Session LB: Minisymposium III: Quantum Turbulence

Quantum turbulence

Turbulence in a superfluid system, such as the low-temperature phases of the two isotopes of liquid helium, $^{4}$He or $^{3}$He, is strongly influenced by three quantum effects: the existence of two interpenetrating fluids, the normal and superfluid components, which can have separate velocity fields; the inviscid nature of the superfluid component; and quantum restrictions that exist on rotational motion in the superfluid component. These quantum restrictions mean that the only form of rotational motion in the superfluid component must be a quantized vortex filament. We discuss in general terms how these effects modify types of turbulence that can occur in classical fluids and how they can lead to new types of turbulence. We shall refer to the effect on Richardson cascades and Kolmogorov energy spectra, how energy is dissipated in a system without viscosity, and how forced relative motion of the two fluids can lead to a type of turbulence that is unknown in classical fluid dynamics.   

Numerical study of quantum turbulence.

The relationship between classical and quantum turbulences has attracted much attention recently. The former arises from the complicated dynamics of eddies in a classical fluid. However, it is difficult to investigate how statistical properties are related to the dynamics of eddies, because of the obscure definition of eddies. In contrast, quantum turbulence comprises a tangle of quantized vortices that are stable topological defects characteristic of Bose-Einstein condensation. Here, we investigate our recent numerical study on the dynamics and statistics of quantized vortices in quantum turbulence by solving a modified Gross-Pitaevskii equation. To obtain the steady state of turbulence, we introduce a dissipation term that is applicable only at scales below the vortex core size, and an external potential term is introduced as the energy source at large scales. By calculating the energy dissipation rate and energy flux, we first clarify the inertial range and energy cascade in quantum turbulence. Furthermore, the energy spectrum is consistent with the Kolmogorov spectrum, which suggests a similarity between classical and quantum turbulences. We discuss the decay of a vortex tangle after turning off the energy source at large scales. This study shows that quantum turbulence can be studied as a prototype of turbulence much simpler than classical conventional turbulence.   

``Classical" experiments in a quantum fluid

The canonical method of creating a nearly isotropic and homogeneous turbulent flow is to force a fluid through a grid of crossed bars, usually by placing a stationary grid past a stream of air or water in a wind or water tunnel. Particular focus in this talk will therefore be placed on the development of a series of analogous measurements in which a grid is towed through a stationary sample of a quantum fluid, superfluid $^4 $He, contained in a small, 1 cm$^2$, cross-section square channel, for mesh Reynolds numbers up to 200,000. The rate of decay of the length of quantized vortex line per unit volume can be measured with some precision over a period during which it has decayed by roughly six orders of magnitude, and is indirectly reconciled with a classical Kolmogorov description with an effective kinematic viscosity that is proportional to the quantum of circulation. As the development of novel instrumentation for use in turbulent flows at low temperatures remains an important problem, some recent experimental developments, particularly in providing optical diagnosis and visualization of superfluid $^4$He flows, will also be highlighted.   

Dynamics of small tracer particles in superfluid turbulence

The study of low temperature fluid dynamics has been held back over the years by the lack of direct flow visualisation. Recently, two experimental groups have successfully implemented the Particle Image Velocimetry method (PIV) in liquid helium II using micron-size particle of various materials. It is hoped that this method will help understanding quantum turbulence and the origin of the observed similarities between quantum turbulence and ordinary turbulence. The difficulty is that helium II consists of two components, the viscous normal fluid (associated with the thermal excitations) and the inviscid superfluid (associated with the ground state), so an important issue of interpretation arises: do the trajectories of the PIV particles trace the normal fluid or the superfluid? The issue is complicated by the possibility that the particles may become trapped in the quantised superfluid vortex lines, in which case the PIV method would visualise vorticity rather than velocity. In this talk I shall present recent theoretical work on this problem.   

Vorticity in the Extreme Quantum Limit

Superfluid $^3$He is an ideal material for studying quantum turbulence as we can currently cool the superfluid to below 100 $\mu$K where the normal fluid fraction is negligible. This means that whatever decay processes occur they must be quantum processes and not mediated by classical frictional dissipation. The superfluid also has some serendipitous properties which make the detection of vorticity very straightforward unlike in many other quantum systems. We shall review the various methods by which vorticity can be locally generated in the superfluid. We then examine the various detection methods available. Finally we discuss the specific case of turbulence produced by a grid. Here the vorticity is produced as a gas of similar micron-scale vortex loops which then combine by reconnecion to create a vortex tangle. We can detect the sudden onset of this tangle creation and also confirm that the decay process is mediated by quantum rather than classical processes. Future possibilities, including the vortex video, will also be discussed.   

Transition to turbulence and its dependence on vortex damping in superfluids

In superfluids the motion of quantized vortex lines with respect to normal excitations is damped by mutual friction dissipation. In the B phase of superfluid helium-3 at millikelvin temperatures mutual friction has steep exponential temperature dependence: At higher temperatures vortex motion is overdamped, as is typical in superconductors, and the vortex number remains constant in dynamic processes. In contrast, at lower temperatures and low damping turbulence becomes possible, similar to superfluid helium-4, where the tangled turbulent motion of quantized vortices is present at essentially all temperatures. In our rotating measurements the characteristics of such a temperature dependent onset of turbulence is explored for the first time. Within the critical temperature regime of vortex damping we find power-law dependence between the perturbation required to achieve turbulence and a mutual friction controled dynamical parameter, which here in superfluid dynamics corresponds to Reynolds number. This result is similar to recent measurements on the onset of turbulence in viscous pipe flow, where the amplitude of the critical flow perturbation has been measured to have power-law dependence on Reynolds number.