Creation and evolution of quantum turbulence in novel geometries

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Turbulence is ubiquitous in the real world and affects almost every aspect of our daily lives, including transport, energy production, climate, and biological processes. Despite its universal importance, turbulence is not well understood. Richard Feynman called it the "most important unsolved problem of classical physics". Turbulence is hard to understand at a fundamental level because of the complexity of turbulent motion of the fluid over an extremely wide range of length scales. Quantum mechanics often makes complex problems conceptually simpler, and quantum turbulence (QT) in superfluids is a prime example. At low temperatures, superfluids are the closest attainable approximation to an ideal fluid in that they can flow without friction, are (almost) incompressible, and their vortices are quantised, making all of them identical.Like classical turbulence, QT is a non-equilibrium phenomenon: remove the driving force, and it decays - though perhaps not completely in He II due to residual quantised vortices pinned metastably to the walls. In He II, the creation of QT usually seems to be "seeded" by such remanent vortices. Earlier experiments on oscillating structures have hinted that evolution to fully-developed QT as the oscillatory amplitude increases may occur via at least 2-stages. (i) Above a first critical velocity, shaking of the pinned lines creates a vortex tangle where motion only occurs on length scales comparable with the line spacing. (ii) At a higher critical velocity, a second transition occurs in which laminar flow of the tangle breaks down into turbulence, like flow in a classical fluid. We now propose two closely-related experiments, each utilising novel technology, first to explore the fundamental properties of the remanent vortices and, secondly, to investigate the intrinsic vortex creation process in the absence of remanent vortices.The first set of experiments will explore vortex nucleation in superfluid within a pill-box-shaped cell where there is no flow over convex surfaces when the cell is oscillated about its axis of symmetry. We expect the cell movements to generate Kelvin waves on remanent vortices if they are pinned to the parallel faces, resulting in reconnections above a critical velocity and creation of the quasi-classical vortex tangle in laminar flow. The absence of a convex surface within the superfluid means that the second critical velocity, leading to fully developed QT will be raised, enabling it to be resolved. We will also investigate the pinning of remanent vortices. At finite temperature, we might expect that thermal fluctuations will enable a line to de-pin/re-pin sequentially, sliding its end across the surface whereas, at T=0, the lines would become frozen on pinning sites. However, measurements at UC Davis have questioned this widely-accepted picture, suggesting decreased pinning as the temperature falls, i.e. the opposite of expectation. We will resolve this enigma and will try to account theoretically for what we find. In the second set of experiments, we will study diverse motions of a small, magnetically-levitated, superconducting sphere through the superfluid. Although nothing like this has been attempted previously, we are confident of being able to oscillate the sphere (to make contact with earlier experiments) and, for the first time, to be able to move it in a circle at a steady velocity. Measurements of the drag as a function of time will provide information about the presence/absence of pinned vortex loops and their growth and separation as free vortex rings, as functions of velocity and temperature. We envisage these experiments opening a new chapter in the study of quantized vortex lines in superfluids, quite generally, not just in He-4. The flying sphere experiments will prepare the way for a possible cryogenic "wind tunnel" where a levitated model structure is moved through stationary He-4, with Reynolds numbers up to 100,000,000.