Experimental investigation of the dynamics of a vibrating grid in superfluid 4He over a range of temperatures and pressures

Phenomenology of transition to quantum turbulence in flows of superfluid helium

Transition from laminar to turbulent states of classical viscous fluids is complex and incompletely understood. Transition to quantum turbulence (QT), by which we mean the turbulent motion of quantum fluids such as helium II, whose physical properties depend on quantum physics in some crucial respects, is naturally more complex. This increased complexity arises from superfluidity, quantization of circulation, and, at finite temperatures below the critical, the two-fluid behavior. Transition to QT could involve, as an initial step, the transition of the classical component, or the intrinsic or extrinsic nucleation of quantized vortices in the superfluid component, or a simultaneous occurrence of both scenarios-and the subsequent interconnected evolution. In spite of the multiplicity of scenarios, aspects of transition to QT can be understood at a phenomenological level on the basis of some general principles, and compared meaningfully with transition in classical flows.

Oscillating-grid experiments in water and superfluid helium

Passing a fluid through a grid is a well-known mechanism used to study the properties of turbulence. Oscillating a horizontal grid vertically in a tank has also been used extensively and is considered to be a source of almost homogenous isotropic turbulence. When the oscillating grid is turned on a turbulent flow is induced. A front translates into the experimental tank, behind which the flow is highly turbulent. Long predicted that the growth of such a front would grow diffusively as the square root of time (i.e., d ∼ sqrt[t]) and Dickinson and Long presented experimental evidence for the diffusive result at a low mesh Reynolds number of 555. This paper revisits these experiments and attempts a set of two models for the advancing front in both square and round tanks. We do not observe significant differences between runs in square and round tanks. The experiments in water reach mesh Reynolds numbers of order 30000. Using some data from superfluid helium experiments we are able to explore mesh Reynolds numbers to about 43000. We find the power law for the advancing front decreases weakly with the mesh Reynolds number. Using a very long tank we find that the turbulent front stops completely at a certain depth and attempt a simple explanation for that behavior. We study the propagation of the turbulent front into tubes of different diameters inserted into the main tank. We show that these tubes exclude wavelengths much larger than the tube diameter. We explore the variation of the position of the steady-state boundary H on tube diameter D and find that H = cD with c ∼ 2. We suggest this may be explained by saturation of the energy-containing length scale ℓ(e). We also report on the effect of plugging up just one hole of the grid. Finally, we recall some earlier oscillating grid experiments in superfluid (4)He in the light of the present results.

Quantum turbulence generated by oscillating structures

The paper summarizes important aspects of quantum turbulence that have been studied successfully with oscillating structures. It describes why some aspects are proving hard to interpret, and it outlines the need for new types of experiment and new developments in theoretical and computational work.

Transition from laminar to turbulent drag in flow due to a vibrating quartz fork

Flow due to a commercially available vibrating quartz fork is studied in gaseous helium, He I and He II, over a wide range of temperatures and pressures. On increasing the driving force applied to the fork, the drag changes in character from laminar (characterized by a linear drive vs velocity dependence) to turbulent (characterized by a quadratic drive vs velocity dependence). We characterize this transition by a critical Reynolds number Recrdelta=Ucrdelta/nu, where Ucr is the critical velocity, nu stands for the kinematic viscosity, delta=sqrt[2nu/omega] is the viscous penetration depth, and omega is the angular frequency of oscillations. We have experimentally verified that the corresponding scaling Ucr proportional, sqrt[nuomega] holds in a classical viscous fluid over two decades of nu.