Chapter 4 The Use of Vibrating Structures in the Study of Quantum Turbulence

Abstract

Abstract Vibrating structures such as discs, spheres, grids and wires have been widely used in research on quantum fluids and are playing a valuable role in the investigation of quantum turbulence. Quantum turbulence, a form of turbulence observed in superfluids, differs from that in classical fluids for three reasons: except at the lowest temperatures, superfluids exhibit two-fluid behaviour; the superfluid component can flow without dissipation; and superflow is subject to severe quantum restrictions, so that rotational motion can exist only through the presence of quantised vortex lines. In spite of these differences, there is evidence that quantum turbulence can exhibit features similar to those observed in its classical counterpart, especially on large length scales. Therefore, we first describe and try to understand how the simplest form of laminar flow breaks down around various oscillating structures in a classical fluid, leading at high enough Reynolds number to fully turbulent flow. Then we address analogous questions in the quantum cases so that our study combines the challenges met in the study of classical turbulence with those associated with quantum phenomena in condensed matter systems. We emphasise that, in spite of undoubted similarities between the quantum and classical cases, there must be an important difference relating to the initial transition from the simplest laminar flow: in the classical case, this simplest flow is of a viscous laminar type with no slip at a solid boundary, whereas in the quantum case the simplest flow is irrotational with complete slip. We discuss evidence that the transition to quantum turbulence can take place in two steps: the first occurs in the superfluid component and leads to the generation of a random tangle of vortex lines; the second involves the generation of large-scale rotational motion in both the superfluid and, if appropriate, the normal fluid, the motion mimicking the behaviour observed in a classical fluid.