic research. We seek fundamental scientific understanding, and we do not anticipate immediate commercial applications. Nonetheless, given the universality and importance of turbulence, the work promises to have significant technological impact in the longer term as well as educational and cultural impact now. We envisage early impact in the following areas:

1. Public and schools. An improved understanding of turbulence promises to make a significant cultural contribution to everyday life. In practice, we disseminate our research far beyond our academic beneficiaries in order to provide cultural enrichment for a wide audience. Our low temperature laboratories are showcased in extensive outreach programmes involving 1000+ visitors/year. The resultant enhancement of knowledge and understanding benefits society as a whole.

2. Industry. Although immediate industrial applications are not envisaged, the research impinges on an area of enormous practical and financial importance. Much of the energy used in air or sea transport, for example, goes into the creation of turbulence. If improved understanding leads eventually to even a small reduction in turbulence production, the corresponding energy savings would pay for the cost of the present research programme many times over. We note that the cooling of large superconducting magnets (e.g. for the LHC at CERN) is achieved through the forced flow of liquid 4He at about 1.9K. Here again, any advances in reducing the turbulent dissipation will increase the performance and reliability of the magnets. More generally, the proposed research can be expected to benefit the cryogenic industries. The use of advanced cooling techniques is continuing to grow. In hospitals there is a growing demand for MRI scanners which require large superconducting magnets cooled by helium. Through companies such as Oxford Instruments, the UK plays a leading role in the supply of cryogenic equipment. In the longer term, this fuels advances in commercial technology. Commercial development is facilitated by Lancaster Cryogenics Ltd, and Lancaster Helium Ltd, two companies founded by members of the Lancaster ULT group to export knowledge, specialist equipment, and supplies of isotopically pure 4He.

The novel techniques that we are going to develop (in-situ injection of excimer and nanoparticle fluorescent tracers, low intensity imaging using a deeply-cooled customised CCD camera, novel means of forcing flow in cryogenic liquids, sensitive and tunable torsional oscillators) have the potential for applications in both academic and industrial research on turbulence. Links with UK cryogenic companies such as Oxford Instruments (who built the customized dilution refrigerator used on our rotating cryostat) and Princeton Instruments (who will build the customized window-less CCD camera) will be maintained.

3. Staff training. 2 PDRAs and 2 graduate students will be trained in various aspects of this highly multi-disciplinary programme.

4. Collaborations and engagement. We plan to use and broaden our network of collaborators. These will include different communities such as classical fluid mechanics (in particular, the Manchester flow visualization group), quantum fluids (Prague; Newcastle; Maryland), matrix isolation spectroscopy (Leicester, Berkeley, Tallahassee). Through participation in the Network in Emergence and Physics Far From Equilibrium, our research will help to formulate specific Grand Challenges and to enable UK researchers to plan targeted research programmes.

5. Outreach. The University Press Offices will publicize our findings. Photographs and videos of tangles of vortex lines should make their way to the covers of magazines, thereby helping to popularize our research. A website with information, images and videos of vortex tangles, suitable for public and educational media, will be maintained.